Satellite Energy and Orbit problem

In summary, when a spy satellite in circular orbit suddenly fires its thrusters, giving it an additional velocity in the outward radial direction, the new total energy is equal to the old total energy. This results in an infinite radius and an open orbit. The general rule for vertical escape velocity from a given orbit is that it must be equal to or greater than the tangential velocity.
  • #1
Dextrine
102
7

Homework Statement


A spy satellite of mass m is in a circular orbit with radius R and velocity v around
the earth. One of the satellites thrusters suddenly fires giving it an additional
velocity v in the outward radial direction (same v). What is the new total energy
of the satellite? What is the new orbit of the satellite?

Homework Equations


mv^2/r
GMm/r^2
-K=.5U
2K+U=0

The Attempt at a Solution


I honestly don't really have an idea how to even set up the problem. From what I understand mv^2=GMm/r^2 for circular orbit which should I could then use to find the energy, but I don't know how the velocity increasing radially will affect this. Any helpful nudge in the right direction would be greatly appreciated.
 
Physics news on Phys.org
  • #2
Dextrine said:
mv^2=GMm/r^2
I think you mistyped the left hand side. As a result you have energy on the left and a force on the right.

What is the initial KE?
What is the initial PE?
How much energy was added?
 
  • #3
haruspex said:
I think you mistyped the left hand side. As a result you have energy on the left and a force on the right.

What is the initial KE?
What is the initial PE?
How much energy was added?
So initially I got my K=1/2GMm/r and my U=-GMm/r

Since we are adding another V, which is Sqrt[GM/r], i get that my new total energy = -.5GMm/r+.5GMm/r=0

however, this doesn't seem right
 
  • #4
Dextrine said:
So initially I got my K=1/2GMm/r and my U=-GMm/r

Since we are adding another V, which is Sqrt[GM/r], i get that my new total energy = -.5GMm/r+.5GMm/r=0

however, this doesn't seem right
It's right :). Remember, the total energy beforehand was negative.
So what do you get for the new orbit?
 
  • Like
Likes Dextrine
  • #5
haruspex said:
It's right :). Remember, the total energy beforehand was negative.
So what do you get for the new orbit?
AH, infinite radius? so we get an open orbit? Thanks a ton. Didn't think it would be so simple
 
  • #6
Dextrine said:
AH, infinite radius? so we get an open orbit? Thanks a ton. Didn't think it would be so simple
That's it. So what general rule do you deduce for vertical escape velocity from a given orbit?
 
  • #7
Hmm, it must be equal to or greater than tangential velocity?
 
  • #8
Dextrine said:
Hmm, it must be equal to or greater than tangential velocity?
Equal. ("Escape velocity" means the minimum necessary to escape the gravitational field.)
 
  • Like
Likes Dextrine

Related to Satellite Energy and Orbit problem

1. What is satellite energy and how is it generated?

Satellite energy refers to the energy that is required to keep a satellite in orbit around a celestial body. It is primarily generated through a process called orbital mechanics, which involves a combination of the satellite's velocity and the gravitational pull of the celestial body it is orbiting.

2. How does a satellite's orbit affect its energy?

The orbit of a satellite directly affects its energy. Specifically, the higher the orbit, the more potential energy a satellite has. This is because the farther a satellite is from the gravitational pull of the celestial body it is orbiting, the less energy it needs to maintain its orbit.

3. What are the factors that impact a satellite's orbit and energy?

The main factors that impact a satellite's orbit and energy include the mass and velocity of the satellite, the mass of the celestial body it is orbiting, and the distance between the satellite and the celestial body. Other factors such as atmospheric drag and solar radiation can also play a role.

4. How is satellite energy and orbit problem solved?

The satellite energy and orbit problem is typically solved using mathematical equations and calculations, specifically Newton's laws of motion and the laws of universal gravitation. These equations can determine the necessary velocity and distance for a satellite to maintain a stable orbit and the amount of energy required to do so.

5. What are some common applications of satellite energy and orbit problem?

Satellite energy and orbit problem is essential for many practical applications, including satellite communication, navigation, weather forecasting, and remote sensing. It is also crucial in space exploration and astronomy, as it allows us to understand and study celestial bodies and their movements.

Similar threads

A satellite in orbit in a system with one planet and two moons
    • Introductory Physics Homework Help
Replies
1
Views
955
Potential Energy and raising a satellite from Earth into a Circular Orbit
    • Introductory Physics Homework Help
Replies
5
Views
1K
Find at what rate the orbit radius will grow
    • Introductory Physics Homework Help
Replies
30
Views
765
Doubling speed in circular orbit to attain elliptical orbit
    • Introductory Physics Homework Help
Replies
3
Views
1K
From circular orbit to elliptical orbit
    • Introductory Physics Homework Help
Replies
3
Views
1K
Energy of particle when under a central force
    • Introductory Physics Homework Help
Replies
11
Views
2K
Circular orbit change after gaining mass ejected from sun
    • Introductory Physics Homework Help
Replies
1
Views
942
Find the speed of a satellite at a distance R from Earth
    • Introductory Physics Homework Help
2
Replies
39
Views
3K
Finding r of a Jovian-synchronous orbit and escape velocity
    • Introductory Physics Homework Help
Replies
7
Views
1K
A 1 500kg satellite is in orbit 250km above earth's surface.
    • Introductory Physics Homework Help
Replies
14
Views
3K

Hot Threads

Recent Insights

Back
Top