Kepler’s third law of planetary motion states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The constant k in this law can be defined for solar orbits as follows:
The value of the constant k is given by the formula:
k = G * M / (4 * π²)
Where:
- G is the gravitational constant, approximately 6.67430 × 10-11 m3 kg-1 s-2.
- M is the mass of the Sun, approximately 1.989 × 1030 kg.
By substituting these values into the formula for k:
k = (6.67430 × 10-11 m3 kg-1 s-2) * (1.989 × 1030 kg) / (4 * π²)
Calculating the value:
k ≈ 1.327 × 1020 m3 s-2
This value of k is often used in discussions relating to the gravitational effects of the Sun on the orbits of planets, moons, and other celestial bodies within the solar system. Therefore, the value of Kepler’s solar orbit constant k in standard international (SI) units is approximately 1.327 × 1020 m3 s-2.