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

In summary, to find a combination of G, c, and M with units of length, we can use the equation (G)(M)(1/c)=(m^2)/(s). Taking the square root of m^2, we can get rid of the squared unit. For the mass of the Sun, we can use the value of G, c, and M to calculate a characteristic length in units of km. This length represents the gravitational effect of the Sun and its escape velocity.
  • #1
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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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  • #2
Would GM/c^2 give the right units?
 
  • #3
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?
 
  • #4
Its more to do with escape velocities.
 

1. What is the equation for finding the length of Sun mass in kilometers using G, c, and M units?

The equation for finding the length of Sun mass in kilometers using G, c, and M units is L = (GM)/c^2, where L is the length in kilometers, G is the gravitational constant, c is the speed of light, and M is the mass of the Sun.

2. How is G, c, and M measured for the calculation?

G, c, and M are all fundamental physical constants that have been measured through various experiments and observations. G, or the gravitational constant, is typically measured using torsion balance experiments. c, or the speed of light, is measured using techniques such as the Foucault pendulum. M, or the mass of the Sun, is determined through astronomical observations and calculations.

3. What are the units of measurement for G, c, and M?

G is typically measured in units of Newtons times meters squared per kilogram squared (N*m^2/kg^2). c is measured in meters per second (m/s). M is measured in units of kilograms (kg).

4. Can this equation be used to find the length of mass for other celestial bodies?

Yes, this equation can be used to find the length of mass for any celestial body as long as the values for G, c, and M are known for that specific body. However, the equation may need to be modified slightly depending on the units of measurement used for G, c, and M.

5. How accurate is this equation in determining the length of Sun mass in kilometers?

This equation is very accurate in determining the length of Sun mass in kilometers, as G, c, and M have been measured with high precision. However, there may be slight variations due to uncertainties in the measurements and other factors such as the changing mass of the Sun over time.

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