Study of Kepler’s Laws and Kepler’s Constant in Various Asteroids of the Solar System

Abstract

Kepler’s laws of motion are fundamental planetary motion, planets, asteroids, comets follow these laws with no or minimal deviation. In this paper, we perform statistical analysis on Kepler’s constant, by using 5350 minor planets data from the minor planet center (MPC). According to Kepler’s third law of motion, the square of orbital time period of a minor planet is
proportional to cubed of the semi-major axis distance, the proportionality constant is Kepler’s constant, 𝐺(𝑀 + 𝑚)/4π = r³/T²,  and m are the mass of the sun and minor planet respectively, and G is the universal constant of gravity. Thus, Kepler constant is also related to the mass of the minor planet, suggesting that Kepler constant depends on 2-body interaction.

Our analysis suggests that 𝐿𝑜𝑔 𝑇 = 1. 5×𝐿𝑜𝑔 𝑎 + 5. 7×10 , which is as estimated, the −11 second term of the equation corresponds to the mass of the minor planet, having said that the error in the data was too high, and measurement of the mass of the asteroid was not possible. The average value and the standard deviation of the Kepler’s constant are 1 and 8. 47×10 , −10 which suggest the spreading of the constant to be low, also, a plot of histogram of the error suggests that the distribution is a normal distribution centered at zero. Thus the conclusion is that all the minor planets follow Kepler's law with not much diversion, leading us to believe that many body forces also lead to abiding by Kepler's laws at astronomical level