One question about Parabolic and Hyperbolic trajectory.

  • Context: Undergrad 
  • Thread starter Thread starter IPhO' 2008
  • Start date Start date
  • Tags Tags
    Hyperbolic Trajectory
Click For Summary

Discussion Overview

The discussion revolves around the characteristics of parabolic and hyperbolic trajectories, specifically whether the sun is located at the focus point of these trajectories. The scope includes conceptual clarification regarding celestial mechanics and gravitational interactions.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant questions if the sun is at the focus point of parabolic and hyperbolic trajectories.
  • Another participant affirms that the sun is indeed at the focus point.
  • A further contribution clarifies that the focus is actually at the center of mass (CM) of the two objects involved, noting that if the other body has a mass comparable to the sun, the CM could be outside the sun's surface.
  • This participant provides a specific example regarding the Sun-Jupiter system, indicating that the CM is approximately 83,500 km outside the sun's surface.

Areas of Agreement / Disagreement

There is some agreement that the sun is a focus point, but the discussion reveals nuances regarding the center of mass in systems with significant mass differences, indicating that multiple views remain on the specifics of the focus point in relation to the center of mass.

Contextual Notes

Participants have not fully resolved the implications of mass differences on the location of the focus point, and there may be assumptions regarding the mass of the objects involved that are not explicitly stated.

IPhO' 2008
Messages
44
Reaction score
0
In the Parabolic and Hyperbolic trajectory.Is the sun in the focus point of parabola and hyperbola?
 
Astronomy news on Phys.org
Hi IPhO' 2008! :smile:
IPhO' 2008 said:
In the Parabolic and Hyperbolic trajectory.Is the sun in the focus point of parabola and hyperbola?

Yup! :biggrin:
 
To be more precise, the focus is at the center of mass (CM) of the two objects. If the body on a parabolic/hyperbolic trajectory had a mass comparable to that of the sun, the CM might be outside the surface of the sun.

It might interest you that the CM of the Sun-Jupiter system is outside the surface of the sun by about .12 solar radii = 83,500 km.
 
Thank you.
 

Similar threads

Undergrad Understanding Hyperbolic & Parabolic Trajectories
  • · Replies 2 ·
Replies
2
Views
5K
Undergrad Question about orbits and Kepler's problem
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Propagating a Hyperbolic Trajectory
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad What is the Mathematical Definition of Orbital Eccentricity?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Orbital mechanics: is ballistic capture possible without acceleration?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Collision course trajectory / velocity
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Does Parabolic Motion Follow Kepler's Second Law?
  • · Replies 6 ·
Replies
6
Views
3K
Failed rocket problem (momentum conservation, Kleppner 4-4)
  • · Replies 3 ·
Replies
3
Views
933
High School Capture in a 2-body system (not)
  • · Replies 2 ·
Replies
2
Views
2K
Understanding Hyperbolic Orbits: The Relationship Between Foci and Trajectory
  • · Replies 6 ·
Replies
6
Views
2K