which form of keplers third law can you use to relate the period T and radius r of a planet in our solar system as long as the unit year is used for the period and asrtonmical unit is used for the radius?

Answer 1

In this case, you can use the form of Kepler's Third Law that relates the period (T) and the radius (r) of a planet in our solar system when the unit year is used for the period and the astronomical unit (AU) is used for the radius.

The formula is as follows:

T^2 = (4π^2 / G(M + m)) * r^3

Where:
- T is the period of the planet (in years)
- r is the radius of the planet's orbit (in astronomical units, AU)
- G is the gravitational constant
- M is the mass of the Sun
- m is the mass of the planet

Note: This form of Kepler's Third Law assumes that the planet's mass is small compared to the mass of the Sun, so it can be neglected.