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

[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

 

[PeroK]

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.

 

[gneill]

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?

 

[Cutter Ketch]

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.

 

[jakeginobi]

In

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?

 

[PeroK]

In

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

A circle is an ellipse with eccentricity 0.

 

[Cutter Ketch]

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.