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The Earth orbits the Sun once per year. What is the centripetal force keeping th

ID: 2175661 • Letter: T

Question

The Earth orbits the Sun once per year.

What is the centripetal force keeping the Earth in orbit?

I found how far the earth travels in one year (340,000,000), The Earths Tangential velocity (29814 m/s), and the centripetal acceleration of the earth (5.928e-3 m/s^2), but what is the centripetal force keeping the earth in orbit?

I already know the formula (Fc = m. v^2/r), but I can't for the life of me get the correct answer in Newtons.

T = 1 year (convert to seconds)
r = 1.5e+11 meters
m = 6e+24 kg

Explanation / Answer

Fc = m. v^2/r
M is the star’s mass, m is the planet’s mass, and R is the distance between the planet and star. It’s negative because it’s trying to decrease R.
v is the “tangential velocity” (how fast the planet is moving around the star, and not counting motion toward or away from the star).
m = (6 e+24) = 6×10^24
r = 1.5 e+11 = 1.5 x 10^11
Fc = (6 x 10^24) * (29814 ^2) / (1.5 x 10^11)
Fc = 3.555498384 x 1022 N

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