Gravitational Energy for Satellite: r1 to r2

In summary, the total energy of a satellite can be calculated using the equation E = -(GMm/2r). To determine the energy required to pass a satellite from one radius (r1) to a greater radius (r2), the equation can be rewritten as E = (Rgm/2) * (1/r1 - 1/r2). A good first check is to ensure that the physical dimensions are consistent in each step of the calculation.
  • #1
Karol
1,380
22

Homework Statement


A satellite orbits at radius r1. What is the energy required to pass it to a greater radius r2. express in terms of m and g

Homework Equations


The total energy of a satellite: ##E=-\frac{GMm}{2r}##

The Attempt at a Solution


$$E=-\frac{GMm}{2r_2}+\frac{GMm}{2r_1}=-\frac{RGMm}{R2r_2}+\frac{RGMm}{R2r_1}=\frac{Rgm}{2}\left( \frac{1}{r_1}-\frac{1}{r_2}\right )$$
The answer in the book:
$$\frac{R^2gm}{2}\left( \frac{1}{r_1}-\frac{1}{r_2} \right)$$
 
Physics news on Phys.org
  • #2
A good first check is to make sure that the physical dimensions are consistent in every step. Your answer has dimensions energy/length and is therefore wrong. I suggest controlling the intermediate steps.
 
  • #3
I found the mistake, Thanks, it helped
 

1. What is gravitational energy?

Gravitational energy is the potential energy stored in an object due to its position in a gravitational field. It is the energy an object has by virtue of its mass and its distance from the center of the Earth or another massive object.

2. How is gravitational energy related to satellites?

Satellites in orbit around the Earth have a large amount of gravitational energy. This energy is necessary to keep the satellite in orbit and prevents it from falling back to Earth.

3. What is the equation for calculating gravitational energy?

The equation for calculating gravitational energy is E = -GMm/r, where E is the energy, G is the gravitational constant, M is the mass of the larger object, m is the mass of the smaller object, and r is the distance between the two objects.

4. How does the gravitational energy of a satellite change when it moves from r1 to r2?

As a satellite moves from r1 to r2, its distance from the center of the Earth changes. This affects the amount of gravitational energy it has. As the distance increases, the gravitational energy decreases.

5. Can the gravitational energy of a satellite be converted into other forms of energy?

Yes, the gravitational energy of a satellite can be converted into other forms of energy, such as kinetic energy or thermal energy, when the satellite is in motion or experiences friction with the Earth's atmosphere.

Similar threads

  • Introductory Physics Homework Help
Replies
23
Views
343
Replies
4
Views
809
  • Introductory Physics Homework Help
Replies
5
Views
584
  • Introductory Physics Homework Help
Replies
1
Views
824
  • Introductory Physics Homework Help
Replies
3
Views
865
  • Introductory Physics Homework Help
Replies
1
Views
703
  • Introductory Physics Homework Help
Replies
11
Views
688
  • Introductory Physics Homework Help
Replies
6
Views
923
  • Introductory Physics Homework Help
Replies
1
Views
805
  • Introductory Physics Homework Help
Replies
7
Views
814
Back
Top