Find the altitude of the satellite

In summary, the problem involves finding the altitude and rate of change of a satellite when the angle is 120 degrees and is increasing at a rate of 2.7 degrees per minute. Using the equation r = 4995/(1+0.12cos(theta)) and subtracting the Earth's radius of 3960 mi, the altitude is calculated to be 1354 mi. However, the rate of change is still unclear and further assistance is needed.
  • #1
pyrosilver
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Homework Statement



At the instant when theta is 120 degrees, the angle theta is increasing at the rate of 2.7 degrees per min. Find the altitude of the satellite and the rate at which the altitude is changing at this instant. Express the rate in units of mi/min.

Homework Equations



r = 4995/(1+0.12cos(theta))
earth's radius = 3960 mi

The Attempt at a Solution



I think I found the altitude alright. I plugged in 120 degrees to the equation and subtracted the radius and got 1354 mi. But I've been working on the other part for the past half hour and I haven't gotten anywhere helpful. I tried to take the derivative of the equation but I get 0. And I'm just so stumped. Can anyone help me out?
 
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  • #2
I'm sorry but I don't quite understand this problem. Don't satellites orbit the Earth so the altitude above the surface is constant. Obviously if the satellite is higher but goes faster then the rate at which the angle changes will be equivalent to slower and lower altitude satellite. Obviously I'm not understanding it because I don't even know how the info of the radius of the Earth fits into this.
 

FAQ: Find the altitude of the satellite

What is the purpose of finding the altitude of a satellite?

The altitude of a satellite is an important piece of information for many reasons. It can help determine the satellite's orbit, coverage area, and communication capabilities. It is also crucial for maintaining the satellite's position and preventing collisions with other objects in space.

How is the altitude of a satellite calculated?

The altitude of a satellite is typically calculated using the satellite's orbital parameters, such as its velocity, semi-major axis, and eccentricity. These parameters are used in mathematical equations, such as Kepler's laws, to determine the satellite's altitude at any given time.

What factors can affect the altitude of a satellite?

The altitude of a satellite can be affected by a variety of factors, such as atmospheric drag, solar radiation pressure, and gravitational forces from other objects in space. Changes in these factors can cause the altitude of a satellite to fluctuate over time.

Why is it important to continuously monitor the altitude of a satellite?

Satellites are constantly moving and can be affected by various factors, as mentioned earlier. Therefore, it is crucial to continuously monitor the altitude of a satellite to ensure its proper functioning and prevent potential collisions with other objects in space.

How does the altitude of a satellite impact its performance?

The altitude of a satellite can greatly impact its performance in terms of communication, coverage area, and positioning. A higher altitude can provide a wider coverage area and a longer communication range, while a lower altitude can result in more accurate positioning and faster communication speeds.

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