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 |