- #1

Tryan

- 4

- 0

## Homework Statement

mass of the Earth = 5.97 * 10^24 kg

Polar Radius of Earth = 6.36 * 10^6 m

Satellite = 1.08 * 10^3 Kg

Altitude = 2.02 * 10^7 m

3) for any object orbting around a primary body R^3 ∝ T^2

where R is the radius of the orbit and T is the time period for the orbit.

show that this is true and in doing so:

- state the conditions required for a stable orbit

- show that the conditions do not depend on the mass of the orbiting object.

4) discuss the particular requirements for an orbit that will keep the a satellite vertically above a certain point on Earth's surface.

## Homework Equations

1) calculate the net force on a 1.08 * 10^3 Kg Satellite when it is in a polar orbit 2.02 * 10^7 m above the Earth's orbit...

So I think I get this one - as F=GMm/r^2 which gives the net force of (F= 610 N) 3 sig.fig

2)show that the only stable orbit for the satellite orbiting at an altitude of 2.02 * 10^7 m has a period of appoximatly 12 hours.

This next one I think it's correctly done so I've said working out velocity of the satellite I've come up with F(centripetal)=F(gravitational) so mv^2/r=FMm/r^2 so mv^2/r= the non-rounded answer in question 1 which is 609.6320 so 609.6230/1.08 * 10^3= velocity^2 so velocity = 3872.006122. Now with that substituting it into the formula of v = d/t you can find that the T - time period = 12 hours or 11.97 hours.

## The Attempt at a Solution

Now these two questions 3) and 4) I really don't understand. I just don't know where to even start. I know however that it has something to do with Kepler's Laws of motion.? What I do think for question 4) is the velocity must be greater than the vertical acceleration... but I am still unsure..

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