A comet is discovered that has an orbital period of 85 years. Determine the average distance of this comet from the Sun in AU.

Answer 1

This question is in regards to Kepler's 3rd law of planetary motion, which describes the proportional relationship between the cube of the mean orbital distance (r3) and the square of the orbital period (T2). Since the other values in Newton's gravitation do not change (m and G), this can be solved by a simple proportion.

r³ / T² = constant

In order to solve this, establishing the proportion with idea that Earth has a period of 1 year (T_Earth = 1 year) and an average orbital distance of 1 AU (r_Earth = 1 AU) makes the relationship much easier to use.

Since the same proportional fraction for Earth equals 1 using these units, the resulting proportion can also be established for the comet.

r_comet³ / T_comet² = 1

Rearranging this proportion to solve for the mean distance would provide:

r_comet = (T_comet)^2/3 = (85 yrs)^2/3 = approximately 19 AU