Infrared observations indicate that Saturn gives off 2.8 times the energy it receives from the Sun...

Question

Infrared observations indicate that Saturn gives off 2.8 times the energy it receives from the Sun for a total internal power loss of 2 x 1017 W. Assume that gravitational contraction releases this thermal energy. How much must Saturn shrink per year to account for this output?

Aditi · Accepted Answer

Solution
Let the mass of the Saturn be denoted by 
M = 5.68*1026 kg
Radius of Saturn
R = 5.82*107m
The contraction of a star due to the loss of thermal energy due to gravitational contraction is a mechanism which is called The Kelvin-Helmholtz Mechanism.

Infrared observations indicate that Saturn gives off 2.8 times the energy it receives from the Sun for a total internal power loss of 2 x 1017 W. Assume that gravitational contraction releases this...

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