What is the significance of the foci in gravitational orbits?

  • Context: Undergrad 
  • Thread starter Thread starter MattWakes
  • Start date Start date
  • Tags Tags
    Kepler Orbits
Click For Summary
SUMMARY

The discussion focuses on the significance of foci in gravitational orbits, particularly in relation to the eccentricity of the orbit. It establishes that for elliptical orbits (0 < Ecc < 1), the foci are critical points where the sum of distances from any point on the orbit to each focus remains constant. In contrast, for parabolic (Ecc = 1) and hyperbolic (Ecc > 1) trajectories, only one focus is relevant. The conversation highlights the mathematical properties of these orbits while seeking a deeper understanding of their physical implications.

PREREQUISITES
  • Understanding of orbital mechanics and gravitational forces
  • Familiarity with the concept of eccentricity in conic sections
  • Basic knowledge of ellipses, parabolas, and hyperbolas
  • Mathematical proficiency in geometry and distance formulas
NEXT STEPS
  • Research the physical implications of foci in elliptical orbits
  • Explore the mathematical derivation of eccentricity in conic sections
  • Study the differences in gravitational forces acting on bodies in parabolic and hyperbolic orbits
  • Learn about the applications of orbital mechanics in astrophysics and satellite technology
USEFUL FOR

Students of physics, astronomers, and anyone interested in the mathematical and physical principles of gravitational orbits.

MattWakes
Messages
15
Reaction score
0
hey everyone, this is a qualitative question on gravitational orbits:

I was going through questions in which the trajectory of the orbiting body is determined based upon the eccentricity of the orbit, e.g. 0<Ecc<1, ellipses, Ecc=1, parabola, Ecc>1, hyperbola. I did the math and found out what the foci where for each case. But I would very much like to know, what is the physical meaning of these foci? Yes, they are points such that the sum of distances from a point on the circumference of trajectory to each focus is a constant. But what do they really mean, in terms of forces or whatever?

Okay, thanks!
 
Astronomy news on Phys.org
MattWakes said:
Yes, they are points such that the sum of distances from a point on the circumference of trajectory to each focus is a constant.
As a side point, this is true only for the ellipse, not the parabola or the hyperbola.
 
Only one focus counts.
Here is the basic data sheet, you might get something from it.
 

Attachments

Similar threads

Undergrad Question about Kepler's 1st law and barycentric orbits
  • · Replies 1 ·
Replies
1
Views
2K
High School The Sun's Influence on the Moon's Orbit: Is it Negligible?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Elliptical Orbit and Kepler's equation
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Kepler orbits for planets of similar masses
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Can time on elliptical orbit be expressed analytically?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Expressing Elliptic Orbitals As Speed Functions.
  • · Replies 2 ·
Replies
2
Views
1K
High School Observing Orbital Mechanics from the 2nd Focus of Earth's Orbit
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Physical Significance of Eccentricity & Semi-Latus Rectum of Orbital Ellipse
  • · Replies 3 ·
Replies
3
Views
3K
Graduate N-Body inputs from Keplerian Orbits
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Orbital Velocities and Mass Distribution in Galaxies
  • · Replies 7 ·
Replies
7
Views
2K