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Wajib.","2026-10-08T09:24:41.433Z",{"id":297,"subjectId":15,"levelId":55,"parentId":98,"slug":1455,"name":1456,"description":1457,"order":1458,"createdAt":1459,"updatedAt":1459},"matriks","Matriks","Matriks — Kelas 11 Lanjut.",13,"2026-10-08T09:24:41.441Z",{"id":1461,"subjectId":24,"levelId":55,"parentId":98,"slug":1462,"name":1463,"description":1464,"order":1458,"createdAt":1465,"updatedAt":1465},"cmuzbyhhz003k71r9s7s8evk1","rangkaian-pegas","Rangkaian Pegas","Rangkaian Pegas — Kelas 11.","2026-10-08T09:24:41.111Z",{"id":159,"subjectId":24,"levelId":55,"parentId":98,"slug":1467,"name":1468,"description":1469,"order":1470,"createdAt":1471,"updatedAt":1471},"fluida","Fluida","Fluida — Kelas 11.",14,"2026-10-08T09:24:41.113Z",{"id":273,"subjectId":15,"levelId":55,"parentId":98,"slug":1473,"name":1474,"description":1475,"order":1470,"createdAt":1476,"updatedAt":1476},"polinomial","Polinomial","Polinomial — Kelas 11 Lanjut.","2026-10-08T09:24:41.454Z",{"id":189,"subjectId":15,"levelId":55,"parentId":98,"slug":1478,"name":1479,"description":1480,"order":1481,"createdAt":1482,"updatedAt":1482},"fungsi-trigonometri","Fungsi Trigonometri","Fungsi Trigonometri — Kelas 11 Lanjut.",15,"2026-10-08T09:24:41.469Z",{"id":183,"subjectId":24,"levelId":55,"parentId":98,"slug":1484,"name":1485,"description":1486,"order":1481,"createdAt":1487,"updatedAt":1487},"gerak-harmonik-sederhana-ghs","Gerak Harmonik Sederhana (GHS)","Gerak Harmonik Sederhana (GHS) — Kelas 11.","2026-10-08T09:24:41.119Z",{"id":213,"subjectId":24,"levelId":55,"parentId":98,"slug":1489,"name":1490,"description":1491,"order":1492,"createdAt":1493,"updatedAt":1493},"gelombang-mekanik","Gelombang Mekanik","Gelombang Mekanik — Kelas 11.",16,"2026-10-08T09:24:41.132Z",{"id":279,"subjectId":15,"levelId":55,"parentId":98,"slug":1248,"name":1249,"description":1495,"order":1492,"createdAt":1496,"updatedAt":1496},"Vektor — Kelas 11 Lanjut.","2026-10-08T09:24:41.485Z",{"id":135,"subjectId":24,"levelId":55,"parentId":98,"slug":1498,"name":1499,"description":1500,"order":1501,"createdAt":1502,"updatedAt":1502},"gelombang-cahaya","Gelombang Cahaya","Gelombang Cahaya — Kelas 11.",17,"2026-10-08T09:24:41.150Z",{"id":219,"subjectId":15,"levelId":55,"parentId":98,"slug":1504,"name":1505,"description":1506,"order":1501,"createdAt":1507,"updatedAt":1507},"transformasi-geometri","Transformasi Geometri","Transformasi Geometri — Kelas 11 Lanjut.","2026-10-08T09:24:41.498Z",{"id":165,"subjectId":15,"levelId":55,"parentId":98,"slug":1509,"name":1510,"description":1511,"order":1512,"createdAt":1513,"updatedAt":1513},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":201,"subjectId":24,"levelId":55,"parentId":98,"slug":1515,"name":1516,"description":1517,"order":1512,"createdAt":1518,"updatedAt":1518},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":75,"subjectId":15,"levelId":55,"parentId":98,"slug":1520,"name":83,"description":1521,"order":1522,"createdAt":1523,"updatedAt":1523},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":374,"subjectId":24,"levelId":55,"parentId":98,"slug":1525,"name":1526,"description":1527,"order":1522,"createdAt":1528,"updatedAt":1528},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":105,"subjectId":15,"levelId":55,"parentId":98,"slug":1530,"name":1531,"description":1532,"order":1533,"createdAt":1534,"updatedAt":1534},"bunga","Bunga","Bunga — Kelas 12 Wajib.",20,"2026-10-08T09:24:41.518Z",{"id":171,"subjectId":24,"levelId":55,"parentId":98,"slug":1536,"name":1537,"description":1538,"order":1533,"createdAt":1539,"updatedAt":1539},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":380,"subjectId":15,"levelId":55,"parentId":98,"slug":1541,"name":1542,"description":1543,"order":1544,"createdAt":1545,"updatedAt":1545},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":398,"subjectId":24,"levelId":55,"parentId":98,"slug":1547,"name":1548,"description":1549,"order":1544,"createdAt":1550,"updatedAt":1550},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":326,"subjectId":15,"levelId":55,"parentId":98,"slug":1552,"name":1553,"description":1554,"order":1555,"createdAt":1556,"updatedAt":1556},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":267,"subjectId":24,"levelId":55,"parentId":98,"slug":1558,"name":1559,"description":1560,"order":1555,"createdAt":1561,"updatedAt":1561},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":237,"subjectId":24,"levelId":55,"parentId":98,"slug":1563,"name":1564,"description":1565,"order":1566,"createdAt":1567,"updatedAt":1567},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":285,"subjectId":15,"levelId":55,"parentId":98,"slug":1569,"name":1418,"description":1570,"order":1566,"createdAt":1571,"updatedAt":1571},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":249,"subjectId":15,"levelId":55,"parentId":98,"slug":1573,"name":1574,"description":1575,"order":1576,"createdAt":1577,"updatedAt":1577},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":243,"subjectId":24,"levelId":55,"parentId":98,"slug":1579,"name":1580,"description":1581,"order":1576,"createdAt":1582,"updatedAt":1582},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":117,"subjectId":15,"levelId":55,"parentId":98,"slug":1584,"name":1585,"description":1586,"order":1587,"createdAt":1588,"updatedAt":1588},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":68,"subjectId":24,"levelId":55,"parentId":98,"slug":1590,"name":1591,"description":1592,"order":1587,"createdAt":1593,"updatedAt":1593},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":308,"subjectId":24,"levelId":55,"parentId":98,"slug":1595,"name":1596,"description":1597,"order":1598,"createdAt":1599,"updatedAt":1599},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":123,"subjectId":15,"levelId":55,"parentId":98,"slug":1601,"name":1602,"description":1603,"order":1598,"createdAt":1604,"updatedAt":1604},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":332,"subjectId":15,"levelId":55,"parentId":98,"slug":1606,"name":1607,"description":1608,"order":1609,"createdAt":1610,"updatedAt":1610},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":362,"subjectId":24,"levelId":55,"parentId":98,"slug":1612,"name":1613,"description":1614,"order":1609,"createdAt":1615,"updatedAt":1615},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":207,"subjectId":15,"levelId":55,"parentId":98,"slug":1617,"name":1618,"description":1619,"order":1620,"createdAt":1621,"updatedAt":1621},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":350,"subjectId":24,"levelId":55,"parentId":98,"slug":1623,"name":1624,"description":1625,"order":1620,"createdAt":1626,"updatedAt":1626},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":356,"subjectId":24,"levelId":55,"parentId":98,"slug":1628,"name":1629,"description":1630,"order":1631,"createdAt":1632,"updatedAt":1632},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":255,"subjectId":15,"levelId":55,"parentId":98,"slug":1634,"name":1635,"description":1636,"order":1631,"createdAt":1637,"updatedAt":1637},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":147,"subjectId":15,"levelId":55,"parentId":98,"slug":1639,"name":1640,"description":1641,"order":1642,"createdAt":1643,"updatedAt":1643},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":291,"subjectId":24,"levelId":55,"parentId":98,"slug":1645,"name":1646,"description":1647,"order