Understanding Keplerian Orbits: Equations and Time Dependence

  • Context: Undergrad 
  • Thread starter Thread starter holtto
  • Start date Start date
  • Tags Tags
    Cartesian Orbit
Click For Summary
SUMMARY

The discussion centers on the equations governing the displacement-time graph of Keplerian orbits. Participants confirm that the horizontal displacement is sinusoidal while the vertical displacement is cosinusoidal, or vice versa. The relationship between orbital angle and orbital radius is crucial for deriving the x/y components. However, the time dependence is implicit and requires complex differential equations for a complete understanding.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Familiarity with sinusoidal functions and their properties
  • Knowledge of differential equations
  • Basic concepts of orbital mechanics
NEXT STEPS
  • Study the derivation of Kepler's laws of planetary motion
  • Learn about the mathematical properties of sinusoidal and cosinusoidal functions
  • Explore advanced techniques in solving differential equations
  • Investigate the relationship between orbital angle and radius in detail
USEFUL FOR

Astronomy students, physicists, and mathematicians interested in orbital mechanics and the mathematical modeling of celestial bodies.

holtto
Messages
21
Reaction score
0
Just curious, does anyone know what are the equations for the displacement-time graph of a Keplerian orbit?

The horizontal displacement-time graph should be somewhat sinusoidal, the vertical one cosinusoidal, or vice versa.
 
Physics news on Phys.org
There is a formula relating the orbital angle and the orbital radius, and so one can easily get the x/y components versus the angle. Dependence on time, however, is implicit.
 
voko said:
There is a formula relating the orbital angle and the orbital radius, and so one can easily get the x/y components versus the angle. Dependence on time, however, is implicit.

and it involves really complicated D.E.s
 

Similar threads

Graduate Expressing Elliptic Orbitals As Speed Functions.
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Find period of circular-orbiting source based on max observed freq
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is Hooke's law really not working, or is it me being dummy?
  • · Replies 13 ·
Replies
13
Views
2K
High School Help with the protocol for accurately recording an orbit for the IAU
  • · Replies 0 ·
Replies
0
Views
1K
High School Are planetary orbits elliptical because of a space–time conic section?
  • · Replies 3 ·
Replies
3
Views
1K
High School Sign conventions in torque and non-uniform circular motion
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Simple Harmonic Motion: why sin(wt) instead of sin(t)?
  • · Replies 3 ·
Replies
3
Views
8K
Undergrad Delta V Calculator: Launch in an Atmosphere & Orbit Dimensions
  • · Replies 16 ·
Replies
16
Views
6K
Undergrad Origin of Centripetal force when the net force toward the center is 0?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Statics: When the reactions depend on the displacements
  • · Replies 35 ·
2
Replies
35
Views
5K