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?
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.