":1642,"createdAt":1648,"updatedAt":1648},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1650,"subjectId":15,"levelId":55,"parentId":98,"slug":1651,"name":1652,"description":1653,"order":1654,"createdAt":1655,"updatedAt":1655},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1657,"subjectId":15,"levelId":55,"parentId":98,"slug":1658,"name":1659,"description":1660,"order":1661,"createdAt":1662,"updatedAt":1662},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1664,"subjectId":15,"levelId":55,"parentId":98,"slug":1665,"name":1666,"description":1667,"order":1668,"createdAt":1669,"updatedAt":1669},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1671,"subjectId":15,"levelId":60,"parentId":98,"slug":1672,"name":125,"description":1673,"order":1674,"createdAt":1675,"updatedAt":1675},"demo-v2-topic-matematika-kuliah-1","definisi-turunan-limit","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.",100,"2026-10-14T16:01:44.645Z",{"id":1677,"subjectId":15,"levelId":55,"parentId":98,"slug":1678,"name":1679,"description":1680,"order":1674,"createdAt":1681,"updatedAt":1681},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-14T16:01:44.503Z",{"id":1683,"subjectId":33,"levelId":55,"parentId":98,"slug":1684,"name":1685,"description":1686,"order":1674,"createdAt":1687,"updatedAt":1687},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-14T16:01:45.616Z",{"id":1689,"subjectId":24,"levelId":49,"parentId":98,"slug":1690,"name":1691,"description":1692,"order":1674,"createdAt":1693,"updatedAt":1693},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-14T16:01:44.924Z",{"id":1695,"subjectId":24,"levelId":60,"parentId":98,"slug":1696,"name":1697,"description":1698,"order":1674,"createdAt":1699,"updatedAt":1699},"demo-v2-topic-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-14T16:01:45.223Z",{"id":1701,"subjectId":24,"levelId":55,"parentId":98,"slug":1702,"name":1703,"description":1704,"order":1674,"createdAt":1705,"updatedAt":1705},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-14T16:01:45.084Z",{"id":1707,"subjectId":33,"levelId":60,"parentId":98,"slug":1708,"name":1709,"description":1710,"order":1674,"createdAt":1711,"updatedAt":1711},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-14T16:01:45.769Z",{"id":1713,"subjectId":33,"levelId":43,"parentId":98,"slug":1714,"name":1715,"description":1716,"order":1674,"createdAt":1717,"updatedAt":1717},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-14T16:01:45.355Z",{"id":1719,"subjectId":24,"levelId":43,"parentId":98,"slug":1720,"name":1721,"description":1722,"order":1674,"createdAt":1723,"updatedAt":1723},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-14T16:01:44.803Z",{"id":1725,"subjectId":15,"levelId":43,"parentId":98,"slug":1726,"name":1727,"description":1728,"order":1674,"createdAt":1729,"updatedAt":1729},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-14T16:01:44.034Z",{"id":1731,"subjectId":15,"levelId":49,"parentId":98,"slug":1732,"name":1733,"description":1734,"order":1674,"createdAt":1735,"updatedAt":1735},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-14T16:01:44.305Z",{"id":1737,"subjectId":33,"levelId":49,"parentId":98,"slug":1738,"name":1739,"description":1740,"order":1674,"createdAt":1741,"updatedAt":1741},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-14T16:01:45.472Z",{"id":1743,"subjectId":33,"levelId":60,"parentId":98,"slug":1744,"name":1745,"description":1746,"order":1747,"createdAt":1748,"updatedAt":1748},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-14T16:01:45.800Z",{"id":1750,"subjectId":15,"levelId":55,"parentId":98,"slug":1751,"name":1752,"description":1753,"order":1747,"createdAt":1754,"updatedAt":1754},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-14T16:01:44.555Z",{"id":1756,"subjectId":24,"levelId":43,"parentId":98,"slug":1757,"name":1758,"description":1759,"order":1747,"createdAt":1760,"updatedAt":1760},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-14T16:01:44.840Z",{"id":1762,"subjectId":15,"levelId":43,"parentId":98,"slug":1763,"name":1764,"description":1765,"order":1747,"createdAt":1766,"updatedAt":1766},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-14T16:01:44.140Z",{"id":1768,"subjectId":33,"levelId":55,"parentId":98,"slug":1769,"name":1770,"description":1771,"order":1747,"createdAt":1772,"updatedAt":1772},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-14T16:01:45.659Z",{"id":1774,"subjectId":24,"levelId":49,"parentId":98,"slug":1775,"name":1776,"description":1777,"order":1747,"createdAt":1778,"updatedAt":1778},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-14T16:01:44.967Z",{"id":1780,"subjectId":33,"levelId":49,"parentId":98,"slug":1781,"name":1782,"description":1783,"order":1747,"createdAt":1784,"updatedAt":1784},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-14T16:01:45.518Z",{"id":1786,"subjectId":33,"levelId":43,"parentId":98,"slug":1787,"name":1788,"description":1789,"order":1747,"createdAt":1790,"updatedAt":1790},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-14T16:01:45.408Z",{"id":1792,"subjectId":15,"levelId":49,"parentId":98,"slug":1793,"name":1794,"description":1795,"order":1747,"createdAt":1796,"updatedAt":1796},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-14T16:01:44.363Z",{"id":1798,"subjectId":24,"levelId":60,"parentId":98,"slug":1799,"name":1800,"description":1801,"order":1747,"createdAt":1802,"updatedAt":1802},"demo-v2-topic-fisika-kuliah-2","usaha-oleh-gaya-berubah","Usaha Gaya Berubah","Usaha oleh gaya berubah dengan integral W = ∫F dx, rumus usaha W = F·s sebagai dot product, usaha pegas, dan teorema usaha–energi, plus contoh soal.","2026-10-14T16:01:45.258Z",{"id":1804,"subjectId":15,"levelId":55,"parentId":98,"slug":1805,"name":1806,"description":1807,"order":1808,"createdAt":1809,"updatedAt":1809},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-14T16:01:44.588Z",{"id":1811,"subjectId":33,"levelId":55,"parentId":98,"slug":1812,"name":1813,"description":1814,"order":1808,"createdAt":1815,"updatedAt":1815},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-14T16:01:45.700Z",{"id":1817,"subjectId":33,"levelId":49,"parentId":98,"slug":1818,"name":1819,"description":1820,"order":1808,"createdAt":1821,"updatedAt":1821},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-14T16:01:45.560Z",{"id":1823,"subjectId":33,"levelId":43,"parentId":98,"slug":1824,"name":1825,"description":1826,"order":1808,"createdAt":1827,"updatedAt":1827},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-14T16:01:45.436Z",{"id":1829,"subjectId":15,"levelId":49,"parentId":98,"slug":1830,"name":1831,"description":1832,"order":1808,"createdAt":1833,"updatedAt":1833},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-14T16:01:44.400Z",{"id":1835,"subjectId":33,"levelId":60,"parentId":98,"slug":1836,"name":1837,"description":1838,"order":1808,"createdAt":1839,"updatedAt":1839},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-14T16:01:45.832Z",{"id":1841,"subjectId":15,"levelId":60,"parentId":98,"slug":1842,"name":1843,"description":1844,"order":1808,"createdAt":1845,"updatedAt":1845},"demo-v2-topic-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3D dan Dot