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PChar
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Homework Statement
A small particle of mass m is on a circular orbit of radius R around
a much larger mass M. Suppose we suddenly increase the speed at which the mass m is moving
by a factor (that is, v[itex]_{final}[/itex] = α * v[itex]_{initial}[/itex], with α > 1). Compute the major axis, minor axis,
pericentre distance, and apocentre distance for the new orbit; express your answers in terms
of R and α alone
Homework Equations
Vis-Viva Equation:
(αv)[itex]_{initial}[/itex][itex]^{2}[/itex] = GM [ [itex]\frac{2}{R}[/itex] - [itex]\frac{1}{a}[/itex] ]
Speed of circular orbit:
v[itex]_{initial}[/itex] = [itex]\sqrt{\frac{GM}{R}}[/itex]
Pericentre distance:
a(1 - e)
Apocentre distance:
a(1 + e)
Semi-minor axis:
[itex]b^{2}=a^{2}(1-e^{2})[/itex]
The Attempt at a Solution
By inserting the initial orbital speed into the vis-viva equation I was able to find the semi-major axis as required:
a = [itex]\frac{R}{2-α^{2}}[/itex]
The problem I'm having now is that I can't find the semi-minor axis without the eccentricity of the new elliptical orbit, or the distance between the two foci, and I can't find a way to eliminate them.