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.