Product","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-14T16:01:44.715Z",{"id":1847,"subjectId":15,"levelId":43,"parentId":98,"slug":1848,"name":1849,"description":1850,"order":1808,"createdAt":1851,"updatedAt":1851},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-14T16:01:44.189Z",{"id":1853,"subjectId":15,"levelId":49,"parentId":98,"slug":1854,"name":1855,"description":1856,"order":1857,"createdAt":1858,"updatedAt":1858},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-14T16:01:44.438Z",{"id":1860,"subjectId":33,"levelId":55,"parentId":98,"slug":1861,"name":1862,"description":1863,"order":1857,"createdAt":1864,"updatedAt":1864},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-14T16:01:45.731Z",{"id":1866,"subjectId":15,"levelId":43,"parentId":98,"slug":1867,"name":1868,"description":1869,"order":1857,"createdAt":1870,"updatedAt":1870},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-14T16:01:44.239Z",[1872,1875,1880,1885],{"id":1873,"slug":25,"name":26,"createdAt":1874},"cmvogd3r1000607tdh34zf0vv","2026-10-25T23:22:15.997Z",{"id":1876,"slug":1877,"name":1878,"createdAt":1879},"cmvogctp7000507tdmugcad1g","fisika-statistik","Fisika Statistik","2026-10-25T23:22:02.971Z",{"id":1881,"slug":1882,"name":1883,"createdAt":1884},"cmvhrhrvm00027m1risodrm04","onmipa","ONMIPA","2026-10-21T06:59:26.435Z",{"id":1886,"slug":1887,"name":1887,"createdAt":1888},"cmvhrhm2s00017m1rpjm53zrv","tag","2026-10-21T06:59:18.917Z",[1890],{"code":1891,"nativeName":1892,"isDefault":5},"id","Bahasa Indonesia",{"id":1894,"type":1895,"slug":1896,"title":1897,"excerpt":1898,"coverUrl":98,"status":1899,"publishedAt":1900,"featured":4,"subjectId":24,"blocks":1901,"seoTitle":2059,"seoDescription":98,"readingMinutes":1522,"order":21,"hiddenFromOthers":4,"createdAt":2060,"updatedAt":2061,"subject":2062,"levels":2063,"topics":2067,"tags":2072,"lang":1891,"alternates":2073,"author":2075,"resolved":2080,"related":2476,"sequence":98},"cmvofwe5t000307td805ner2w","ARTICLE","cara-ilmuwan-memprediksi-gerhana-matahari","Cara Ilmuwan Memprediksi Gerhana Matahari Bertahun-tahun Sebelumnya","Pelajari cara ilmuwan memprediksi gerhana Matahari bertahun-tahun sebelumnya lewat orbit Bulan, trigonometri, siklus Saros, dan simulasi Python sederhana.","PUBLISHED","2026-10-25T23:09:26.903Z",[1902,1907,1911,1915,1922,1928,1932,1939,1943,1948,1952,1957,1961,1966,1970,1975,1979,1984,1988,1992,1997,2001,2005,2009,2014,2018,2022,2027,2031,2035,2041,2047,2051,2055],{"id":1903,"data":1904,"type":1906},"ai39222f3b6c",{"markdown":1905},"Ilmuwan bisa **memprediksi gerhana Matahari** bertahun-tahun, bahkan berabad-abad sebelumnya, karena gerak Bumi, Bulan, dan Matahari mengikuti hukum fisika yang teratur dan dapat dihitung. Dengan mengetahui posisi ketiganya secara sangat teliti, lalu \"memajukan waktu\" memakai persamaan gerak, astronom dapat menentukan kapan ketiganya tepat segaris dan ke mana bayangan Bulan jatuh di permukaan Bumi. Kuncinya ada pada tiga hal yang juga kamu pelajari di sekolah: geometri (garis, sudut, kerucut), trigonometri (sinus dan perbandingan sudut), serta pola periodik (periode, KPK, dan barisan).\n\nSebagai gambaran ketelitiannya, NASA menerbitkan katalog *Five Millennium Canon of Solar Eclipses* yang memuat 11.898 gerhana Matahari dalam rentang tahun 2000 SM hingga 3000 M, lengkap dengan peta jalurnya. Artikel ini membahas langkah demi langkah cara kerja prediksi tersebut, mulai dari model paling sederhana sampai gambaran perhitungan profesional, disertai contoh hitungan dan kode Python yang bisa kamu jalankan sendiri.","text",{"id":1908,"data":1909,"type":1906},"aib1a2a7d1e3",{"markdown":1910},"## Apa Itu Gerhana Matahari Secara Geometris?\n\nGerhana Matahari terjadi ketika Bulan lewat di antara Matahari dan Bumi sehingga cahaya Matahari terhalang dan bayangan Bulan jatuh ke Bumi. Karena itu, gerhana Matahari hanya mungkin terjadi pada fase **bulan baru**, saat Bulan dan Matahari berada di sisi Bumi yang sama.\n\nBayangan Bulan berbentuk dua kerucut:\n\n- **Umbra**: kerucut bayangan inti. Pengamat di dalam umbra melihat Matahari tertutup penuh (gerhana total).\n- **Penumbra**: bayangan kabur di sekelilingnya. Pengamat di sini melihat gerhana sebagian.\n- **Antumbra**: perpanjangan kerucut di belakang ujung umbra. Bila ujung umbra tidak sampai ke Bumi, pengamat di antumbra melihat cincin cahaya Matahari di sekeliling Bulan (gerhana cincin).\n\n| Jenis gerhana Matahari | Syarat geometris | Yang terlihat |\n|---|---|---|\n| Total | Segaris dan umbra mencapai permukaan Bumi | Matahari tertutup penuh, korona tampak |\n| Cincin | Segaris, tetapi umbra tidak sampai ke Bumi (Bulan tampak lebih kecil) | Cincin cahaya di sekeliling Bulan |\n| Hibrida | Di sebagian jalur total, di bagian lain cincin | Bergantung lokasi |\n| Sebagian | Hanya penumbra yang mengenai Bumi | Matahari \"tergigit\" sebagian |\n\nJalur totalitas biasanya sempit, sering kurang dari sekitar 80 km lebarnya, sedangkan wilayah penumbra bisa ribuan kilometer. Itulah sebabnya prediksi gerhana bukan hanya soal *kapan*, tetapi juga *di mana*.",{"id":1912,"data":1913,"type":1906},"ai501ee894e4",{"markdown":1914},"## Posisi dan Orbit Bumi, Bulan, dan Matahari\n\nUntuk memprediksi gerhana Matahari, kita perlu tahu tiga fakta orbit berikut.\n\n1. **Bumi mengelilingi Matahari** dalam orbit elips. Bidang orbit ini disebut **bidang ekliptika**. Jarak Bumi–Matahari berubah antara sekitar 147,1 juta km (awal Januari) dan 152,1 juta km (awal Juli), dengan rata-rata sekitar 149,6 juta km.\n2. **Bulan mengelilingi Bumi** juga dalam orbit elips, dengan jarak rata-rata sekitar 384.400 km. Titik terdekatnya disebut *perigee* dan titik terjauhnya *apogee*.\n3. **Orbit Bulan miring sekitar 5,145°** terhadap bidang ekliptika. Dua titik potong orbit Bulan dengan bidang ekliptika disebut **simpul** (*node*).\n\nBentuk orbit yang elips mengikuti hukum Kepler I, sedangkan perubahan kecepatan Bulan di sepanjang orbitnya mengikuti hukum Kepler II. Di balik keduanya ada hukum gravitasi Newton, yang memungkinkan posisi benda langit dihitung untuk waktu kapan pun.\n\n### Kebetulan kosmis: ukuran sudut yang hampir sama\n\nMatahari kira-kira 400 kali lebih besar daripada Bulan, tetapi juga kira-kira 400 kali lebih jauh. Akibatnya, di langit keduanya tampak hampir sama besar. Kita bisa menghitungnya dengan **pendekatan sudut kecil**.",{"id":1916,"data":1917,"type":1921},"ai9130ef5b75",{"title":1918,"variant":1919,"markdown":1920},"Diameter sudut (pendekatan sudut kecil)","info","$$\\theta \\approx \\frac{D}{d}$$\ndengan $\\theta$ diameter sudut dalam radian, $D$ diameter benda (km), dan $d$ jaraknya dari pengamat (km). Untuk mengubah ke derajat, kalikan dengan $\\dfrac{180^\\circ}{\\pi}$.","callout",{"id":1923,"data":1924,"type":1921},"ai8977430a73",{"title":1925,"variant":1926,"markdown":1927},"Contoh 1: Bulan atau Matahari yang tampak lebih besar?","explanation","Diameter Bulan sekitar 3.474,8 km dan jarak rata-ratanya 384.400 km. Diameter Matahari sekitar 1.391.400 km dan jarak rata-ratanya 149,6 juta km.\n\n$$\\theta_{\\text{Bulan}} \\approx \\frac{3.474{,}8}{384.400} \\approx 0{,}00904\\ \\text{rad} \\approx 0{,}518^\\circ$$\n\n$$\\theta_{\\text{Matahari}} \\approx \\frac{1.391.400}{149.600.000} \\approx 0{,}00930\\ \\text{rad} \\approx 0{,}533^\\circ$$\n\nInterpretasi: pada jarak rata-rata, Bulan tampak sedikit lebih kecil daripada Matahari, sehingga gerhana sentral pada jarak ini cenderung berupa gerhana cincin. Bila Bulan berada dekat perigee (sekitar 363.300 km), $\\theta_{\\text{Bulan}} \\approx 3.474{,}8\u002F363.300 \\approx 0{,}548^\\circ$, lebih besar daripada Matahari, sehingga gerhana total menjadi mungkin. Di dekat apogee (sekitar 405.500 km), nilainya hanya sekitar $0{,}491^\\circ$.