Orbit Problem

1. The problem statement, all variables and given/known data

If the mass of the sun were 1/2 it’s current mass suddenly show the orbit of the earth would be a parabola…

3. The attempt at a solution

I’m not sure what kind of approach to apply here, if the total energy equals zero then the orbit is a parabolic trajectory, if it is less than zero the the orbit is circular or elliptical, if I plug in numbers for the mass of the earth, sun, the radius and the average speed I can find escape velocity,

[tex]E=\frac{1}{2}mv^2 -\frac{GMm}{r}[/tex]

and solve for the velocity [tex]v=\sqrt\frac{GM}{r}[/tex]

and show that the earth’s average speed exceeds this value, but since these numbers are going to be approximations it’s difficult to tell whether it should be parabola or bound orbit…E will not be exactly zero…


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