Verifying Circular Orbit of a Spacecraft

AI Thread Summary
To verify if a spacecraft is in a circular orbit around the Sun, one must analyze its speed and distance from the Sun. The relationship between orbital speed, radius, and period is crucial; for a circular orbit, the speed must satisfy specific gravitational equations. If the speed is not radial, the orbit may be degenerate, leading to either a collision with the Sun or escape. Understanding these dynamics is essential for determining the nature of the spacecraft's orbit. Proper analysis of these factors will clarify whether the orbit is circular or not.
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Homework Statement



If given a speed of a spacecraft , and a radius from the sun, how do you prove that it was or was not in a circular orbit about the sun?

Homework Equations





The Attempt at a Solution


To prove it is not do I just find the mass of the spacecraft and the size of its mass will determine this? I am so confused I don't even know where to start?!
 
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The problem statement is not well formed, since it presumes that the speed is not radial, in which case the 'orbit' will be degenerate -- the spacecraft will either plummet directly into the Sun or escape straight outwards.

So assuming that this is not the case...

What do you know about objects in circular orbits around the Sun? Think about how their periods are related to their orbital radii, and how their orbital speeds are related to their periods.
 

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