\n\nCek: perbandingan $\\theta_{\\text{Bulan}}\u002F\\theta_{\\text{Matahari}} = 0{,}518\u002F0{,}533 \\approx 0{,}97$, kurang dari 1, konsisten dengan kesimpulan \"Bulan sedikit lebih kecil\" pada jarak rata-rata.",{"id":1929,"data":1930,"type":1906},"ai7f1cacd1e7",{"markdown":1931},"Model ini memakai jarak dari **pusat Bumi**. Pengamat di permukaan yang Bulannya tepat di atas kepala sekitar 6.371 km lebih dekat ke Bulan, sehingga Bulan tampak sedikit lebih besar. Perhitungan profesional selalu memperhitungkan posisi pengamat ini.\n\nCoba bandingkan sendiri ukuran sudut Bulan dan Matahari untuk berbagai jarak pada visual berikut.",{"id":1933,"data":1934,"type":1938},"ai3cfd387cf5",{"height":1935,"assetId":1936,"caption":1937},520,"cmvo70lhc000307qhqbfahimy","Geser jarak Bumi–Bulan dan Bumi–Matahari: kapan gerhana menjadi total, cincin, atau sebagian?","interactive",{"id":1940,"data":1941,"type":1906},"ai19aeeaf96a",{"markdown":1942},"## Mengapa Gerhana Matahari Tidak Terjadi Setiap Bulan?\n\nBulan baru terjadi kira-kira setiap 29,53 hari. Andaikan orbit Bulan berada tepat di bidang ekliptika, setiap bulan baru akan menghasilkan gerhana Matahari. Kenyataannya tidak, karena orbit Bulan **miring sekitar 5°**. Pada sebagian besar bulan baru, Bulan lewat sedikit di atas atau di bawah Matahari, dan bayangannya meleset dari Bumi.\n\nSeberapa jauh \"meleset\" itu? Dengan trigonometri sederhana, ketinggian maksimum Bulan di atas bidang ekliptika adalah\n\n$$h_{\\text{maks}} = d \\sin i = 384.400 \\times \\sin 5{,}145^\\circ \\approx 34.500\\ \\text{km},$$\n\nhampir tiga kali diameter Bumi (sekitar 12.742 km). Jadi, kemiringan yang \"hanya\" 5° sudah cukup membuat bayangan Bulan sering lewat jauh di atas atau di bawah Bumi.\n\n### Trigonometri bola: seberapa dekat Bulan harus ke simpul?\n\nPosisi Bulan di langit dinyatakan dengan **bujur ekliptika** (posisi sepanjang ekliptika) dan **lintang ekliptika** $\\beta$ (jarak sudut di atas atau di bawah ekliptika). Untuk orbit miring dengan kemiringan $i$, berlaku hubungan trigonometri bola:",{"id":1944,"data":1945,"type":1921},"ai1539ff3efc",{"title":1946,"variant":1919,"markdown":1947},"Lintang ekliptika Bulan","$$\\sin \\beta = \\sin i \\,\\sin u$$\ndengan $\\beta$ lintang ekliptika Bulan, $i \\approx 5{,}145^\\circ$ kemiringan orbit, dan $u$ jarak sudut Bulan dari simpul naik, diukur sepanjang orbitnya. Untuk sudut kecil, $\\beta \\approx i \\sin u$, yaitu sebuah fungsi sinus.",{"id":1949,"data":1950,"type":1906},"ai8d94e1174e",{"markdown":1951},"Gerhana Matahari hanya mungkin bila saat bulan baru $|\\beta|$ cukup kecil. Dalam model sederhana di artikel ini kita pakai batas kasar $|\\beta| \\lesssim 1{,}5^\\circ$. Nilai batas sebenarnya sedikit berubah-ubah, karena bergantung pada jarak Bulan dan Matahari saat itu.",{"id":1953,"data":1954,"type":1921},"aia2c0603c59",{"title":1955,"variant":1926,"markdown":1956},"Contoh 2: bulan baru 30° dari simpul","Misalkan saat bulan baru, Bulan berada $u = 30^\\circ$ dari simpul.\n\n$$\\sin \\beta = \\sin 5{,}145^\\circ \\times \\sin 30^\\circ = 0{,}0897 \\times 0{,}5 = 0{,}0448$$\n\n$$\\beta = \\arcsin 0{,}0448 \\approx 2{,}57^\\circ$$\n\nKarena $2{,}57^\\circ > 1{,}5^\\circ$, bayangan Bulan meleset dan tidak terjadi gerhana. Bandingkan dengan $u = 10^\\circ$: $\\beta = \\arcsin(0{,}0897 \\times 0{,}1736) \\approx 0{,}89^\\circ$, masih di dalam batas, jadi gerhana mungkin terjadi.\n\nCek: dengan pendekatan sudut kecil $\\beta \\approx i \\sin u = 5{,}145^\\circ \\times 0{,}5 \\approx 2{,}57^\\circ$, hasilnya sama.",{"id":1958,"data":1959,"type":1906},"ai291999c03a",{"markdown":1960},"### Musim gerhana\n\nBulan baru yang jatuh dekat simpul hanya terjadi pada dua \"jendela\" setiap tahun yang disebut **musim gerhana**. Simpul orbit Bulan juga tidak diam. Simpul itu bergeser mundur dan menyelesaikan satu putaran dalam sekitar 18,6 tahun. Akibatnya, Matahari kembali ke simpul yang sama bukan setiap 365,25 hari, melainkan setiap **tahun gerhana**.",{"id":1962,"data":1963,"type":1921},"ai7817c40f28",{"title":1964,"variant":1919,"markdown":1965},"Tahun gerhana dari dua periode","$$\\frac{1}{T_{\\text{gerhana}}} = \\frac{1}{D} - \\frac{1}{S} \\quad\\Rightarrow\\quad T_{\\text{gerhana}} = \\frac{1}{\\dfrac{1}{27{,}2122} - \\dfrac{1}{29{,}5306}} \\approx 346{,}62\\ \\text{hari}$$\ndengan $S = 29{,}5306$ hari (bulan sinodis: bulan baru ke bulan baru) dan $D = 27{,}2122$ hari (bulan drakonik: simpul ke simpul yang sama). Karena ada dua simpul, musim gerhana datang kira-kira setiap $346{,}62\u002F2 \\approx 173{,}3$ hari.",{"id":1967,"data":1968,"type":1906},"aif8518abd3c",{"markdown":1969},"Rumus ini sama dengan rumus \"kapan dua pelari di lintasan melingkar bertemu lagi\" yang muncul di gerak melingkar: yang dikurangkan adalah frekuensinya, bukan periodenya.\n\nPada visual di bawah, kurva biru adalah lintang Bulan (model sinus) dan titik-titik menandai setiap bulan baru. Titik merah adalah bulan baru yang jatuh di dalam pita batas, yaitu berpeluang menghasilkan gerhana. Coba ubah kemiringan orbit menjadi 0° dan perhatikan apa yang terjadi.",{"id":1971,"data":1972,"type":1938},"ai7d6e2c56b0",{"height":1935,"assetId":1973,"caption":1974},"cmvo6zwdg000207qhv7avs9g3","Lintang Bulan saat setiap bulan baru: titik merah berpeluang menghasilkan gerhana Matahari.",{"id":1976,"data":1977,"type":1906},"ai17e3cede08",{"markdown":1978},"## Siklus Saros: Pola Kuno yang Masih Berguna\n\nJauh sebelum ada komputer, para pengamat langit di Mesopotamia sudah mengenali bahwa gerhana cenderung berulang setelah sekitar 18 tahun. Pola ini sekarang disebut **siklus Saros**, lamanya sekitar 6.585,3 hari (18 tahun 11 hari 8 jam). Menurut NASA, satu Saros sama dengan 223 bulan sinodis, dan hampir tepat sama dengan 242 bulan drakonik serta 239 bulan anomalistik (perigee ke perigee).\n\n| Periode | Lama satu periode (hari) | Kelipatan | Total (hari) |\n|---|---|---|---|\n| Bulan sinodis $S$ | 29,530589 | 223 | 6.585,32 |\n| Bulan drakonik $D$ | 27,212221 | 242 | 6.585,36 |\n| Bulan anomalistik $A$ | 27,554550 | 239 | 6.585,54 |\n\nArtinya, setelah satu Saros, Bulan kembali ke fase yang sama (bulan baru), ke posisi yang hampir sama terhadap simpul, dan ke jarak yang hampir sama dari Bumi. Geometri gerhananya pun hampir berulang. Secara matematis, ini mirip mencari **kelipatan persekutuan** dari tiga bilangan yang tidak bulat, yang tidak pernah tepat sama tetapi hampir sama.\n\nAda satu masalah: kelebihan sekitar 0,32 hari (kira-kira 7,7 jam). Selama itu Bumi berotasi sekitar $0{,}32 \\times 360^\\circ \\approx 116^\\circ$, sehingga jalur gerhana berikutnya dalam satu seri bergeser sekitar 120° ke arah barat. NASA menyebutkan bahwa setelah tiga Saros (sekitar 54 tahun 1 bulan), jalur gerhana kembali ke kawasan bujur yang kira-kira sama.",{"id":1980,"data":1981,"type":1921},"aiaa2e8c0c1b",{"title":1982,"variant":1926,"markdown":1983},"Contoh 3: meramal gerhana berikutnya dengan Saros","Gerhana Matahari total 8 April 2024 termasuk Saros nomor 139. Tambahkan satu Saros, yaitu 6.585,32 hari, ke tanggal itu:\n\n$$8\\ \\text{April}\\ 2024 + 6.585{,}32\\ \\text{hari} \\approx 20\\ \\text{April}\\ 2042$$\n\nJadi, anggota berikutnya dari seri Saros 139 diperkirakan jatuh sekitar 20 April 2042, dengan jalur yang bergeser jauh ke arah barat. [PERLU DICEK: cocokkan tanggal dan jenis gerhana ini dengan katalog gerhana NASA sebelum terbit.]