Question

The radius of the earth's orbit around the sun (assumed to be circular) is 1.50 X 108 km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? (b) What is the radial acceleration of the earth toward the sun, in m/s2? (c) Repeat parts (a) and (b) for the motion of the planet Mercury (orbit radius = 5.79 X 107 km, orbital period = 88.0 days)

Answer 1

r = 1.5 * 10^11 meters

2 pi r = 9.42 * 10^11 meters circumference
and
365d * 24h/d * 3600 s/h =3.15 * 10^7 seconds

v = 9.42*10^11 m/3.15*10^7 s = 2.99*10^4 m/s

Ac = v^2/r
etc