# How to calculate the speed of a satellite around the sun.

1. Apr 2, 2015

### Francis Forget

Hi guys,
I'm currently doing a little project an I need to calculate the speed of a satellite around the sun! I'm currently trying with the Earth, but i have some problem.
When i'm using this formula : (2*Pi*a*Sqrt(1-e2))/T(1±e)
I get an answer in km/s which seams pretty good. (29,75 km/s)
But when i'm using this one : Sqrt(G*M*(2/r)-(1/a)) i'm getting 1,32*1017
I don't really know how I can transform that answer into something in km/s

If i'm not clear enough, feel free to ask me questions!

Thanks!

2. Apr 2, 2015

3. Apr 2, 2015

### Francis Forget

Yeah, i'm using the equation listed above but i'm gonna link you different image where it's clearly listed ! Thank you very much for helping me !

Eq1 : http://i.imgur.com/GYaHMLJ.png
Where Vp is Speed,
a is the length of the semi-major axis of the elliptical orbit
e is the eccentricity
Where V is Speed,
μ is the standard gravitational parameter,
r is the distance at which the speed is to be calculated
a is the length of the semi-major axis of the elliptical orbit
Image 3 : http://i.imgur.com/zzmlLKQ.png
Here is my project so far, as you can see, my answers aren't good when it comes to the second equation!

Last edited: Apr 2, 2015
4. Apr 2, 2015

5. Apr 2, 2015

### Francis Forget

Thanks you ! But it's worse now... I'm getting :
What's the unit of this? How can I convert it to km/s ?

Thanks!

6. Apr 2, 2015

### Bandersnatch

See the wikipedia link. They do the exact same calculation you're doing as an example, with numbers and units. The $\mu$ in their equation is just the same as $GM$.

7. Apr 2, 2015

### Staff: Mentor

If you get 1016 it is a calculation error. Do you square the product instead of taking the square root?

Quick estimate using SI units: G is 10-10, M is 1030 , r and a are 1011 so 2/r is 10-11 and 1/a is half that value.
That means the product is about 108 and the square root is 10000 with units m/s, or 10km/s - which is the right order of magnitude.