\n\nCek: $6.585{,}32\\ \\text{hari} \\div 365{,}25 \\approx 18{,}03$ tahun, sehingga $2024 + 18 = 2042$, dan sisa sekitar 12 hari menggeser tanggal dari 8 April ke sekitar 20 April.",{"id":1985,"data":1986,"type":1906},"aidc74a1ffc1",{"markdown":1987},"Saros sangat berguna untuk menebak *tanggal kira-kira*. Namun, Saros tidak bisa memberi jalur gerhana yang akurat sampai tingkat kota. Untuk itu dibutuhkan perhitungan modern.",{"id":1989,"data":1990,"type":1906},"ai469946c9a4",{"markdown":1991},"## Bagaimana Ilmuwan Menghitung Waktu dan Lokasi Gerhana?\n\nPrediksi gerhana Matahari modern dilakukan secara bertahap. Berikut gambaran garis besarnya.\n\n### 1. Efemeris: posisi Matahari dan Bulan yang sangat teliti\n\n**Efemeris** adalah tabel atau model matematis yang memberikan posisi benda langit untuk setiap waktu. Efemeris disusun dengan menyelesaikan persamaan gerak gravitasi (Newton, dengan koreksi relativitas) untuk Matahari, planet, dan Bulan, lalu dicocokkan dengan pengamatan selama puluhan hingga ratusan tahun. Untuk katalog lima milenium NASA, posisi Matahari dihitung dengan teori VSOP87 dan posisi Bulan dengan teori ELP-2000\u002F82. Nilai percepatan sekuler Bulan yang dipakai di katalog itu diturunkan dari eksperimen pengukuran jarak Bulan dengan laser (*lunar laser ranging*) pada program Apollo. Laboratorium JPL milik NASA juga menerbitkan efemeris planet dan Bulan modern seperti DE440.\n\n### 2. Elemen Bessel: menyederhanakan bayangan menjadi geometri bidang\n\nMenghitung kerucut bayangan di ruang tiga dimensi itu rumit. Karena itu, astronom memakai **elemen Bessel** (*Besselian elements*), yaitu sekumpulan besaran yang bergantung waktu untuk menggambarkan gerak bayangan Bulan terhadap **bidang fundamental**. Bidang ini melalui pusat Bumi dan tegak lurus terhadap sumbu bayangan Bulan.\n\nPada bidang itu, Bumi tampak sebagai lingkaran berjari-jari 1 (satuan jari-jari Bumi), dan sumbu bayangan menembus bidang di titik $(x, y)$. Elemen Bessel disajikan sebagai **polinomial waktu**:",{"id":1993,"data":1994,"type":1921},"ai596f89ec45",{"title":1995,"variant":1919,"markdown":1996},"Elemen Bessel sebagai polinomial","$$a(t) = a_0 + a_1 t + a_2 t^2 + a_3 t^3, \\qquad t = t_1 - t_0\\ \\text{(jam)}$$\ndengan $a$ salah satu elemen ($x$, $y$, deklinasi $d$, jari-jari penumbra $l_1$, jari-jari umbra $l_2$, atau sudut jam $\\mu$), $t_1$ waktu yang ditanyakan, dan $t_0$ waktu acuan.",{"id":1998,"data":1999,"type":1906},"aib6abc5a31f",{"markdown":2000},"Jarak sumbu bayangan ke pusat Bumi dihitung dengan **teorema Pythagoras**: $r(t) = \\sqrt{x(t)^2 + y(t)^2}$. Nilai minimum $r$ disebut **gamma** ($\\gamma$), dan saat itulah terjadi **puncak gerhana**. Bila $|\\gamma|$ jauh lebih besar dari 1, sumbu bayangan meleset dari Bumi.\n\n### 3. Dari bidang fundamental ke peta\n\nTitik $(x, y)$ lalu diproyeksikan ke permukaan Bumi yang bulat (sedikit pepat), dengan memperhitungkan rotasi Bumi (sudut $\\mu$), lintang dan bujur pengamat, serta ketinggian tempat. Dari sini diperoleh jalur totalitas, waktu kontak pertama sampai keempat di setiap kota, dan lama totalitas.\n\n### 4. Koreksi waktu ΔT\n\nPerhitungan orbit memakai skala waktu yang seragam (*Terrestrial Dynamical Time*, TDT), sedangkan jam sehari-hari mengikuti rotasi Bumi (UT). Rotasi Bumi melambat tidak teratur, terutama akibat gesekan pasang surut oleh Bulan. Selisih keduanya disebut **ΔT**. Untuk gerhana 8 April 2024, NASA memakai ΔT = 70,6 s. Menurut NASA, ketidakpastian terbesar prediksi gerhana justru berasal dari fluktuasi rotasi Bumi ini, terutama untuk gerhana ribuan tahun lalu atau ribuan tahun mendatang. Prediksi waktu terjadinya gerhana bisa sangat tepat, tetapi lokasi jalurnya di peta bergeser bila ΔT keliru, karena Bumi \"sudah berputar lebih jauh atau kurang jauh\" dari perkiraan.",{"id":2002,"data":2003,"type":1906},"aie549a83fb9",{"markdown":2004},"## Model Sederhana vs Perhitungan Profesional\n\nPenting membedakan apa yang bisa dilakukan model kelas dan apa yang dilakukan astronom.\n\n| Aspek | Model sederhana (artikel ini) | Perhitungan profesional |\n|---|---|---|\n| Orbit | Lingkaran atau sinus, periode rata-rata | Efemeris numerik (VSOP87\u002FELP, DE440) dengan gangguan gravitasi planet |\n| Bentuk Bumi | Bola atau lingkaran satuan | Elipsoid pepat, ketinggian topografi |\n| Waktu | Satu skala waktu | TDT, UT, dan koreksi ΔT |\n| Bentuk Bulan | Piringan bulat | Profil tepi Bulan (pegunungan dan lembah) memengaruhi detik kontak |\n| Hasil | \"Kapan kira-kira\" dan \"mungkin atau tidak\" | Jalur di peta dan waktu kontak tiap lokasi |\n| Ketelitian | Hari hingga jam | Hingga detik untuk gerhana dekat masa kini |\n\nModel sederhana tetap bernilai karena menunjukkan *mengapa* gerhana terjadi dan *mengapa* polanya berulang. Untuk keperluan pengamatan, selalu rujuk prediksi resmi seperti katalog NASA atau informasi gerhana dari BMKG. Contohnya, BMKG menginformasikan bahwa gerhana Matahari total 12 Agustus 2026 tidak dapat diamati dari Indonesia karena jalurnya tidak melewati wilayah Indonesia.",{"id":2006,"data":2007,"type":1906},"aied32b63d79",{"markdown":2008},"## Contoh Simulasi Python: Dari Saros sampai Puncak Gerhana\n\n### Program 1: kalender gerhana dari periode Bulan\n\nProgram ini menghitung siklus Saros, tahun gerhana, dan lebar jendela musim gerhana memakai rumus-rumus di atas.\n\n```python\nimport math\n\nS = 29.530589   # bulan sinodis (hari): bulan baru ke bulan baru\nD = 27.212221   # bulan drakonik (hari): simpul ke simpul yang sama\nA = 27.554550   # bulan anomalistik (hari): perigee ke perigee\ni = 5.145       # kemiringan orbit Bulan (derajat)\nb_maks = 1.5    # batas lintang kasar agar gerhana mungkin (derajat)\n\nprint(\"223 S =\", round(223 * S, 2), \"hari\")   # siklus Saros: tiga periode yang hampir \"pas\"\nprint(\"242 D =\", round(242 * D, 2), \"hari\")\nprint(\"239 A =\", round(239 * A, 2), \"hari\")\n\ntahun_gerhana = 1 \u002F (1 \u002F D - 1 \u002F S)          # Matahari kembali ke simpul yang sama\nprint(\"Tahun gerhana    =\", round(tahun_gerhana, 2), \"hari\")\nprint(\"Selang musim     =\", round(tahun_gerhana \u002F 2, 2), \"hari\")\n\nlam = math.degrees(math.asin(math.sin(math.radians(b_maks)) \u002F math.sin(math.radians(i))))\nlaju = 360 \u002F tahun_gerhana                   # derajat per hari, Matahari relatif terhadap simpul\nprint(\"Jarak maks dari simpul =\", round(lam, 1), \"derajat\")\nprint(\"Lebar jendela          =\", round(2 * lam \u002F laju, 1), \"hari\")\n```\n\nKeluaran program:\n\n```text\n223 S = 6585.32 hari\n242 D = 6585.36 hari\n239 A = 6585.54 hari\nTahun gerhana    = 346.62 hari\nSelang musim     = 173.31 hari\nJarak maks dari simpul = 17.0 derajat\nLebar jendela          = 32.7 hari\n```\n\n**Interpretasi.** Dalam model ini, setiap musim gerhana berlangsung sekitar 32,7 hari, lebih panjang daripada satu bulan sinodis (29,53 hari). Artinya, minimal satu bulan baru pasti jatuh di dalam setiap musim gerhana, sehingga **setiap tahun minimal terjadi dua gerhana Matahari** (salah satunya bisa berupa gerhana sebagian). Bila bulan baru jatuh di awal jendela, bulan baru berikutnya kadang masih masuk, sehingga satu musim bisa menghasilkan dua gerhana Matahari sebagian. Ingat, angka 32,7 hari bergantung pada batas 1,5° yang kita pilih. Kalau batasnya diubah, lebar jendelanya juga berubah.