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What is the relationship between satellite altitude and the time needed to complete on orbit?
Wiki User
∙ 8y ago
You need to know a little physics here. The force on the satellite (mass m) is F = GMm/r^2 where M = the mass of the planet, G the gravitational constant and r the distance from the centre of the planet.
From Newton we know that force = mass X acceleration. When you study circular motion you will learn that the acceleration of an object moving in a circle is rw^2 where w = angular velocity (radians/ second). A radian is nearly 60 degrees (actually 180/pi) so there are 2.pi radians in a revolution.
There is therefore a relationship between w and T (time for a revolution) in that T = 2.pi/w.
So we can write m.r. 4.pi^2/T^2 = GMm/r^2
The mass of the satellite cancels out (just as well) and so by rearranging we get
r^3 . 4.pi^2 / GM = T^2 - which gives you Kepler's law.
Since we can measure r and t very easily we can work out GM very accurately as a product (much more accurately than we can measure G or M individually)
The maths is complicated by the fact that the satellite will probably be moving in a slightly elliptical orbit (in which case we replace r by the semi-major axis) and is also affected by variable density of the rocks of the planet (this is very noticeable in satellites going round the moon)
Dortha Miller
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