The earth is about 1.50 x 1011 m from the sun and has a period of about 365 days orbiting around the sun. suppose that the orbit of the earth is circular, what is the magnitude of the acceleration of the earth in m/s2?

To solve this problem it is necessary to apply the concepts presented in Kepler's third law in which the period is described, as well as the theorems developed for acceleration based on gravity.

Acceleration in gravitational terms can be expressed as

Where,

G = Gravitational Universal Constant

M = Mass of Earth

r = Distance

At the same time the Period by Kepler's law the Period is described as

That is equal to

Using the equation of acceleration,

Re-arrange to find a,

Our values are given as

Replacing we have,

Therefore the magnitude of the acceleration of the earth is

. west