\n\nCek: $2 \\times 17{,}0^\\circ \\div 1{,}0386^\\circ\u002F\\text{hari} \\approx 32{,}7$ hari, dengan $1{,}0386^\\circ\u002F\\text{hari} = 360^\\circ \u002F 346{,}62\\ \\text{hari}$.\n\n### Program 2: mencari puncak gerhana dari elemen Bessel NASA\n\nProgram kedua memakai **data asli**: koefisien polinomial $x(t)$ dan $y(t)$ dari tabel elemen Bessel NASA untuk gerhana total 8 April 2024, dengan $t_0 = 18{,}00$ TDT. Tugas kita adalah mencari waktu ketika jarak sumbu bayangan ke pusat Bumi paling kecil.\n\n```python\nimport math\n\nx = [-0.318157, 0.5117105, 0.0000326, -0.0000085]   # elemen Bessel 8 April 2024 (NASA), t0 = 18.00 TDT\ny = [0.219747, 0.2709586, -0.0000594, -0.0000047]\n\ndef polinom(koef, t):\n    return sum(a * t**n for n, a in enumerate(koef))\n\ndef jarak(t):\n    return math.hypot(polinom(x, t), polinom(y, t))   # teorema Pythagoras\n\nt_min = min((k \u002F 10000 for k in range(-30000, 30001)), key=jarak)   # coba t = -3 s.d. 3 jam\n\njam = 18 + t_min\nj, m = int(jam), int((jam % 1) * 60)\nd = ((jam % 1) * 60 - m) * 60\nprint(f\"Puncak gerhana : {j:02d}:{m:02d}:{d:04.1f} TDT\")\nprint(f\"Gamma (model)  : {jarak(t_min):.4f} jari-jari Bumi\")\n```\n\nKeluaran program:\n\n```text\nPuncak gerhana : 18:18:28.8 TDT\nGamma (model)  : 0.3431 jari-jari Bumi\n```\n\n**Interpretasi.** Tabel NASA mencantumkan puncak gerhana pada 18:18:29,0 TDT dengan $\\gamma = 0{,}3431$. Program sederhana kita menghasilkan nilai yang sama sampai selisih sekitar 0,2 detik, yang berasal dari langkah pencarian 0,0001 jam (0,36 detik). Karena $\\gamma \\approx 0{,}34$, jauh lebih kecil dari 1, sumbu bayangan mengenai Bumi cukup dekat ke pusatnya, sehingga gerhana ini bersifat sentral. Bila waktu dikonversi ke UT dengan ΔT = 70,6 s, puncaknya sekitar 18:17:18 UT, sesuai dengan tabel NASA.\n\nCek: substitusi $t = 0{,}308$ jam memberi $x \\approx -0{,}1606$ dan $y \\approx 0{,}3032$, sehingga $\\sqrt{(-0{,}1606)^2 + 0{,}3032^2} \\approx 0{,}3431$.\n\nPerhatikan bahwa yang kita lakukan hanyalah *memakai* elemen Bessel. Bagian tersulit, yaitu menurunkan koefisien itu dari efemeris Matahari dan Bulan, sudah dikerjakan para astronom. Program ini juga belum menghitung jalur di peta, karena langkah itu memerlukan proyeksi ke elipsoid Bumi dan rotasi Bumi.\n\nGeser slider waktu pada visual berikut untuk melihat titik tembus sumbu bayangan bergerak melintasi \"piringan\" Bumi.",{"id":2010,"data":2011,"type":1938},"ai1b6856510a",{"height":2012,"assetId":2013},460,"cmvofkz2k000107td85nvurnm",{"id":2015,"data":2016,"type":1906},"aie0bf2f47a6",{"markdown":2017},"Dengan model sederhana ini, sumbu bayangan berada di dalam lingkaran Bumi ($r \u003C 1$) kira-kira dari pukul 16.41 sampai 19.56 TDT. Angka ini hanya perkiraan model, karena belum memperhitungkan bentuk Bumi yang pepat dan ukuran kerucut bayangan.",{"id":2019,"data":2020,"type":1906},"aibce4b285aa",{"markdown":2021},"## Konsep Matematika Sekolah di Balik Prediksi Gerhana\n\nHampir setiap langkah prediksi gerhana Matahari memakai materi yang kamu pelajari di kelas.\n\n| Konsep | Jenjang | Dipakai untuk |\n|---|---|---|\n| Perbandingan dan skala | SMP | Ukuran sudut $\\theta \\approx D\u002Fd$, kebetulan \"400 kali\" |\n| Kesebangunan segitiga dan kerucut | SMP | Panjang kerucut umbra, umbra dan penumbra |\n| Teorema Pythagoras | SMP | Jarak sumbu bayangan $r = \\sqrt{x^2 + y^2}$ |\n| Perbandingan trigonometri, $\\arcsin$ | SMA | Lintang Bulan $\\sin\\beta = \\sin i \\sin u$ |\n| Fungsi sinus dan periode | SMA | Naik-turun Bulan terhadap ekliptika |\n| Periode, frekuensi, KPK | SMP–SMA | Tahun gerhana, siklus Saros |\n| Polinomial dan nilai minimum | SMA | Elemen Bessel, mencari gamma |\n| Persamaan diferensial, metode numerik | Kuliah | Menyusun efemeris dari hukum gravitasi |",{"id":2023,"data":2024,"type":1921},"ai64a0ffd94d",{"title":2025,"variant":1926,"markdown":2026},"Contoh 4: panjang kerucut umbra dengan kesebangunan","Kerucut umbra dibentuk oleh garis-garis singgung luar Matahari dan Bulan. Dari kesebangunan segitiga, panjang umbra dari Bulan ke ujung kerucutnya adalah\n\n$$L = d\\,\\frac{r}{R - r},$$\n\ndengan $d$ jarak Matahari–Bulan, $r = 1.737{,}4$ km jari-jari Bulan, dan $R = 695.700$ km jari-jari Matahari. Saat bulan baru dengan jarak rata-rata, $d \\approx 149{,}6\\ \\text{juta} - 384.400 \\approx 149{,}2$ juta km, sehingga\n\n$$L \\approx 149.215.600 \\times \\frac{1.737{,}4}{693.962{,}6} \\approx 373.600\\ \\text{km}.$$\n\nJarak Bulan ke permukaan Bumi terdekat pada jarak rata-rata sekitar $384.400 - 6.371 \\approx 378.000$ km. Karena $373.600 \u003C 378.000$, ujung umbra tidak sampai ke Bumi, sehingga terjadi gerhana cincin. Bila Bulan dekat perigee, jaraknya lebih pendek dari $L$ sehingga umbra mencapai Bumi dan terjadi gerhana total.\n\nCek: kesimpulan ini sama dengan Contoh 1, yaitu pada jarak rata-rata Bulan tampak sedikit lebih kecil daripada Matahari.",{"id":2028,"data":2029,"type":1906},"ai73c37cc0cc",{"markdown":2030},"## Ide Eksplorasi untuk Kelas atau Proyek\n\n- **Visual ukuran sudut**: ubah jarak Bumi–Bulan dari perigee ke apogee pada visual pertama, lalu catat kapan rasio diameter sudut melewati angka 1.\n- **Hitung musim gerhanamu sendiri**: ubah `b_maks` di Program 1 menjadi 1,4° dan 1,6°, lalu amati perubahan lebar jendela dan apakah kesimpulan \"minimal dua gerhana per tahun\" masih berlaku.\n- **Grafik lintasan bayangan**: tambahkan `matplotlib` pada Program 2 untuk menggambar lingkaran Bumi dan kurva $\\big(x(t), y(t)\\big)$, lalu bandingkan dengan visual interaktif di atas.\n- **Uji Saros**: ambil satu gerhana dari katalog NASA, tambahkan 6.585,32 hari, dan periksa apakah gerhana pada tanggal hasil hitunganmu memang tercantum di katalog.",{"id":2032,"data":2033,"type":1906},"ai27c5683f9c",{"markdown":2034},"## Kesalahan yang Sering Terjadi",{"id":2036,"data":2037,"type":1921},"ai166c73250b",{"title":2038,"variant":2039,"markdown":2040},"Hati-hati","warning","- Mengira gerhana Matahari terjadi setiap bulan baru. Padahal kemiringan orbit Bulan sekitar 5° membuat bayangan sering meleset.\n- Menganggap Saros memberi lokasi yang sama. Kelebihan sekitar 8 jam menggeser jalur sekitar 120° ke barat.\n- Mencampur periode sinodis (29,53 hari) dengan periode drakonik (27,21 hari).\n- Lupa mengubah derajat ke radian saat memakai $\\theta \\approx D\u002Fd$ atau fungsi `math.sin` di Python.\n- Menganggap hasil model sederhana setara dengan prediksi resmi. Untuk pengamatan, pakailah data NASA atau BMKG.\n- Menatap Matahari langsung saat gerhana sebagian atau cincin. Selalu gunakan kacamata gerhana bersertifikat atau metode proyeksi.",{"id":2042,"data":2043,"type":2046},"ai9ef4d9cb5d",{"title":2044,"questionSetId":2045},"Uji pemahamanmu: kemiringan orbit, ukuran sudut, Saros, musim gerhana, dan umbra.","cmvo7297n000907qh1iiwjq8i","quiz",{"id":2048,"data":2049,"type":1906},"aidf39a74258",{"markdown":2050},"## Ringkasan\n\n- Ilmuwan memprediksi gerhana Matahari dengan menghitung posisi Matahari dan Bulan memakai hukum gravitasi dan efemeris yang dicocokkan dengan pengamatan.\n- Gerhana Matahari butuh bulan baru **dan** Bulan yang dekat simpul orbitnya. Kemiringan orbit sekitar 5,145° membuat gerhana hanya terjadi pada dua musim gerhana per tahun.\n- Trigonometri ($\\sin\\beta = \\sin i \\sin u$) menentukan apakah bayangan Bulan meleset atau mengenai Bumi.