# Height and Acceleration of a Satellite in Orbit

• benca
In summary, the conversation discusses the calculation of the radius and height of a satellite orbiting the Earth using the equations for gravitational force and centripetal acceleration. The direction of acceleration is towards the center of the Earth and the calculated height of over 3000 km is deemed reasonable based on the given force. There is also a mention of the inverse relationship between distance and gravitational force.

#### benca

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 the 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?
Relevant Equations
Eg = Gme/r^2

me = mass of the earth
a)

Eg = Gme/r^2
r = √Gme/Eg
r = √[(6.67x10^-11 N*m^2*kg^2)(5.98x10^24 kg)]/(4.5 N/kg)
r = 9.41x10^6 m

h = r2 - r1
h = 9.41x10^6 m - 6.38x10^6 m
h = 3.03x10^6 m

that's over 3000 km. Did I not use for right equation? Is Eg not 4.5 N/kg?

Also for b), isn't the force of gravity the centripetal acceleration? so wouldn't it be the same equation? ac = Gme/r^2

and I don't know what it means by direction. isn't it accelerating in a circular motion? This one has really got me confused.

benca said:
that's over 3000 km. Did I not use for right equation? Is Eg not 4.5 N/kg?

Also for b), isn't the force of gravity the centripetal acceleration? so wouldn't it be the same equation? ac = Gme/r^2

and I don't know what it means by direction. isn't it accelerating in a circular motion? This one has really got me confused.

Why do you think over 3000km is wrong?

Acceletration is a vector, and has a direction. What is the directioin for uniform circular motion?

PeroK said:
Why do you think over 3000km is wrong?

Acceletration is a vector, and has a direction. What is the directioin for uniform circular motion?

Well in examples provided the satellites were much less. I guess I thought it should have been similar. And now that I say it, the direction of acceleration is towards the centre of the Earth (?)

benca said:
Well in examples provided the satellites were much less. I guess I thought it should have been similar. And now that I say it, the direction of acceleration is towards the centre of the Earth (?)
Yes. That's what "centripetal" means.

By the way, you can get the radius by noticing that the gravitational force is inversely proportional to the square of the distance. So:

##\frac{r^2}{R^2} = \frac{g_R}{g_r}##

The force you were given was just under half the Earth's surface gravity, so ##r \approx 1.5 R##. ##R \approx 6,000km##, so ##h \approx 3,000 km## looks about right.