Solve Satellite Altitude Above Earth's Surface | 16.7 kN, -1.43e11 J

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In summary, the conversation discusses finding the altitude of a communication satellite above Earth's surface by using the formulas for gravitational force and potential energy. The method involves solving for the unknown variables of mass and height and substituting them into the equations. The post also provides a link to a previous discussion on the same topic for further clarification.
  • #1
ninjagowoowoo
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When in orbit, a communication satellite attracts the Earth with a force of 16.7 kN and the earth-satellite gravitational potential energy (relative to zero at infinite separation) is - 1.43*10^11 J. Find the satellite's altitude above the Earth's surface. The radius of the Earth is 6.38*10^6.

OK, I must be making this harder than it needs to be. What I've been trying to do is to use the formulas for gravitational force to get an equation with two unknow variables (Mass of the satellite and height above Earth's surface) And I do the same for gravitational potential energy. Then, since both equations have the same two unknown variables, I solve for one of them and substitute. Is there another way of doing this? Am I doing it copmletely wrong? Please help me! :confused:
 
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  • #2
You sound like you have the right idea. Give it a shot.
 
  • #3
Total Energy of a satellite revolving around Earth is given by:

[itex]- \frac{GMm}{2r}[/itex]

BJ


Note:This post has been edited after Older Dan's remarks.
 
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  • #4
Dr.Brain said:
Potential Energy of a satellite revolving around Earth is given by:

[itex]- \frac{GMm}{2r}[/itex]

BJ
There is no 2 in the potential energy. Perhaps you meant the total energy

[itex] U = - \frac{GMm}{r} [/itex]

[itex] T = \frac{1}{2}mv^2 = \frac{r}{2} \left( \frac{mv^2}{r} \right) = \frac{r}{2} \left| F_c \right| = \frac{r}{2} \left( \frac{GMm}{r^2} \right) = \frac{GMm}{2r} = -\frac{1}{2} U [/itex]

[itex] E\ \ =\ \ T\ \ +\ \ U = \frac{GMm}{2r}\ \ -\ \ \frac{GMm}{r}\ \ =\ \ - \frac{GMm}{2r} [/itex]
 
  • #5

FAQ: Solve Satellite Altitude Above Earth's Surface | 16.7 kN, -1.43e11 J

What is the significance of the satellite's altitude and how is it determined?

The altitude of a satellite is the distance between the satellite and the Earth's surface. It is typically measured in kilometers or miles. The altitude of a satellite is determined by its orbital parameters, such as its speed, direction, and the gravitational pull of the Earth.

What does the unit "kN" stand for in this context?

The unit "kN" stands for kilonewtons, which is a unit of force. In this context, it is likely referring to the thrust force of the satellite's engines.

What does the negative value in the energy measurement (-1.43e11 J) indicate?

The negative value in the energy measurement indicates that the satellite is losing energy. This could be due to atmospheric drag or other forces acting on the satellite as it orbits the Earth.

How does the satellite's altitude affect its orbit?

The satellite's altitude affects its orbit by determining the shape, size, and speed of its orbit. A higher altitude can result in a larger and slower orbit, while a lower altitude can result in a smaller and faster orbit. The altitude also affects the amount of gravitational force acting on the satellite.

How is the satellite's altitude above the Earth's surface important for its function?

The satellite's altitude above the Earth's surface is important for its function because it affects its line of sight and communication with ground stations. It also determines the amount of time the satellite spends in sunlight and shadow, which can impact its power supply and thermal regulation. Additionally, the altitude can affect the satellite's ability to capture data and images of the Earth's surface.

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