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

[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!

 

[Drakkith]

But when I'm using this one : Sqrt(G*M*(2/r)-(1/a)) I'm getting 1,32*1017

I'm not too familiar with orbital mechanics. Could you tell me what equation you're using here?

Edit: Forgot to say ask if it's one of the equations listed here: http://www.physicsclassroom.com/class/circles/Lesson-4/Mathematics-of-Satellite-Motion

 

[Francis Forget]

I'm not too familiar with orbital mechanics. Could you tell me what equation you're using here?

Yeah, I'm using the equation listed above but I'm going to 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
Eq2 : http://upload.wikimedia.org/math/6/6/d/66dd08fa58f176503e2f0b6603769f4d.png
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!

 

[Bandersnatch]

Sqrt(G*M*(2/r)-(1/a))

Is that the actual equation you're using? You missed a pair of brackets there.
Should be:
$\sqrt{GM(2/r-1/a)}$
see here:
http://en.wikipedia.org/wiki/Orbital_speed#Precise_orbital_speed

 

[Francis Forget]

Is that the actual equation you're using? You missed a pair of brackets there.
Should be:
$\sqrt{GM(2/r-1/a)}$
see here:
http://en.wikipedia.org/wiki/Orbital_speed#Precise_orbital_speed

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!

 

[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 $GM$.

 

[mfb]

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.