Determine the orbital speed of the Earth. (4U Physics)

Question

How do you determine the orbital speed of the earth? Thats all the question says and I'n not sure how to answer it. Thanks

Answer 1

If you know the earth-sun distance and the mass of the sun, you can get the speed of the earth by equating the centripetal force on the earth to the gravitational force exerted by the sun.

 

m = mass of earth

M = mass of sun

r = earth-sun distance

G = constant of universal gravitation

 

mv²/r = GMm/r² ⇒

 

v² = GM/r

 

v = √(GM/r)