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

AI Thread Summary
To find a length associated with the Sun's mass using G, c, and M, the expression GM/c^2 is derived, yielding units of length. This calculation leads to a characteristic length that reflects gravitational effects related to the Sun's mass. The discussion highlights the relationship between this length and escape velocities, suggesting it represents the gravitational influence of the Sun. Participants express curiosity about the physical significance of this length in the context of gravitational fields. Ultimately, the derived length connects fundamental constants with astrophysical concepts.
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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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