What Is the Weight of a Satellite Orbiting Mars?

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Homework Help Overview

The discussion revolves around calculating the weight of a satellite orbiting Mars, given its kinetic energy and distance from the planet's center. The subject area includes concepts of gravity and orbital mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the definition of weight, questioning how it applies to an orbiting satellite. There are discussions about using gravitational force equations and the relationship between kinetic energy and centripetal force.

Discussion Status

Some participants are clarifying the definition of weight in the context of orbital mechanics, while others are suggesting relevant equations to relate kinetic energy and gravitational force. The discussion is active, with various interpretations being explored.

Contextual Notes

There is a mention of different definitions of weight, particularly in relation to orbiting bodies, and the need to consider gravitational force at a distance from Mars.

GrkFizzix
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Hi Guys I am in year 12 and have my exam shortly would just like to ask a question to do with gravity.

A small satellite orbits Mars. It has a kinetic energy of 3.0x10^10 J, and is at a constant distance of 8.0x10^7 m from the center of Mars. What is the weight of the satellite at this height?
 
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How is weight defined?

ehild
 
it gives no further explanation but I am guessing mg?
 
No, mg is at the surface of Earth. I asked what you have learned about weight, as there are two different definitions and one says that the orbiting bodies are weightless. Here, I think weight is meant as the gravitational force of Mars on the satellite.

To get the force of gravity at distance R from Mars, you can use the equations for the kinetic energy related to the centripetal force along a circular orbit. If m is the mass of the satellite and M is that of Mars, and G is the gravitational constant, the gravitational force is GmM/R^2. The kinetic energy is KE= .5 mv^2.
For a circular orbit, the centripetal force = the force of gravity, and this is the weight of the satellite.

The centripetal force is mv^2/R,

mv^2/R = GmM/R^2.

Go ahead.


ehild
 

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