Equation of an ellipse word problem

Question

Good day,

the problem is this : The distance of Jupiter from the sun ranges from 741 million km to 816 million km. Find the equation of its elliptical orbit where the sun is one of the foci. Assume again that the center is the origin and its major axis is the x axis. Im having trouble in answering this one and I dont know if I should add then to get the major axis. Please help.

Draw a picture showing the 741 and the 816, and things should then be obvious — bubba, Nov 05 '16 at 07:46

score 1 · Accepted Answer · answered Nov 05 '16 at 07:48

1

The given values are positions of apogee,perigee thus its closest ,farthest at those value so $a-ae=741,a+ae=816$ from them you get value of $e,a $ also we know that $e=\sqrt {1-\frac {b^2}{a^2}} $ from this you get $b$ and as its centre is at origin so you get the standard equation of the ellipse.

answered Nov 05 '16 at 07:48

Archis Welankar

15,910

is there a way without getting the eccentricity? – Codex Nov 05 '16 at 08:22
I dont know of one sorry – Archis Welankar Nov 05 '16 at 08:53
Substitute $ae=d$ and, then, use $d^2=a^2-b^2$ to find $b$ – N74 Nov 05 '16 at 09:34
got it . if you add them it will be the mahor acis and then you subtract the apogee from that to get c – Codex Nov 05 '16 at 10:01

Equation of an ellipse word problem

1 Answers1