Closest distance between two conics (ellipse,hyp.,par.)

  • Context: Graduate 
  • Thread starter Thread starter petra
  • Start date Start date
  • Tags Tags
    Conics
Click For Summary
SUMMARY

The discussion focuses on calculating the closest distance between two conics, specifically ellipses, in three-dimensional space. The orbits are defined by the equations r = (p1)/(1 + epsilon1*cos(theta1)) and r = (p2)/(1 + epsilon2*cos(theta2)), with the same focal point, the sun. The conversation also touches on the use of Euler angles (a1, b1, c1) to describe the orientation of the ellipses and seeks both symbolic and approximation techniques for solving the problem. Additionally, the user expresses interest in extending the solution to hyperbolas and parabolas.

PREREQUISITES
  • Understanding of conic sections, specifically ellipses, hyperbolas, and parabolas.
  • Familiarity with polar coordinates and their application in orbital mechanics.
  • Knowledge of Euler angles and their role in three-dimensional geometry.
  • Basic skills in approximation techniques for mathematical solutions.
NEXT STEPS
  • Research symbolic methods for calculating distances between conic sections.
  • Explore approximation techniques for non-closed orbits, including hyperbolas and parabolas.
  • Study the application of Euler angles in three-dimensional transformations.
  • Investigate computational tools for simulating conic distances in orbital mechanics.
USEFUL FOR

Mathematicians, physicists, and aerospace engineers interested in orbital mechanics, particularly those working with conic sections and distance calculations in three-dimensional space.

petra
Messages
8
Reaction score
0
I have question for you,How calculate closest distance between two
ellipse in space.
orbit first : r = (p1)/(1+epsilon1*cos(theta1))

second orbit : r = (p2)/(1+epsilon2*cos(theta2))

the relation between two ellipse is some euler angles call them
first angle :a1
second angle :b1 (these three euler angles)
third angle :c1

(taking in account they have same focus :the sun)

? symbolic solution for this problem
? how solve this with approximation techniques.


what when orbit is not closed:hyperbole,parabole
 
Astronomy news on Phys.org
I have the same type of problem and I am looking for a formula for the distance between two quadratic figures in \Re^n but I haven't seen it anywhere.
 

Similar threads

High School Measuring distance between two stars in a binary system
  • · Replies 10 ·
Replies
10
Views
5K
Graduate What is Laplace-Runge-Lenz vector
  • · Replies 1 ·
Replies
1
Views
7K
Time that a comet spends inside Earth's orbit
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Meteor radiant angle. Is this computation right?
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Anti-dual numbers and what are their properties?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How Do You Describe the Motion of Two Bodies Relative to Their Center of Mass?
  • · Replies 9 ·
Replies
9
Views
5K
Graduate Distance between two uncertain points using haversine?
  • · Replies 12 ·
Replies
12
Views
3K
Two body problem, velocities of two bodies, relative velocity given
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • · Replies 2 ·
Replies
2
Views
2K
MHB Finding the Distance Between Buoys: A Cruise Ship Balcony Problem
  • · Replies 3 ·
Replies
3
Views
3K