Height and Acceleration of a Satellite in Orbit

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.
  • #1
benca
19
0
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.
 
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  • #2
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?
 
  • #3
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 (?)
 
  • #4
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.
 

1. What is the relationship between height and acceleration of a satellite in orbit?

The height and acceleration of a satellite in orbit are inversely related. This means that as the height of the satellite increases, the acceleration decreases. Similarly, as the height decreases, the acceleration increases.

2. Why does the acceleration of a satellite decrease with increasing height?

This is due to the decreasing influence of the Earth's gravitational force at higher altitudes. As the satellite moves away from the Earth's surface, the force of gravity weakens, resulting in a decrease in acceleration.

3. What is the significance of the height and acceleration of a satellite in orbit?

The height and acceleration of a satellite in orbit determine the speed and stability of its orbit. The higher the satellite's height, the slower its speed and the more stable its orbit. On the other hand, a lower height and higher acceleration can result in a faster but less stable orbit.

4. Can the acceleration of a satellite be changed while in orbit?

Yes, the acceleration of a satellite can be changed while in orbit through the use of thrusters. These thrusters can be used to adjust the satellite's speed and direction, allowing it to maintain its desired orbit.

5. How does the height of a satellite affect its communication capabilities?

The height of a satellite can greatly impact its communication capabilities. A higher altitude can provide a wider coverage area, allowing the satellite to communicate with more ground stations. However, a lower altitude may result in a stronger signal and faster communication due to the shorter distance between the satellite and the ground station.

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