Saturn orbits the Sun with an orbital radius of 1.43 x 10^12m. Given that the mass of the Sun is 2.0 x 10^30 kg, calculate the period of Saturn's orbit.

Question

Saturn orbits the Sun with an orbital radius of 1.43 x 10^12m. Given that the mass of the Sun is 2.0 x 10^30 kg, calculate the period of Saturn's orbit.

Answer 1

I will explain how to solve this, but YOU do the calculations.

 

r = radius of Saturn's orbit (given)

M = mass of sun (given)

m = mass of Saturn (you will see in a few lines that we really do not need this)

G = constant of universal gravitation (look it up in your physics book)

T = period = ?

 

Equate the gravitational attraction of the sun to the centripetal force on Saturn.

 

GMm/r² = mv²/r ⇒

 

GM/r = v²

 

v = 2πr/T ⇒

 

GM/r = 4π²r²/T²

 

Solve for T and get

 

T = 2π [r³/(GM)]^1/2

 

Plug in the numbers in appropriate units and get T.  This is actually Kepler's 3rd law of planetary motion.