How Is the Moon's Mass Calculated Using Satellite Orbit Data?

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Homework Help Overview

The discussion revolves around calculating the mass of the moon using data from a satellite's orbit. The satellite orbits at a height of 250.0 km above the moon's surface, with a total orbital radius of 1987.4 km, and takes 2.000 hours and 14.00 minutes for one complete revolution.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using formulas related to centripetal force and gravitational force to derive the moon's mass. There is mention of adapting an equation typically used for the sun to apply to the moon's context. Questions arise regarding specific terms and constants, such as "μ" and the gravitational constant.

Discussion Status

The discussion is active, with participants exploring different approaches to the problem. Some guidance has been offered regarding relevant equations and concepts, though there is no explicit consensus on the method to be used.

Contextual Notes

Participants are navigating the problem with some uncertainty about fundamental concepts, such as the gravitational constant and specific variables in the equations. There is an implication of assumed knowledge regarding gravitational equations that may not be universally understood among all participants.

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Homework Statement


A satellite is in circular orbit around the moon 250.0km above the moon's surface, and takes 2.000 hours and 14.00 minutes for one revolution of the moon. Calculate the moons mass.

The radius of the moon is 1737.4km, so if you add the extra 250.0km the satellite is above, the total radius is 1987.4km

please help
 
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what sort of attempt have you made? You should have some formulas about centripetal force and the force due to gravity that you could use.
 
Would you be able to use the equation in this picture? instead of solving for the time, which we could figure out easy enough, we solve for the mass, but instead of the sun, we change all the values to the ones for the moon, if you get my meaning
 

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yes, that would work
 
What does "μ" mean?
 
it says there in the image

it's the gravitational constant G multiplied by the mass of what's being orbited. In the image, the sun is being orbited; in your problem, the moon is being orbited.
 
Whats the gravitational constant?
 

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