# Satellite Velocity

## Homework Statement

A satellite is designed to orbit Earth at an altitude above its surface that will place it in a gravitational field with a strength of 4.5 N/kg.

a) Calculate the distance above the surface of Earth at which the satellite must orbit.

b)Assuming the orbit is circular, calculate the acceleration of the satellite and its direction.

c)At what speed must the satellite travel in order to maintain this orbit?

mass of earth : 5.98 x 10^24 kg
radius of the earth : 6.38 x 10^6 m

## Homework Equations

Fg= G mE / r^2
ac=v^2/r
v= sqrt ( GmE/r )
ac= 4Pi^2 r / T^2

## The Attempt at a Solution

a)
4.5N/Kg=G(5.98x10^24kg)/r^2

r=9.4168x10^6m

h=re-r=3.0x10^6

Distance above the surface at which the satellite must orbit is 3.0x10^6m.

b)

No clue, I have searched many resources and they fail to give any clear ideas on how to tackle this question.

c)

Using

v=sqt(GMe/r)
v=sqt(G(5.98x10^24kg)/9.4168x10^6)
v=6.5097x10^6 m/s

Seems a bit too much. Could someone verify c) and I would appreciated any help with b), also verification of a) but I think I got it.

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gneill
Mentor
v=sqt(GMe/r)
v=sqt(G(5.98x10^24kg)/9.4168x10^6)
v=6.5097x10^6 m/s

Seems a bit too much. Could someone verify c) and I would appreciated any help with b), also verification of a) but I think I got it.
Check your math for (c). You may have slipped up on the exponents.

For (b), consider N/kg by another name...

Check your math for (c). You may have slipped up on the exponents.

For (b), consider N/kg by another name...
c)
v=sqt(GMe/r)
v=sqt(G(5.98x10^24kg)/9.4168x10^6)
v=6509.6776m/s
I had forgotten to take the square root.

for b)

Other sources suggested that 4.5N/Kg is equal to 4.5m/s^2, that being its only acceleration. Seems that someone else who has taken my course before had confirmed that 4.5m/s^2 is not the correct acceleration.

I believe finding the acceleration from centreifual, and circular motions is my best bet.

However, I'm limited in terms of variables.

gneill
Mentor
I suspect that 'other sources' failed to provide a direction for the acceleration.

I suspect that 'other sources' failed to provide a direction for the acceleration.
Yes, they failed to provide a direction. All that was explained is in the direction towards the earth.