Orbital Mechanics: Find Eqns of Motion w/ Initial Conditions

Click For Summary

Discussion Overview

The discussion revolves around the challenge of deriving equations of motion for a satellite in orbit, given initial conditions such as tangential velocity, distance from a central mass, and the satellite's mass. The focus is on the theoretical aspects of orbital mechanics, particularly the two-body problem.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that there is no completely general method to calculate the position of an orbiting body and seeks a derivation of the equations of motion based on specific initial conditions.
  • Another participant identifies the problem as the two-body problem, providing a reference for further reading.
  • A different participant questions whether the inquiry pertains to a particular object, indicating a need for clarification.
  • One participant proposes that if the mass of the satellite is ignored, the rotation rate can be calculated simply as the tangential velocity divided by the radius.
  • This same participant mentions that if the mass of the orbited body is known, it may be possible to derive the necessary equations using provided materials, suggesting that further exploration could yield useful results.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the methods for deriving the equations of motion, and multiple viewpoints regarding the approach and assumptions remain present.

Contextual Notes

There are limitations regarding the assumptions made about the mass of the satellite and the central mass, as well as the dependence on specific conditions for deriving the equations of motion.

Timothy S
Messages
49
Reaction score
0
Hello,

After searching on the internet, I have come to the conclusion that there is no completely general way to calculate the position of an orbiting body. My question is whether there is a way to find the equations of motion with respect to time of a satellite orbit given only the initial tangential velocity, distance from the central mass, and mass of the satellite. If there is, I would appreciate a derivation of the equation.

Thank you.
 
Physics news on Phys.org
you are looking for paticular object?
 
If you ignore the mass of the satellite, its easy, its rotation rate = v / r (radians per second)

If you had the mass of the orbited body:
Using the attached word document, given both masses, and the centre to centre distance, you can derive what you need, if not you may get some mileage from it anyway.
 

Attachments

Similar threads

Undergrad Is there a way in Lagrangian mechanics to incorporate the inertial response from initial momentum when using initial conditions instead of BCs?
  • · Replies 9 ·
Replies
9
Views
1K
Graduate Can Sci-Fi Spacecraft Achieve Stable Orbit with Plasma Technology?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate The method of finding periodic three-body orbits
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad "Unexpected" Symmetry in Elliptical Orbit
  • · Replies 11 ·
Replies
11
Views
3K
Graduate On orbital mechanics and the standard model
  • · Replies 1 ·
Replies
1
Views
3K
Initial conditions for orbits around a wormhole
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Motion of a spring that has mass
  • · Replies 3 ·
Replies
3
Views
1K
Graduate What is meant by "the body is on the point of ...." in mechanics?
  • · Replies 3 ·
Replies
3
Views
1K
High School Constant jerk motion: acceleration vs. position
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Local mechanism for nonlocal anticorrelations inside spin theory
  • · Replies 74 ·
3
Replies
74
Views
5K