Energy principle and circular/ellipse orbits

In summary, the question is how much energy is needed to move an object with mass M from a circular orbit with radius R_1 to an ellipse orbit with aphelion radius R_2. The energy principle is the way to approach this, but there is a question about assuming the perihelion radius of the new orbit is the same as the circular orbit's radius. The Total Specific Mechanical Energy of an orbit is inversely proportional to the size of its major axis, and can be calculated using the formula \xi = -\frac{\mu}{2a}. The energy change needed is equal to the difference between the total energies of the ellipse orbit and the circular orbit. Since only the aphelion radius is given, the
  • #1
Uniquebum
55
1
Question is as follows:
How much energy do i need when i move an object with a mass M from a circular orbit with a radius of R_1 to an ellipse orbit with aphelion radius of R_2.

I'm assuming energy principle is the way to go here but it leads to a question i'd like someone to help me out with.

Do i need to assume the perihelion radius of the new orbit (aphelion radius R_2) is the circular orbit's radius R_1?

Thanks in advance.
 
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  • #2
Uniquebum said:
Question is as follows:
How much energy do i need when i move an object with a mass M from a circular orbit with a radius of R_1 to an ellipse orbit with aphelion radius of R_2.

I'm assuming energy principle is the way to go here but it leads to a question i'd like someone to help me out with.

Do i need to assume the perihelion radius of the new orbit (aphelion radius R_2) is the circular orbit's radius R_1?

Thanks in advance.

You can assume anything you like; The answer you get will depend upon your assumptions :smile:

The Total Specific Mechanical Energy, [itex] \xi [/itex], of an orbit is inversely proportional to the size of its major axis. Thus [itex] \xi = -\frac{\mu}{2 a} [/itex] . The length of the major axis, in turn, is the sum of the perihelion and aphelion distances. Specific Mechanical Energy is the energy per unit mass; Multiply by mass of the orbiting object to get the energy.

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  • #3
Yea, i presumed as much. To get the energy change needed i'd have to go

[itex]\Delta E = -\frac{GMm}{2a} - \frac{1}{2}mv_1^2 + \frac{GMm}{R_1}[/itex]

So basically ellipse orbit total energy minus circular orbit total energy. Since i wasn't given the semi-major axis but only the aphelion radius of the ellipse orbit, i would think i'd need to assume the perihelion radius is the R_1. Either way, i think I'm going with this.
Whatever the case, thanks for the reply!
 

1. What is the energy principle in relation to orbits?

The energy principle states that the total energy of an object in an orbit remains constant, meaning it neither gains nor loses energy as it moves along its path. This is known as conservation of energy.

2. How does the energy principle affect circular orbits?

In circular orbits, the energy principle states that the kinetic energy of the object is equal to the potential energy. This means that the object's speed remains constant throughout the orbit.

3. What about elliptical orbits?

In elliptical orbits, the energy principle still applies, but the energy is not constant. As the object moves closer to the center of its orbit, its speed increases and its potential energy decreases. As it moves farther away, its speed decreases and its potential energy increases.

4. How does the energy principle relate to gravitational force?

The energy principle is closely related to the gravitational force between two objects. As an object moves in an orbit, it experiences a gravitational force from the object it is orbiting, which affects its energy. The energy principle helps us understand how this force affects the object's motion.

5. Can the energy principle be applied to other types of orbits?

Yes, the energy principle can be applied to any type of orbit, as long as the orbit is closed and the object is moving under the influence of a central force, such as gravity. This includes orbits around planets, moons, and even artificial satellites.

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