\n- Siklus Saros (223 bulan sinodis ≈ 6.585,3 hari) memperkirakan tanggal gerhana yang mirip, tetapi jalurnya bergeser sekitar 120° ke barat.\n- Elemen Bessel mengubah masalah bayangan 3D menjadi geometri bidang. Gamma adalah jarak minimum sumbu bayangan ke pusat Bumi.\n- Model sederhana menjelaskan *mengapa*. Perhitungan profesional (efemeris, elipsoid Bumi, ΔT, profil tepi Bulan) memberikan *kapan dan di mana* sampai ketelitian detik.",{"id":2052,"data":2053,"type":1906},"aieaee736bd3",{"markdown":2054},"## Materi dan Latihan Terkait\n\n- [Teorema Pythagoras](\u002Fmateri\u002Fteorema-pythagoras): dasar menghitung jarak sumbu bayangan $r = \\sqrt{x^2 + y^2}$.\n- [Rumus Tabung dan Kerucut](\u002Fmateri\u002Frumus-tabung-dan-kerucut): mengenal bentuk kerucut seperti umbra dan penumbra.\n- [Persamaan Garis Lurus](\u002Fmateri\u002Fpersamaan-garis-lurus): garis singgung luar Matahari–Bulan yang membentuk kerucut bayangan.\n- [Gerak Harmonik Sederhana](\u002Fmateri\u002Fgerak-harmonik-sederhana): fungsi sinus, periode, dan fase yang sama dengan naik-turun Bulan terhadap ekliptika.\n- [Vektor 3 Dimensi dan Dot Product](\u002Fmateri\u002Fvektor-3-dimensi-dot-product): alat untuk menyatakan posisi Bumi, Bulan, dan Matahari di ruang.\n- [Perulangan Python: For dan While](\u002Fmateri\u002Fperulangan-python-for-while): dasar pencarian nilai minimum dengan mencoba banyak nilai $t$.\n- [Fungsi Python: def dan return](\u002Fmateri\u002Ffungsi-python-def-return): membuat fungsi `polinom()` dan `jarak()` seperti di Program 2.\n- [Latihan Soal Matematika dan Fisika Gerhana Matahari](\u002Flatihan\u002Flatihan-soal-matematika-dan-fisika-gerhana-matahari): uji pemahamanmu tentang kemiringan orbit, ukuran sudut, Saros, dan umbra.",{"id":2056,"data":2057,"type":1906},"ai9be5645cce",{"markdown":2058},"## Sumber belajar\n\n- [NASA Science: Why Do Eclipses Happen?](https:\u002F\u002Fscience.nasa.gov\u002Feclipses\u002Fgeometry\u002F)\n- [NASA Eclipse Web Site: Eclipses and the Saros](https:\u002F\u002Feclipse.gsfc.nasa.gov\u002FSEsaros\u002FSEsaros.html)\n- [NASA: Five Millennium Canon of Solar Eclipses (-1999 to +3000)](https:\u002F\u002Feclipse.gsfc.nasa.gov\u002FSEpubs\u002F5MCSE.html)\n- [NASA: Besselian Elements for the Total Solar Eclipse of 2024 Apr 08](https:\u002F\u002Feclipse.gsfc.nasa.gov\u002FSEbeselm\u002FSEbeselm2001\u002FSE2024Apr08Tbeselm.html)\n- [NASA Eclipse Web Site: Glossary of Solar Eclipse Terms](https:\u002F\u002Feclipse.gsfc.nasa.gov\u002FSEhelp\u002FSEglossary.html)\n- [NASA JPL: The Planetary and Lunar Ephemerides DE440 and DE441](https:\u002F\u002Fssd.jpl.nasa.gov\u002Fdoc\u002Fde440_de441.html)\n- [BMKG: Gerhana Matahari Total 12 Agustus 2026, Tidak Dapat Diamati dari Indonesia](https:\u002F\u002Fwww.bmkg.go.id\u002Ftanda-waktu\u002Fhilal-gerhana\u002Fgerhana-matahari-total-12-agustus-2026-tidak-dapat-diamati-dari-indonesia)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.","Cara Ilmuwan Memprediksi Gerhana Matahari Bertahun-tahun","2026-10-25T23:09:16.337Z","2026-10-25T23:09:26.913Z",{"id":24,"slug":25,"name":26,"color":29,"icon":28},[2064,2065,2066],{"id":49,"slug":50,"name":51},{"id":55,"slug":56,"name":57},{"id":60,"slug":61,"name":62},[2068,2069,2070,2071],{"id":320,"slug":1344,"name":1345,"subjectId":24},{"id":319,"slug":321,"name":322,"subjectId":24},{"id":176,"slug":178,"name":179,"subjectId":24},{"id":520,"slug":521,"name":522,"subjectId":24},[],[2074],{"lang":1891,"slug":1896},{"name":2076,"slug":2077,"photoUrl":2078,"profession":2079},"Risyad Raflan","risyad-raflan","https:\u002F\u002Fmyfismat.com\u002Fuploads\u002F3f3eca84-9800-4c5f-97ed-1dec08f03152.jpg","Mahasiswa Jurusan Sistem Informasi",{"assets":2081,"videos":2469,"questionSets":2470},{"cmvo70lhc000307qhqbfahimy":2082,"cmvo6zwdg000207qhv7avs9g3":2187,"cmvofkz2k000107td85nvurnm":2389},{"id":1936,"slug":2083,"kind":2084,"title":2085,"description":2086,"url":98,"posterUrl":98,"config":2087,"subject":2186},"gerhana-total-atau-cincin-ukuran-sudut-bulan-dan-matahari","SCENE_2D","Gerhana total atau cincin? Ukuran sudut Bulan dan Matahari","Tampilan langit dari pengamat yang tepat berada di bawah Bulan: piringan oranye adalah Matahari, piringan gelap adalah Bulan, dengan ukuran sudut dihitung dari jari-jari dan jarak sebenarnya. Geser jarak Bumi–Bulan, jarak Bumi–Matahari, dan pergeseran Bulan untuk melihat kapan gerhana menjadi total, cincin, atau sebagian.",{"v":30,"alt":2088,"view":2089,"params":2097,"derived":2121,"objects":2138,"presets":2151,"sources":2171,"readouts":2172},"Dua piringan di langit: Matahari oranye dan Bulan gelap. Ukuran Bulan berubah mengikuti jaraknya; bila lebih besar dari Matahari dan segaris terjadi gerhana total, bila lebih kecil terjadi gerhana cincin, dan bila bergeser terjadi gerhana sebagian.",{"x":2090,"y":2093,"axes":5,"grid":5,"xLabel":2096,"yLabel":2096,"equalScale":5},[2091,2092],-1.3,1.3,[2094,2095],-0.75,0.75,"derajat",[2098,2106,2114],{"id":2099,"max":2100,"min":2101,"step":1674,"unit":2102,"label":2103,"value":2104,"digits":21,"control":2105},"dm",407000,356000,"km","Jarak pusat Bumi–Bulan",384400,"slider",{"id":2107,"max":2108,"min":2109,"step":2110,"unit":2111,"label":2112,"value":2113,"digits":30,"control":2105},"rs",152.1,147.1,0.1,"juta km","Jarak Bumi–Matahari",149.6,{"id":2115,"max":2116,"min":2117,"step":2118,"unit":2119,"label":2120,"value":21,"digits":39,"control":2105},"sep",1.2,-1.2,0.01,"°","Pergeseran pusat Bulan dari pusat Matahari",[2122,2126,2130,2134],{"id":2123,"expr":2124,"unit":2119,"label":2125},"aM","atan(1737.4\u002F(dm - 6371))*180\u002Fpi","jari-jari sudut Bulan",{"id":2127,"expr":2128,"unit":2119,"label":2129},"aS","atan(695700\u002F(rs*1000000))*180\u002Fpi","jari-jari sudut Matahari",{"id":2131,"expr":2132,"label":2133},"ratio","aM\u002FaS","rasio diameter Bulan\u002FMatahari",{"id":2135,"expr":2136,"unit":2102,"label":2137},"Lu","rs*1000000*1737.4\u002F(695700 - 1737.4)","panjang kerucut umbra",[2139,2143,2146],{"fill":5,"type":2140,"color":2141,"center":2142,"radius":2127},"circle","orange",[21,21],{"fill":5,"type":2140,"color":2144,"center":2145,"radius":2123},"ink",[2115,21],{"at":2147,"text":2150,"type":1906},[2148,2149],-1.25,0.65,"Bulan\u002FMatahari = {ratio:3}",[2152,2156,2161,2166],{"id":2153,"label":2154,"values":2155},"rata","Jarak rata-rata",{"dm":2104,"rs":2113,"sep":21},{"id":2157,"label":2158,"values":2159},"total","Bulan di perigee (total)",{"dm":2160,"rs":2108,"sep":21},363396,{"id":2162,"label":2163,"values":2164},"cincin","Bulan di apogee (cincin)",{"dm":2165,"rs":2109,"sep":21},405504,{"id":2167,"label":2168,"values":2169},"sebagian","Tidak segaris (sebagian)",{"dm":2104,"rs":2113,"sep":2170},0.35,[],[2173,2176,2179,2181,2183],{"expr":2174,"unit":2119,"label":2175,"digits":64},"2*aM","Diameter sudut Bulan",{"expr":2177,"unit":2119,"label":2178,"digits":64},"2*aS","Diameter sudut Matahari",{"expr":2131,"label":2180,"digits":64},"Rasio diameter Bulan\u002FMatahari (>1 total, \u003C1 cincin)",{"expr":2135,"unit":2102,"label":2182,"digits":21},"Panjang umbra Bulan",{"expr":2184,"unit":2102,"label":2185,"digits":21},"Lu - (dm - 6371)","Panjang umbra − jarak Bulan ke permukaan Bumi (+ berarti umbra sampai)",{"id":24,"slug":25,"name":26,"color":29},{"id":1973,"slug":2188,"kind":2084,"title":2189,"description":2190,"url":98,"posterUrl":98,"config":2191,"subject":2388},"mengapa-gerhana-matahari-tidak-terjadi-setiap-bulan-baru","Mengapa