With a circular orbit, when do I use 1/2mv^2

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Homework Help Overview

The discussion revolves around the application of kinetic energy equations in the context of circular and elliptical orbits, specifically when to use the equation \( \frac{1}{2}mv^2 \) versus \( E_k = \frac{GMm}{2r} \). Participants are exploring the differences in outcomes when applying these equations to a satellite's kinetic energy at different points in its orbit.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the conditions under which different kinetic energy equations are applicable, particularly in relation to circular versus elliptical orbits. There are questions about the validity of the equations and the implications of using them in specific scenarios, such as at perigee.

Discussion Status

Some participants have offered insights into the nature of total mechanical energy in orbits, suggesting a distinction between kinetic energy and total energy. There is ongoing exploration of the assumptions regarding the radius used in the equations and whether total energy conservation applies to both types of orbits.

Contextual Notes

Participants are navigating the complexities of gravitational forces and energy conservation in orbital mechanics, with specific attention to the definitions and conditions of circular and elliptical orbits. There is a noted confusion regarding the application of kinetic energy equations based on the type of orbit.

jakeginobi

Homework Statement


At a circular orbit and at an elliptical orbit when do I use 1/2mv^2 instead of the kinetic equation from which I derived from F=GMm/r^2 which is Ek = GMm/2r

Homework Equations


F=GMm/r^2, Ek = GMm/2r,
Ek = 1/2mv^2

The Attempt at a Solution


For instance, when I tried to use the other kinetic energy equation (GMm/2r) to solve the kinetic energy of a satellite at perigee, it gave a totally different answer if I use 1/2mv^2
 
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jakeginobi said:

Homework Statement


At a circular orbit and at an elliptical orbit when do I use 1/2mv^2 instead of the kinetic equation from which I derived from F=GMm/r^2 which is Ek = GMm/2r

Homework Equations


F=GMm/r^2, Ek = GMm/2r,
Ek = 1/2mv^2

The Attempt at a Solution


For instance, when I tried to use the other kinetic energy equation (GMm/2r) to solve the kinetic energy of a satellite at perigee, it gave a totally different answer if I use 1/2mv^2

You need to quote the precise question and show your working.
 
Perhaps you're confusing the total mechanical energy which includes both kinetic and potential energy and is a constant over the whole orbit, with the kinetic energy alone at a particular location?
 
Your kinetic equation is valid only for circular orbits. It is derived by balancing the forces.

GMm/r2 = m v2 / r

The problem is that the r on the left is the distance from the sun (or whatever) and the r on the right is the radius of curvature of the motion. These are only the same if the orbit is circular.
 
In
Cutter Ketch said:
Your kinetic equation is valid only for circular orbits. It is derived by balancing the forces.

GMm/r2 = m v2 / r

The problem is that the r on the left is the distance from the sun (or whatever) and the r on the right is the radius of curvature of the motion. These are only the same if the orbit is circular.
Is total energy conserved in a circular orbit or just an elliptical orbit?
 
jakeginobi said:
In

Is total energy conserved in a circular orbit or just an elliptical orbit?

A circle is an ellipse with eccentricity 0.
 
jakeginobi said:
In

Is total energy conserved in a circular orbit or just an elliptical orbit?

In this system you have only gravitational potential energy and kinetic energy, so between those two quantities energy must be conserved for any orbit.
 

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