Calculadora da Terceira Lei de Kepler

Aplique a terceira lei de Kepler para relacionar período orbital e semieixo maior.

yr

Semieixo Maior

1.000000 AU

Semi-Major Axis (km)149,597,871 km

Semi-Major Axis vs Orbital Period

Formula

## 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)**

Exemplo Resolvido

Mars has an orbital period of 1.881 years. Find its semi-major axis.

  1. 01a = T^(2/3)
  2. 02T² = 1.881² = 3.538
  3. 03a = 3.538^(1/3) = 1.524 AU
  4. 04In km: 1.524 × 149 597 870.7 ≈ 228 million km

Perguntas Frequentes

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.

Calculadoras Relacionadas