gerhana Matahari tidak terjadi setiap bulan baru","Kurva biru menunjukkan seberapa jauh Bulan berada di atas atau di bawah bidang ekliptika (model sinus dengan periode bulan drakonik 27,21 hari), sedangkan titik menandai setiap bulan baru (tiap 29,53 hari). Geser kemiringan orbit, posisi awal terhadap simpul, dan batas lintang: titik merah menandai bulan baru yang berpeluang menghasilkan gerhana Matahari.",{"v":30,"alt":2192,"view":2193,"params":2201,"derived":2216,"objects":2268,"presets":2368,"sources":2382,"readouts":2383},"Grafik lintang ekliptika Bulan terhadap waktu berbentuk gelombang sinus dengan amplitudo sebesar kemiringan orbit. Titik menandai setiap bulan baru; titik merah berada di dalam pita oranye, artinya gerhana Matahari mungkin terjadi.",{"x":2194,"y":2197,"axes":5,"grid":5,"xLabel":2199,"yLabel":2200,"equalScale":4},[2195,2196],-10,410,[2198,1414],-9,"waktu (hari)","lintang Bulan dari ekliptika (°)",[2202,2207,2211],{"id":2203,"max":1403,"min":21,"step":2204,"unit":2119,"label":2205,"value":2206,"digits":39,"control":2105},"inc",0.005,"Kemiringan orbit Bulan",5.145,{"id":2208,"max":2209,"min":21,"step":30,"unit":2119,"label":2210,"value":21,"control":2105},"fase",360,"Posisi awal relatif simpul",{"id":2212,"max":64,"min":2213,"step":2110,"unit":2119,"label":2214,"value":2215,"digits":30,"control":2105},"blim",0.5,"Batas lintang agar gerhana mungkin",1.5,[2217,2220,2223,2226,2229,2232,2235,2238,2241,2244,2247,2250,2253,2256,2259,2262,2265],{"id":2218,"expr":2219},"b0","inc*sin(2*pi*0.0\u002F27.212221 + fase*pi\u002F180)",{"id":2221,"expr":2222},"b1","inc*sin(2*pi*29.5306\u002F27.212221 + fase*pi\u002F180)",{"id":2224,"expr":2225},"b2","inc*sin(2*pi*59.0612\u002F27.212221 + fase*pi\u002F180)",{"id":2227,"expr":2228},"b3","inc*sin(2*pi*88.5918\u002F27.212221 + fase*pi\u002F180)",{"id":2230,"expr":2231},"b4","inc*sin(2*pi*118.1224\u002F27.212221 + fase*pi\u002F180)",{"id":2233,"expr":2234},"b5","inc*sin(2*pi*147.6529\u002F27.212221 + fase*pi\u002F180)",{"id":2236,"expr":2237},"b6","inc*sin(2*pi*177.1835\u002F27.212221 + fase*pi\u002F180)",{"id":2239,"expr":2240},"b7","inc*sin(2*pi*206.7141\u002F27.212221 + fase*pi\u002F180)",{"id":2242,"expr":2243},"b8","inc*sin(2*pi*236.2447\u002F27.212221 + fase*pi\u002F180)",{"id":2245,"expr":2246},"b9","inc*sin(2*pi*265.7753\u002F27.212221 + fase*pi\u002F180)",{"id":2248,"expr":2249},"b10","inc*sin(2*pi*295.3059\u002F27.212221 + fase*pi\u002F180)",{"id":2251,"expr":2252},"b11","inc*sin(2*pi*324.8365\u002F27.212221 + fase*pi\u002F180)",{"id":2254,"expr":2255},"b12","inc*sin(2*pi*354.3671\u002F27.212221 + fase*pi\u002F180)",{"id":2257,"expr":2258},"b13","inc*sin(2*pi*383.8977\u002F27.212221 + fase*pi\u002F180)",{"id":2260,"expr":2261},"jmlA","(sign(blim-abs(b0))+1)\u002F2+(sign(blim-abs(b1))+1)\u002F2+(sign(blim-abs(b2))+1)\u002F2+(sign(blim-abs(b3))+1)\u002F2+(sign(blim-abs(b4))+1)\u002F2+(sign(blim-abs(b5))+1)\u002F2+(sign(blim-abs(b6))+1)\u002F2",{"id":2263,"expr":2264},"jmlB","(sign(blim-abs(b7))+1)\u002F2+(sign(blim-abs(b8))+1)\u002F2+(sign(blim-abs(b9))+1)\u002F2+(sign(blim-abs(b10))+1)\u002F2+(sign(blim-abs(b11))+1)\u002F2+(sign(blim-abs(b12))+1)\u002F2+(sign(blim-abs(b13))+1)\u002F2",{"id":2266,"expr":2267},"jml","jmlA + jmlB",[2269,2272,2278,2283,2286,2290,2293,2296,2299,2302,2305,2308,2311,2314,2317,2320,2323,2326,2329,2332,2335,2338,2341,2344,2347,2350,2353,2356,2359,2362,2365],{"expr":2270,"type":2271,"color":2141},"abs(y) \u003C blim","region",{"expr":2273,"type":2274,"color":2275,"domain":2276},"inc*sin(2*pi*x\u002F27.212221 + fase*pi\u002F180)","function","blue",[21,2277],400,{"to":2279,"from":2280,"type":2281,"color":2282,"dashed":5},[30,21],[21,21],"line","gray",{"x":21,"y":2218,"id":2284,"type":2285,"color":2282},"N0","point",{"x":21,"y":2218,"id":2287,"type":2285,"color":2288,"visible":2289},"E0","red","blim - abs(b0)",{"x":2291,"y":2221,"id":2292,"type":2285,"color":2282},29.5306,"N1",{"x":2291,"y":2221,"id":2294,"type":2285,"color":2288,"visible":2295},"E1","blim - abs(b1)",{"x":2297,"y":2224,"id":2298,"type":2285,"color":2282},59.0612,"N2",{"x":2297,"y":2224,"id":2300,"type":2285,"color":2288,"visible":2301},"E2","blim - abs(b2)",{"x":2303,"y":2227,"id":2304,"type":2285,"color":2282},88.5918,"N3",{"x":2303,"y":2227,"id":2306,"type":2285,"color":2288,"visible":2307},"E3","blim - abs(b3)",{"x":2309,"y":2230,"id":2310,"type":2285,"color":2282},118.1224,"N4",{"x":2309,"y":2230,"id":2312,"type":2285,"color":2288,"visible":2313},"E4","blim - abs(b4)",{"x":2315,"y":2233,"id":2316,"type":2285,"color":2282},147.6529,"N5",{"x":2315,"y":2233,"id":2318,"type":2285,"color":2288,"visible":2319},"E5","blim - abs(b5)",{"x":2321,"y":2236,"id":2322,"type":2285,"color":2282},177.1835,"N6",{"x":2321,"y":2236,"id":2324,"type":2285,"color":2288,"visible":2325},"E6","blim - abs(b6)",{"x":2327,"y":2239,"id":2328,"type":2285,"color":2282},206.7141,"N7",{"x":2327,"y":2239,"id":2330,"type":2285,"color":2288,"visible":2331},"E7","blim - abs(b7)",{"x":2333,"y":2242,"id":2334,"type":2285,"color":2282},236.2447,"N8",{"x":2333,"y":2242,"id":2336,"type":2285,"color":2288,"visible":2337},"E8","blim - abs(b8)",{"x":2339,"y":2245,"id":2340,"type":2285,"color":2282},265.7753,"N9",{"x":2339,"y":2245,"id":2342,"type":2285,"color":2288,"visible":2343},"E9","blim - abs(b9)",{"x":2345,"y":2248,"id":2346,"type":2285,"color":2282},295.3059,"N10",{"x":2345,"y":2248,"id":2348,"type":2285,"color":2288,"visible":2349},"E10","blim - abs(b10)",{"x":2351,"y":2251,"id":2352,"type":2285,"color":2282},324.8365,"N11",{"x":2351,"y":2251,"id":2354,"type":2285,"color":2288,"visible":2355},"E11","blim - abs(b11)",{"x":2357,"y":2254,"id":2358,"type":2285,"color":2282},354.3671,"N12",{"x":2357,"y":2254,"id":2360,"type":2285,"color":2288,"visible":2361},"E12","blim - abs(b12)",{"x":2363,"y":2257,"id":2364,"type":2285,"color":2282},383.8977,"N13",{"x":2363,"y":2257,"id":2366,"type":2285,"color":2288,"visible":2367},"E13","blim - abs(b13)",[2369,2373,2377],{"id":2370,"label":2371,"values":2372},"nyata","Orbit miring 5,145°",{"inc":2206,"blim":2215,"fase":21},{"id":2374,"label":2375,"values":2376},"datar","Andai orbit tidak miring",{"inc":21,"blim":2215,"fase":21},{"id":2378,"label":2379,"values":2380},"geser","Simpul bergeser 90°",{"inc":2206,"blim":2215,"fase":2381},90,[],[2384,2386],{"expr":2266,"label":2385,"digits":21},"Bulan baru berpeluang gerhana (dari 14)",{"expr":2218,"unit":2119,"label":2387,"digits":39},"Lintang Bulan saat bulan baru ke-0",{"id":24,"slug":25,"name":26,"color":29},{"id":2013,"slug":2390,"kind":2084,"title":2391,"description":2392,"url":98,"posterUrl":98,"config":2393,"subject":2468},"lintasan-sumbu-bayangan-bulan-pada-bidang-fundamental-gerhana-8-april-2024","Lintasan bayangan Bulan saat gerhana 8 April 2024","Lingkaran biru adalah Bumi (jari-jari 1) dilihat dari arah Matahari, dan titik merah adalah tempat sumbu bayangan Bulan menembus bidang fundamental, dihitung dari elemen Bessel NASA untuk gerhana total 8 April 2024. Geser slider waktu untuk melihat kapan sumbu bayangan mengenai Bumi dan kapan jaraknya ke pusat Bumi paling kecil (gamma).",{"v":30,"alt":2394,"view":2395,"params":2402,"derived":2410,"objects":2423,"presets":2444,"sources":2459,"readouts":2460},"Lingkaran satuan mewakili Bumi. Kurva putus-putus menunjukkan lintasan sumbu bayangan Bulan dari kiri bawah ke kanan atas. 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