How Does Orbital Radius Change with a Time-Varying Solar Mass?

  • Thread starter Thread starter fizzwhiz
  • Start date Start date
  • Tags Tags
    Mass Orbit
Click For Summary
SUMMARY

The discussion focuses on the relationship between orbital radius and solar mass, specifically how the orbital radius (D) is inversely proportional to the solar mass (M). Participants suggest solving the radial equation of motion under the influence of a time-varying solar mass, represented as M(t). The key equation discussed is the balance between gravitational force and centripetal force, expressed as mv²/D = GMm/D², with the challenge of incorporating the time-dependent solar mass into the analysis.

PREREQUISITES
  • Understanding of gravitational force and centripetal force dynamics
  • Familiarity with differential equations and their application in physics
  • Knowledge of angular momentum conservation principles
  • Basic numerical methods for solving equations of motion
NEXT STEPS
  • Research numerical methods for solving time-dependent differential equations
  • Study the implications of angular momentum conservation in variable mass systems
  • Explore gravitational dynamics with a focus on time-varying forces
  • Learn about the effects of mass loss on orbital mechanics in astrophysics
USEFUL FOR

Students and researchers in astrophysics, physics educators, and anyone interested in the dynamics of orbital mechanics and gravitational interactions involving variable mass systems.

fizzwhiz
Messages
1
Reaction score
0

Homework Statement


An approach to the problem of finding how orbital radius changes with solar mass is to solve the radial equation of motion for a gravitational force that has an explicit time dependence based on the assumed rate of mass loss. Show by numerically solving this equation of motion that one gets the result D proportional to 1/M.


Homework Equations



I'm not entirely sure what equation of motion the question requires. We can equate the gravitational force with the centripetal force,

mv2/D = GMm/D2

but I'm unsure as to how to include the time-dependent solar mass.

I think we can assume the changes in mass per orbit are small and uniform.


The Attempt at a Solution




I tried replacing the constant mass M in the above equation with M(t) and differentiating with respect to t, and using the angular momentum to express v in terms of D, but it's not really getting me anywhere.

Any advice on how to approach this problem would be greatly appreciated. :D
Thanks!
 
Physics news on Phys.org
welcome to pf!

hi fizzwhiz! welcome to pf! :wink:

i think they mean, what happens to the same planet as the solar mass changes?

so v won't be constant, but the angular momentum of the planet will :smile:
 

Similar threads

How to derive the period of non-circular orbits?
  • · Replies 5 ·
Replies
5
Views
3K
Calculations using the Standard Solar Model & Solar Equations of State
  • · Replies 1 ·
Replies
1
Views
2K
What is the relationship between tension and mass for an artificial satellite?
  • · Replies 10 ·
Replies
10
Views
2K
How Does a Variable Mass Affect a Simple Pendulum?
  • · Replies 9 ·
Replies
9
Views
3K
Red/blueshift due to orbiting planet
  • · Replies 1 ·
Replies
1
Views
2K
Find at what rate the orbit radius will grow
  • · Replies 30 ·
2
Replies
30
Views
2K
Equation of motion for oscillations about a stable orbit
  • · Replies 2 ·
Replies
2
Views
5K
Conservation of the Laplace-Runge-Lenz vector in a Central Field
  • · Replies 3 ·
Replies
3
Views
2K
Using Lagrangian to show a particle has a circular orbit
  • · Replies 4 ·
Replies
4
Views
3K
Velocity required to escape the solar system
  • · Replies 15 ·
Replies
15
Views
2K