Hi.
I'm trying to figure out the path of Jupiter around the sun.
It is an ellipse, so I'm trying to get it into the x^2/a^2+y^2/b^2=1 form.
I have the minimum (460,000,000 miles) and maximum(508,000,000 miles) distances.
My teacher has given me three equations to work with, to help me figure the problem out:
Max distance+Min distance=length of Major Axis
A=Length of major axis/2
Major axis-Minor axis/2=C
With these three equations, I have the following information:
Major Axis=968,000,000 miles
A=484,000,000 miles
B=?
C=?
I was wondering if someone could explain how to figure out the minor axis?
Also, the sun is at a point of (C,0) ...so does that mean that my C value would be the C in that ordered pair?
Hi. Thank you for the reply.
I have a few questions though, if you don't mind. Eccentricity is measured from c/a, correct? How did you get: ?
Also, am I supposed to take the square root of everything, once I plug in the numbers, or am I supposed to square the numbers I plugged in?
Thank you so much for your help. It's really appreciated.
Hello lpaige2004
In your original post, I'm not sure what you mean by this:so let me see if I can clarify things.
The equation of the ellipse, as you have said, is:and you have correctly calculated to be .
These are the other things you need to know:
- The centre of the ellipse is at .
- The foci of the ellipse are at .
- The relation between and is:
(1)
- In the case of the elliptical orbit of a planet around the sun, the sun is at one of the foci of the ellipse.
- The greatest distance from a focus to a point on the ellipse is ; the shortest distance is .
Opalg has used this last fact, together will the values and , to write down an expression for .
What you now need to do:
- Evaluate .
- Use equation (1) above to find the value of .
- Use your values of and to write down the equation of the ellipse.
- If you also need to know the distance of the sun from the centre of the orbit - the distance I think you have called - then it's (as stated above).
Grandad