# Circular Motion of earth's orbit Problem

1. Sep 23, 2010

Hello everyone! Please, help me understand the following problem:

1. The problem statement, all variables and given/known data
Earth's orbit around the Sun is nearly circular. The period is 1 yr = 365.25 d.
(a) In an elapsed time of 5 d, what is Earth's angular displacement? Solved!
(b) What is the change in Earth's velocity, Δv? Confused!

2. Relevant equations
ω = Δθ/Δt
v = rω

3. The attempt at a solution
I easily solved the first problem doing this: Δθ = (2π x 5 days)/365.25 days = 0.0860 rads
However, whenever I enter a solution for the second problem, the computer does not accept my answer, even though I'm solving it correctly. This is what I did:
First, I tried to solve for the angular velocity of the object. Since the computer wants the answer in meters per second, I converted Δt to seconds:
ω = Δθ/Δt = 0.0860121192 rads / (5 days x 86,400 sec) = 1.99x10^-7 rads/sec
Now, I substitute the distance between the sun and the earth in meters and the angular velocity into v = rω to solve for v.
v = rω = (1.5x10^14 m)(1.99x10^-7 rads/sec) = 2.99x10^7 m/s
The correct answer, according to the computer, should be 2570 m/s.
What am I doing wrong?

2. Sep 23, 2010

### sachinism

3. Sep 23, 2010

Are you sure? That's similar to what I did, and that's not the answer, as I stated above.

4. Sep 23, 2010

### sachinism

its 2 days over there in the link i gave

and its 5 days in your case

5. Sep 24, 2010

Well... I exactly followed their whole procedure. I'm getting the wrong answer still, the correct answer should be 2570 m/s. Thank you for the link though! Anyone else? Help

6. Sep 24, 2010

### sachinism

well may be the answer what u think is right is wrong

7. Sep 24, 2010