# Homework Help: Average speed of earth in its orbit of sun

1. Apr 20, 2007

### bilbobaggins

1. The problem statement, all variables and given/known data
The earths orbit around the sun is very nearly circular, with an average radius of 1.5x10^11 m. What is the average speed of the earth in orbit around sun.

2. Relevant equations

d/t= 2pi/t

3. The attempt at a solution

2pi*1.5x10^11/ 31556926
it comes out to be 29865.95
answer is supposed to be v=28,886 m/s
so can anyone tell me what i did wrong

31556926 is a year so thats why i used it in the equation

Last edited: Apr 20, 2007
2. Apr 20, 2007

### hage567

Your t value is a little off. Can you explain how you got it?

Hmm, I get the same answer you do though.

Last edited: Apr 20, 2007
3. Apr 20, 2007

### bilbobaggins

I used google to find t, lol.

4. Apr 20, 2007

### chroot

Staff Emeritus
5. Apr 20, 2007

### hage567

Try calculating it yourself! I'm inclined to believe the book's answer is wrong.

6. Apr 20, 2007

### D H

Staff Emeritus
The relevant data are
a=1.00000011 au
e=0.01671022
T=365.242190 days (tropical year)

Using Ramanujan's approximation of the circumference of an ellipse,

$$C=\pi a \left(3\left(1+\sqrt{1-e^2}\right)-\sqrt{\left(3+\sqrt{1-e^2}\right)\left(1+3\sqrt{1-e^2}\right)}\right)$$

the Earth's orbital velocity is 0.01720159 au/day, or 29.7838 m/s

From http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html, the Earth's minimum orbital velocity is 29.29 km/s, larger than the supposedly correct answer. (In other words, the book is wrong.)