Solve Circular Motion: Satellite Height, Speed, Location

In summary, a satellite must have a higher speed than the Earth in order to remain stationary with a point on the Earth.
  • #1
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At what height above the Earth's surface would a satellite have to orbit in order that it be stationary in reference to a point on the earth? What would be it's speed? How would you describe the general location of that point in relation to the Earth's surface?



Homework Equations


v=2PIr/T, ac=v^2/r, ac=4PI^2r/T^2
Fc=M v^2/r, Fc=M 4PI^2r/T^2, Fg=G m1m2/r^2


I know that the satellite would have to be moving faster than the Earth because if not the satellite could not stay stationary with that point on the earth. I have the radius and mass of the Earth so I can figure out everything as far as speed, force, acceleration, and the period for the Earth but because nothing is given for the satellite I do not know how I should figure out the speed of the satellite. I also know that to get the height you can use the equation (H = radius of Earth - radius of satellite), but am not sure how I am supposed to get the radius of the satellite because again no inoformation is given for the satellite. I have tried combining some of the above equations but have come up empty handed. Any help would be appreciated.
 
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  • #2
If the satellite is to remain above a fixed reference point on the Earth then it must have the same period of rotation as the Earth (i.e. the angular speed of the satellite must be the rotational speed of the Earth). You've got enough formulae to be able to link the period of the satellie's orbit to the force on the satellite (or the acceleration this is the same as the field strength at the height of the satellite's orbit). After that it's just a matter of putting in the values for the mass of the Earth and G and calculating.

You can check you've got the right answer quite easily as the altitude of a geo-stationary orbit around the Earth is easy to look up using any search engine.
 
  • #3
Thanks for your help.
 

1. How is satellite height related to its speed in circular motion?

The height of a satellite in circular motion is directly related to its speed. As the satellite's height increases, the speed decreases and vice versa. This is because the gravitational force acting on the satellite decreases as it moves farther away from the Earth's surface, causing its speed to decrease due to the conservation of angular momentum.

2. How can the location of a satellite be determined in circular motion?

The location of a satellite in circular motion can be determined by using the radius of the circular orbit and the angle at which the satellite is located. This can be calculated using the cosine and sine functions and the satellite's orbital period. The location of the satellite can also be determined by using tracking devices and GPS technology.

3. What factors affect the speed of a satellite in circular motion?

The speed of a satellite in circular motion is affected by several factors, including the mass and radius of the planet it is orbiting, the distance from the center of the planet, and the gravitational force acting on the satellite. Additionally, any external forces such as atmospheric drag or other celestial bodies can also affect the speed of a satellite.

4. Can a satellite's height and speed change over time in circular motion?

Yes, a satellite's height and speed can change over time in circular motion. This can be due to various factors such as atmospheric drag, gravitational pull from other celestial bodies, or intentional changes made by ground control. However, in the absence of any external forces, the satellite's height and speed will remain constant due to the conservation of angular momentum.

5. How does the mass of a planet affect the height and speed of a satellite in circular motion?

The mass of a planet has a direct impact on the height and speed of a satellite in circular motion. A planet with a larger mass will have a stronger gravitational pull, causing the satellite to orbit at a lower height and with a higher speed. On the other hand, a planet with a smaller mass will result in a higher orbit and a lower speed for the satellite.

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