केप्लर का तीसरा नियम कैलकुलेटर
केप्लर के तीसरे नियम से कक्षीय मापदंड निकालें।
अर्ध-दीर्घ अक्ष
1.000000 AU
Semi-Major Axis vs Orbital Period
सूत्र
## Kepler's Third Law For bodies orbiting the same central mass, the square of the period is proportional to the cube of the semi-major axis. ### Simplified Form (Solar System) **T² = a³** when T is in Earth years and a is in AU. Rearranging: **a = T^(2/3)**
हल किया गया उदाहरण
Mars has an orbital period of 1.881 years. Find its semi-major axis.
- 01a = T^(2/3)
- 02T² = 1.881² = 3.538
- 03a = 3.538^(1/3) = 1.524 AU
- 04In km: 1.524 × 149 597 870.7 ≈ 228 million km
अक्सर पूछे जाने वाले प्रश्न
Does this work for moons of other planets?
Yes, but the constant changes because it depends on the central body's mass. The simplified form uses Solar mass implicitly.
Who was Johannes Kepler?
Kepler (1571-1630) was a German astronomer who discovered three empirical laws of planetary motion from Tycho Brahe's observations.
How precise is T² = a³?
Exact for a massless test particle orbiting the Sun. For real planets the correction factor (1 + m_planet/m_Sun) is typically less than 0.001.