How High Must a Satellite Orbit to Maintain Specific Gravitational Strength?

[the_morbidus]

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?

Given values in the book:
mass of Earth : 5.98 x 10^24 kg
radius of the Earth : 6.38 x 10^6 m
g : 6.67 x 10^-11 Nm^2/kg^2

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) So we have to find the distance of the satellite above the surface of the Earth and for that we will find its distance from the centre of the Earth and then subtract it from the Earth's radius to obtain the final result.

Fg= GmE/r^2
4.5=(6.67x10^-11)(5.98x10^24) / r^2
r^2= 3.98866x10^14 / 4.5
r= sqrt (8.8637x10^13)
r=9.4x10^6 m

r surface = r total - r earth
r surface = 9.4x10^6 - 6.38x10^6
r surface = 3.02x10^6 m

The satellite must orbit at 3.02x10^6 m from the surface of the earth.

b)
This is the one i don't get it althought I'm not sure which one the centripetal acceleration formulas to use, i have no idea how to figure out its direction, please help !

c)

v= sqrt (GmE / r)
v=sqrt ( (6.67x10^-11)(5.98x10^24)/3.02x10^6)
v=sqrt (3.98866x10^14/3.02x10^6)
v=sqrt (1.32x10^8)
v=11489.16 m/s

The satellite must travel at 11489.16 m/s in order to maintain its orbit.


again if possible to help me with question b) and perhaps review my work for questions a) and c) , thank you everyone!

 

[Mindscrape]

The principles of a and c are right, so as long as you did the numbers okay, those looks good.

For part b), try using Newton's second law since you don't know the period. :)