Question

Which is the correct statement of Kepler's Third Law pf planetary motion

A. p= a^3

b. p^2=a

c. p^3=a^2

D. p=a

Answer 1

c. p^3=a^2

Step-by-step explanation:

Kepler´s laws of planetary motion are based on calculations with elliptical orbits, of the planets around the sun, there are 3 laws:

Law of orbits: The planets move in elliptical orbits and the sun is positioned in one of the focal points

Law of areas: Based on conservation of momentum, it states that planets go faster closer to the sun and slower far from it, such that the areas enclosed by the movement of the planet in a fixed time interval remains constant, thus, conforming to the conservation of momentum

Law of periods: there is a relationship between period and the semimajor axis of the orbit, such that:

`P^(2) =(4*\pi ^(2) )/(G(Msun+Mplanet)) A^(3)`

where G=gravitational constant; M=solar masses; P=period in years and A=semimayor axis in AU

Then, we can simplify by only taking into account the mass of the sun, because is way bigger than the masses of the other planets, and we get:

`(4*\pi ^(2) )/(GM) =1`

`P^(2) =A^(3)`

where P=period and A=semimayor axis