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Question: A new planet is discovered 100(times the radius of earth) away from the Earth. With only this information, what else can we determine about this planet?
A) Both its mass and its orbital velocity
B) Mass only
C) Orbital velocity only
D) Nothing else can be determined.
BR lists the answer as C, citing that equating centripetal force and force of gravity we can obtain an equation that is essentially v = (GM/r)^(0.5)
But I seriously disagree with this. That equation is only valid for a circular orbit with constant velocity, and the problem explicitly states that the only information that we have is the radius away from the earth that it was found. To know a satellites speed in an elliptical path, we must know the semimajor axis length, as can be described here. http://en.wikipedia.org/wiki/Elliptic_orbit#Velocity
Am I supposed to be assuming, across the entire MCAT, that any orbit is a perfectly circular orbit? That is a rather large assumption to make given that most planetary orbits are not circular orbits and it would require one line for them to tell us to assume this is the case (I read the passage a billion times, no such assumption is in there).
A) Both its mass and its orbital velocity
B) Mass only
C) Orbital velocity only
D) Nothing else can be determined.
BR lists the answer as C, citing that equating centripetal force and force of gravity we can obtain an equation that is essentially v = (GM/r)^(0.5)
But I seriously disagree with this. That equation is only valid for a circular orbit with constant velocity, and the problem explicitly states that the only information that we have is the radius away from the earth that it was found. To know a satellites speed in an elliptical path, we must know the semimajor axis length, as can be described here. http://en.wikipedia.org/wiki/Elliptic_orbit#Velocity
Am I supposed to be assuming, across the entire MCAT, that any orbit is a perfectly circular orbit? That is a rather large assumption to make given that most planetary orbits are not circular orbits and it would require one line for them to tell us to assume this is the case (I read the passage a billion times, no such assumption is in there).