Find Length of Sun Mass in km: Solving G, c, M Units

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Homework Help Overview

The problem involves finding a combination of the gravitational constant G, the speed of light c, and an arbitrary mass M that results in units of length. The original poster seeks to evaluate this expression specifically for the mass of the Sun and express the result in kilometers.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to manipulate the units of G, c, and M to derive a length, questioning how to eliminate time from the expression. Another participant suggests using the expression GM/c^2 to achieve the correct units. The original poster then inquires about the physical meaning of the resulting length in the context of the Sun's mass, speculating on its relation to gravitational effects and escape velocities.

Discussion Status

The discussion is active, with participants exploring different expressions and questioning their implications. Some guidance has been offered regarding unit manipulation, and there is an ongoing inquiry into the physical significance of the derived length.

Contextual Notes

Participants are navigating the implications of their mathematical expressions and the physical interpretations of the results, particularly in relation to gravitational concepts and the characteristics of the Sun.

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Homework Statement


Find some combination of G, the speed of light c, and some arbitrary mass M, that has units of length. Then evaluate your expression for the mass of the Sun (that is, find the characteristic length associated with that mass). Give your answer in units of km.



The Attempt at a Solution


G has units (m^3)/[(kg)(s^2)]
c= m/s
M= kg

(G)(M)(1/c)= (m^2)/(s)

To get rid of the m^2, I can take a square root, but how can I get rid of the time in seconds in the denominator?
 
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Would GM/c^2 give the right units?
 
Oh, yes! Thank you...But I don't know what the physical meaning of this length is when using the sun's mass in the equation. Does it have something to do with the gravitational effect the sun has?...and something with the square of the reciprocal of the speed of light...

What about ...this length denoted here is the length of the field of the gravitational constant relative to the sun?
 
Its more to do with escape velocities.
 

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