Astrophysics - elliptical orbit proof help.

[Kiwithepike]

A.)
Assume a rectangular coord system has its origin at the center of an elliptical planetary orbit and that the coord system x-axis lies along the major axis of the ellipse. Show that the equation for the ellipse is given by x^2/a^2 + y^2/b^2 =1.
where a and b are the lengths if the semi-major axis and the semi-minor axis, respectively.

b.)
using the results from a, prove the area of an ellipse is given by A=(pi)ab.

Im am completely lost right now. Any ideas?

 

[diazona]

For starters, what facts do you know about an ellipse that you could use in the proof?

 

[Kiwithepike]

(x-h)^2/a^2 + y-k)^2/b^2=1

c^2= a^2 -b^2

while a ≥b>0

 

[diazona]

OK, well for part a, for the ellipse in question, what would h and k be?

 

[Kiwithepike]

zero, so (x-h)^2 = x^2 and (y-k)^2= y^2 right?

 

[diazona]

Right, so that part's done. (Although it seems really simple, are you sure you can use that equation as a starting point?)

Now what about part b? How could you find area?

 

[Kiwithepike]

thats what the text tell you to use. That does seem really simple, maybe that's why I am so lost.

B) i know the area A=piab
so the way i was looking at it
solve for y? then integrate it, with trig sub get pi ab?

 

[diazona]

Yep, sounds like you're on the right track with that. (Obviously make sure you actually do it to verify that you get the right answer)

 

[Kiwithepike]

Thank you so much for your help