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Old December 1st, 2008, 11:37 AM
ccbc101 ccbc101 is offline
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Default Hard Calc question

NO one seems to know how to do this.

According to Kepler's laws, the planets in our solar system move in
elliptical orbits around the sun. If a planet's closest approach to
the sun occurs at time t=0, then the distance r from the center of the
planet to the center of the sun at some later time t can be determined
from the equation

r=a(1-ecos(x))

where a is the average distance between centers, e is the positive
constant that measures the "flatness" of the elliptical orbit, and "x"
is the solution of Kepler's equation:

(2*pi*t)/T=x-esin(x)

in which T is the time it takes for one complete orbit of the planet.

a) Estimate the distance from the planet mars to the sun when t=1 year. a= 228 m km..e=.0934..t=1.88 years (Newton's Law)

b) calculate dr/dt. Show that r reaches a maximum value at t=T/2
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