Question

The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. A planet's distance from the sun is 224,000,000 km at perihelion and 232,000,000 km at aphelion. Find an equation for the planet's orbit. (Place the origin at the center of the orbit with the sun on the x-axis.

Answer 1

Taking astronomy?

Answer 2

lol no this is supposed to be "college algebra"

Answer 3

well, you can take the average of the two distances and make that the center point I suppose. then the sun would be off to the left on the x axis and you'd have an ellipse and know where it crosses the x-axis, but I can't see how to find the y intercepts of the elipse.. like I said, -need to study these much more..

Answer 4

ok so then the center point is 228,000,000. Wouldn't the center point have something to do with the origin?

Answer 5

that's what I'm trying.. yea, the center is at 228,000,000 and so the sun is off to the left by 4,000,000 right?? :/

Answer 6

yeah that would seem right

Answer 7

I'm confused.. I'm not sure I'm doing it right...

Answer 8

yea that's right.

Answer 9

yeah it's logical

Answer 10

so, umm what was the equation for an ellipse? uummmm..

\{x^2}{a^2} + {y^2}{b^2} = 1.

Answer 11

division there between them..

Answer 12

You can try reposting this to see if someone else bites too. I'm just trying..

Answer 13

yeah i'm pretty sure that's the equation for an ellipse. I'll try that

Answer 14

You can look at http://en.wikipedia.org/wiki/Ellipse

Answer 15

is "a" the distance from 0 to the x intercept? and "b" the distance to the y intercept?

Answer 16

Here, I think this will help.
http://www.webassign.net/v4cgi/extra/bc_enhanced/index.tpl?asset=read_it&asset_url=/bc_enhanced/srca05/read_it/srca05s.08.02.swf&UserPass=8054aeaac493d0e319ef87a4a2bb6d3a

Answer 17

I think I know how to do it... by using this focus formula.... we can find b...

Focus

The distance from the center C to either focus is f = ae, which can be expressed in terms of the major and minor radii:

f = sqrt{a^2-b^2}.

Answer 18

4,000,000 = root(a^2 - b^2)

Answer 19

solve for b

Answer 20

because we know a...

Answer 21

what was a again?

Answer 22

319,000,000 "the difference of the aphilion and the distance from the sun to the origin...
232,000,000-4,000,000

Answer 23

wait I'm on crack..

Answer 24

a = 228000000.. lol

Answer 25

(x^2)/(2.28x10^8)^2 + (y^2)/b^2 = 1

were b is to be solved in this... 4,000,000 = root(a^2 - b^2)

That's the best I can do right now and am not totally sure it's right...

Answer 26

sorry i didn't respond for a while... i had to reboot my computer lol. thanks for helping

Answer 27

NP i'm sorta going back and forth between this and other things anyway..

Answer 28

but I think that's the one...so after solving for b I get...

b = 227964909.6 , so sub that in and if we haven't made any mistakes it should be ...close.. lol I would run through it again though to be sure if you care to..

Answer 29

i just need the equation for the planet's orbit

Answer 30

(x^2)/(2.28x10^8)^2 + (y^2)/(2.27^8)^2 = 1

That's what I got...

Answer 31

ok thanks