Gravitation/Average Force Problem

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In summary, the conversation discusses the calculation of the speed, period, altitude, and mechanical energy of a satellite in a circular orbit around the Earth. It also raises questions about the magnitude of the average retarding force on the satellite and the conservation of angular momentum for both the satellite and the satellite-Earth system. The speaker has solved parts a-e correctly and is now seeking help to solve parts f-h, which involve finding the unknown force, distance, and angle in the equation FDcos(x)=-2.1x10^8 J. The speaker is unsure about how to approach the problem and is considering using a calculus-based solution.
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brendan3eb
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Homework Statement


What are (a) the speed and (b) the period of a 220 kg satellite in an approximately circular orbit 640 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of 1.4x10^5 J per orbital revolution. Adopting the reasonable approximation that the satellite's orbit becomes a "circle of slowly diminishing radius," determine the satellite's (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (f) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth's center conserved for (g) the satellite and (h) the satellite-Earth system?


Homework Equations


w=change in mechanical energy
w=FDcos(x)

The Attempt at a Solution


First and foremost, I've solved parts a-e correctly. I just need to get f-h.
(1500 revs)((-1.4x10^5 J)/rev)=-2.1x10^8 J
W=change in mechanical energy
W=-2.1x10^8 J
W=FDcos(x)
FDcos(x)=-2.1x10^8 J
So F is definitely the unknown I have to solve for, therefore I should be able to get D and x. Do I just assume that x is 0 degrees? And for finding D, do I just choose one of the two radius values and multiply the amount of revs by the circumference?

It seems to me as though the above way of solving is a little questionable. The only alternative would be a calc-based solution, but I am not quite sure how to go about that.
 
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  • #2
I'm not asking for a solution, but some help as to what equations and steps I should take to solve this problem. Thanks.
 
  • #3


I would approach this problem by first recognizing the given information and identifying the unknowns. In this case, the unknowns are the magnitude of the average retarding force on the satellite and whether angular momentum is conserved for the satellite and the satellite-Earth system.

To solve for the magnitude of the average retarding force, I would use the equation W=FDcos(x), where W is the change in mechanical energy, F is the magnitude of the average retarding force, D is the displacement of the satellite, and x is the angle between the force and the displacement. Since we have already calculated W and know the displacement (the circumference of the orbit), we can solve for F by assuming x to be 0 degrees and solving for D.

To check for conservation of angular momentum, I would use the equation L=mvR, where L is the angular momentum, m is the mass of the satellite, v is the speed of the satellite, and R is the distance between the satellite and the center of the Earth. For the satellite-Earth system, I would use the total mass of the system and the total angular momentum, which would include the angular momentum of the satellite and the Earth's rotation.

In conclusion, as a scientist, I would solve for the unknowns using the given information and relevant equations, and then check for conservation of angular momentum to ensure the accuracy of my calculations.
 

1. What is the formula for calculating gravitational force?

The formula for calculating gravitational force is F = G * (m1 * m2) / r^2, where F is the force, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.

2. How does the distance between two objects affect the gravitational force?

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force of gravity decreases.

3. What is the difference between weight and mass?

Weight is a measure of the gravitational force exerted on an object, while mass is a measure of the amount of matter in an object. Weight can vary depending on the strength of gravity, while mass remains constant.

4. How does the mass of an object affect the gravitational force it experiences?

The greater the mass of an object, the greater the gravitational force it experiences. This is because the gravitational force is directly proportional to the masses of the two objects involved.

5. What is the relationship between gravitational force and acceleration due to gravity?

The acceleration due to gravity is the acceleration that an object experiences when falling due to the force of gravity. The magnitude of this acceleration is equal to the gravitational force divided by the mass of the object, according to Newton's second law of motion (F=ma).

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