Help deriving this elliptical orbit equation?

In summary, the conversation is about a student seeking help in deriving an equation for an elliptical orbit in a mechanics course. The equation is given as \frac{(x + ae)^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, where e is the eccentricity and for an ellipse e < 1. The conversation suggests using Newton's second law and the geometry of an ellipse to derive the equation. The book "Mechanics" by David Morin and "Kleppner & Kolenkow" are recommended as good resources for this topic. The student also expresses difficulty in understanding classical mechanics.
  • #1
skiz
3
0
help deriving this elliptical orbit equation??

Hi guys, this is my first post on these boards. just found out about this forum and I am really happy because i often find i need a place like this to ask questions and my prayers are answered!

im a physics/computer science major in my second year at the University of the Witwatersrand in Johannesburg, South Africa.

any way.. enough history..

i need help deriving this equation for an elliptical orbit :

[tex]\frac{(x + ae)^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]

where e is the eccentricity and for an ellipse e < 1

i can't find anything useful in my books and don't even know where to start.

any help would be awesome! thanks!

-skiz
 
Last edited:
Physics news on Phys.org
  • #2
David Morin's book on mechanics explains very clearly on how to derive this equation
 
  • #3
hmm i don't have david morin's book on mechanics..

any tips on how to go about deriving this? am i supposed to use the geometry of an ellipse?

bah
 
  • #4
I assume that you are doing a course in Introductory Mechanics. The book by Kleppner & Kolenkow is really good for such a course. However in that book, the authors have begun from Law of conservation of energy and angular momentum and have derived the polar form of the equation. I believe that this is a good way to do this as it begins from conservation principles.
 
  • #5
Welcome to PF!

Hi skiz! Welcome to PF! :smile:

Is this a mechanics question (find the orbit of a particle in an electric or gravitational field), or a geometry question (find the equation for an ellipse)?

Assuming it's mechanics, start with Newton's second law, and remember that the force perpendicular to the "radius" vector is zero. :smile:
 
  • #6
hey tim, thanks for the welcome!

yeah its a mechanics course. Our first 6 months are split between "Classical Mechanics" and "Modern Physics/Relativity"

i find modern physics and relativity really interesting and easy to grasp but classical mechanics is kicking my ass...
 
  • #7
Hi skiz! :smile:

Just remember that nearly all classical mechanics boils down to good ol' Newton's second law …

force in a particular direction = (rate of) change of momentum in that direction :smile:​

… and in each case you just have to work out which direction gives you the best information (in this case, it's the "transverse" direction).
 
  • #8
please anyone help me?

please anyone help me to find the equation of eccentricity of object moves in elliptical orbit
 

What is an elliptical orbit equation?

An elliptical orbit equation is a mathematical formula that describes the path of an object in space that is orbiting around another object in an elliptical shape. It takes into account the gravitational force between the two objects and the initial position and velocity of the orbiting object.

How do you derive an elliptical orbit equation?

To derive an elliptical orbit equation, you can use Kepler's laws of planetary motion and Newton's law of universal gravitation. These laws provide the necessary equations to determine the shape, size, and position of an elliptical orbit.

What are the inputs needed to derive an elliptical orbit equation?

The inputs needed to derive an elliptical orbit equation include the mass and radius of the two objects, the initial position and velocity of the orbiting object, and the gravitational constant. These values can be obtained through observations or experiments.

What are the applications of an elliptical orbit equation?

An elliptical orbit equation has many applications in astronomy and space exploration. It can be used to accurately predict the path of planets, satellites, and other objects in space. It is also essential for calculating orbital trajectories for spacecraft and studying the dynamics of celestial bodies.

Can an elliptical orbit equation be used for any type of orbit?

No, an elliptical orbit equation can only be used for orbits that have an elliptical shape. Other types of orbits, such as circular or parabolic orbits, have their own specific equations that describe their paths.

Similar threads

I Kepler's second law derivation from angular momentum conservation
    • Classical Physics
Replies
6
Views
1K
I Elliptical Orbit and Kepler's equation
    • Classical Physics
Replies
1
Views
813
B The Sun's Influence on the Moon's Orbit: Is it Negligible?
    • Classical Physics
Replies
4
Views
713
I Orbital maneuver by applying a thrust in the radial direction
    • Classical Physics
2
Replies
62
Views
5K
From circular orbit to elliptical orbit
    • Introductory Physics Homework Help
Replies
3
Views
1K
I Can time on elliptical orbit be expressed analytically?
    • Astronomy and Astrophysics
Replies
5
Views
1K
I Stability of circular orbits in an arbitrary central force field
    • Classical Physics
Replies
3
Views
1K
I Deriving the relativistic rocket equation with exhaust efficiency
    • Classical Physics
Replies
1
Views
139
Time period of an object traveling in an elliptical orbit
    • Introductory Physics Homework Help
Replies
10
Views
2K
I Inverting an Equation Containing Elliptic Integrals
    • Differential Equations
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top