From circular orbit to elliptical orbit

In summary, the particle will brush against the back of the planet if the impulse given to the rocket causes it to have an elliptical orbit.
  • #1
physicsnmathstudent0
3
5
Thread moved from the technical forums to the schoolwork forums
Problem: a particle of mass m is in a circular orbit around a planet at a distance R from the center. The planet mass is M and it's radius is R_0.
What is the tangential impulse that will cause the particle to brush against the back of the planet? Describe the orbit.

The attempt at solution:

So I was reading Resnik's and Halliday's fundamental of physics to get a better understanding of this problem, and I found a similar problem in the sense that this ship was given a tangential impulse such that it's orbit changed from circular to elliptical, but in that problem the desired unknown was the new period in the new orbit. Anyway, I thought that that sample problem was useful to get a general idea of my problem.

So in the book it was illustrated that although the ship changes orbit, it always returns to the same point at which the impulse was given, so if I were to give my rocket an impulse such that it brushes (I don't now if this is the right word but English is not my language sorry) this planet's back, then that would mean that my rocket would change it's circular orbit for an elliptical orbit such that the perihelion would be when the rocket is at a distance R_0 from the center of the planet and the aphelion would be at a distance R (as I mentioned before I took this idea from sample problem 13.06 of Resnik's and Halliday's fundamental of physics fig. 13-17), so since it is an elliptical orbit it obeys R + R_0 = 2a, (1) where a is the semimajor axis, and we also know that the mechanical energy is E=-GmM/2a (2), but it also is the sum of kinetic energy and potential energy E = K + U, (3) where K= 1/2(mv^2), (3a) and U= -GmM/R, (3b), and since v would be the velocity just after it is impulse, then v = v_0 + delta v (4), then I substitute (4) in (3a), and I do all the algebra to find delta v. At least that's what I think, but I do have some questions regarding U and the fact that the rocket returns to the same point where it was when we gave it the impulse.

First, again, in the book it says that it takes the U just after it was given the impulse, but why is it valid to do that? And why does the rocket return to that point?

Thank you, I hope it's not too long
 
Physics news on Phys.org
  • #2
physicsnmathstudent0 said:
And why does the rocket return to that point?
Think of it as a mass or a satellite, not a rocket.
Before the impulse it was in repeating circular orbit.
After the impulse it is in a repeating elliptical orbit.
Both those orbits share a common point in space.
 
  • Like
Likes physicsnmathstudent0
  • #3
Baluncore said:
Think of it as a mass or a satellite, not a rocket.
Before the impulse it was in repeating circular orbit.
After the impulse it is in a repeating elliptical orbit.
Both those orbits share a common point in space.
Thank you! Could you help me reviewing my logic in this problem, I'm not sure how to make clear that the delta v decreases the velocity, I think the sign is wrong
 
  • #4
physicsnmathstudent0 said:
Thank you! Could you help me reviewing my logic in this problem, I'm not sure how to make clear that the delta v decreases the velocity, I think the sign is wrong
This should come out of your equations. If you have defined it as positive when increasing velocity you should get a negative result.

physicsnmathstudent0 said:
an elliptical orbit such that the perihelion
Pet peeve: Perihelion means the point closest to the sun … If you want to talk about the orbit around a general celestial object the word is periapsis.
 
  • Like
Likes physicsnmathstudent0

Related to From circular orbit to elliptical orbit

1. What is a circular orbit?

A circular orbit is the path that an object takes around another object, where the distance between the two objects remains constant. This results in a circular shape.

2. What is an elliptical orbit?

An elliptical orbit is the path that an object takes around another object, where the distance between the two objects varies. This results in an oval or elliptical shape.

3. How does an object transition from a circular orbit to an elliptical orbit?

An object can transition from a circular orbit to an elliptical orbit through the influence of external forces, such as gravity. If the object is pulled or pushed by another object, its orbit can become more elliptical.

4. What factors can affect the transition from a circular orbit to an elliptical orbit?

The strength and direction of external forces, such as gravity, can affect the transition from a circular orbit to an elliptical orbit. Additionally, the mass and velocity of the object can also play a role in the transition.

5. Can a circular orbit become an elliptical orbit without any external influences?

No, a circular orbit cannot become an elliptical orbit without any external influences. In order for the orbit to change shape, there needs to be a force acting on the object, such as gravity from another object or a change in the object's velocity.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
761
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
932
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
900
  • Introductory Physics Homework Help
Replies
1
Views
864
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Classical Physics
2
Replies
58
Views
2K
Back
Top