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Trizz
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Homework Statement
I have to prove that A1=A2, or the fact that planets will sweep out equal areas in equal amounts of time. The planet I have to do this for is Pluto. Basically, I need help finding the area it "sweeps out" over any length of time of my choosing.
Homework Equations
major axis = 11.8 x 10^9 km
eccentricity = .25
minimum orbital velocity = 3.7 km/s
The Attempt at a Solution
So far, I've found the distance of the perihelion and the aphelion.
To do this I did: eccentricity = distance b/w foci / major axis
then i solved for the foci by doing: dis b/w foci = .25 * 11.8e9
that gave me the distance between the foci, so I was able to find out that the perihelion is 4425000000 km away and the aphelion is 7375000000 km.
Now do I just make a triangle for each with the legs being the distance away and the other being time traveled. It's hard to explain, but this picture shows it well:
http://outreach.atnf.csiro.au/education/senior/cosmicengine/images/cosmoimg/kepler2ndlaw.gif
So basically, how do I prove that those two areas equal with the info I now have
Any help would be appreciated.
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