How do you calculate the mass of the sun, M_"sun", using Kepler's third law (T^2=(4 pi^2 r^3)/(G M_"sun"))?

Assume the period of the Earth is T=3.156xx10^7 seconds and the Earth's distance from the Sun is 1.496xx10^11 meters.

1 Answer
May 13, 2017

Plug the given values into the given equation. Answer: ~~1.98955xx10^30 "kg"

Explanation:

Since we are given the equation:
T^2=(4pi^2r^3)/(GM_(sun))
where T=3.156xx10^7 seconds, r=1.496xx10^11 meters, pi~~3.14 is the mathematical constant, and G=6.67xx10^-11 as the gravitational constant, we can first solve for M_(sun) with variables then substitute the given values to find M_(sun):

First, we will use variables to solve for M_(sun) to avoid the amount of numbers in the equation:
T^2=(4pi^2r^3)/(GM_(sun))
T^2(GM_(sun))=4pi^2r^3
M_(sun)=(4pi^2r^3)/(T^2G)

Now, we can substitute our given values:
M_(sun)=(4pi^2(1.496xx10^11)^3)/((3.156xx10^7)^2(6.67xx10^-11))

~~1.98955xx10^30 "kg" rounded to 5 decimals