Deriving Vr and V(sub-theta) from Kepler's second law and

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Homework Help Overview

The discussion revolves around deriving expressions for the radial and angular components of velocity (Vr and Vθ) for a mass in an elliptical orbit, using Kepler's second law and the given orbital parameters. The context includes the relationship between orbital period, eccentricity, and semi-major axis.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the connection between position and velocity, with one participant seeking guidance on how to initiate the derivation process.

Discussion Status

The discussion is in an early stage, with participants sharing their thoughts and questions. One participant has expressed uncertainty about how to start, while another has prompted them to consider the relationship between position and velocity.

Contextual Notes

The original poster has specified that the final expressions should only involve the orbital period, eccentricity, semi-major axis, and the angle theta. There may be constraints related to the assumptions of elliptical orbits and the application of Kepler's laws.

LordCalculus
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Deriving Vr and V(sub-theta) from Kepler's second law and...

Homework Statement



Beginning with r=[a(1-e2)]/(1+e*cos \theta) and Kepler's second law, derive general expressions for vr and v\theta for a mass m1 in an elliptical orbit about a second mass m2. The final answers should be functions of P, e, a, and \theta only.

P=orbital period
e=eccentricity
a=semimajor axis

That's supposed to be v(subtheta) and cosine of theta!

Homework Equations



A'(t)=L/(2*\mu)
 
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v_\theta, understood. What have you done so far and where exactly did you get stuck?
 


Not far at all. I don't even know where to begin. If you do, then please start me off. Thanks!
 


Well, here would be my first thought: you have some information about position, and you are asked to find velocity. What does that tell you?
 

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