- 23

- 1

**Problem:**

The earth's orbit (assumed circular) around the sun is 1.5e11 m in radius, and it makes this orbit once a year. What is the centripetal acceleration of the earth?

**Equations:**

a = (v^2) / r

T = (2*pi*r) / v

**My work:**

T = (2*pi*r) / v;

1 year = (365 days / 1 year)*(24 hours / 1 day)*(60 mins / 1 day)*(60 secs / 1 min) = 3.1536e7 s;

3.1536e7 s = (2*pi*1.5e11 m) / v;

algebraically rearranged is: v = (2*pi*1.5e11 m) / (3.1536e7 s)

v = 29885.8 m/s

a = (v^2) / r;

a = ((29885.8 m/s)^2) / (1.5e11 m);

a =

__0.005954 m/s^2 MY ANSWER__

My question is if this is correct? I've been bombarded with tough questions up until this one and I am curious to know if I solved this correctly. It 'seemed' too easy. Confirmation on the answer would be appreciated since I can't find any information on presumed circular rotation around the sun. Thank you.