TBR Physics CH2 passage 10 #68 (planetary orbit)

[Narmerguy]

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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).

 

[gentlebeast]

I would say assuming orbit is circular unless it is explicitly stated not

 

[Narmerguy]

I would say assuming orbit is circular unless it is explicitly stated not

Yeah I'm looking at more stuff in this book and it seems they are working under this assumption. If that's the same assumption the MCAT makes, I guess that's fine. It's a weird assumption to make. It's like having people assume a frictionless surface unless stated otherwise (which of course no one does)...should be the other way around.

 

[Tatiana3325]

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).

The question says that the planet is "100 times the radius of the Earth" away. This would mean circular.

Elliptic orbit is a fairly advanced physics concept that would not be presented in a problem like this.