Homework Question: The earth travels around the sun on a path that is roughly circular with a radius of 93 million miles. How fast is the earth moving through space?

Answer 1

You are looking for the tangential velocity of the earth as it rotates about the sun:

the tangential velocity, V_t= 2 π r / T , where r is the radius in this case it is 93,000,000 miles, and T is the period, which is the time it takes for the earth to complete one revolution about the sun.

This time is 365 days / revolution. thus,

V_t = 2 π (93,000,000 miles ) / 365 days = 1,600, 921 Miles/day or 66,705 mph

Recall that 2 π r is the circumference and you can write V_t = S / T , and 1/T = f ( frequency)

then V_t = 2 π f r , and 2 π f = ω, Therefore V_t = ω r the tangential velocity in a circular motion