(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Graph the relationship between the speed of a satellite orbiting a large mass in uniform circular motion. Also I need to learn how to properly write proportionality constant and proportionality equation.

2. Relevant equations

in the equation below, m is the mass of the larger mass. G is gravitational constant 6.67x10^-11.

v = [tex]\sqrt{Gm/r}[/tex]

3. The attempt at a solution

I think that:

V is directly proportional to sqrt of Gm (v [tex]\propto[/tex] [tex]\sqrt{Gm/r}[/tex]]

and

V is inversely proportional to sqrt of r ( v [tex]\propto[/tex] 1/r )

Now how do i graph these, i have ideas:

Remove the square root by making the y axis squared.

And first proportionality is linear and the second one is decreasing from value of 1 because its 1/r relationship and maximum y value is 1.

For writing proportionality statements is everything in the numerator directly proportional, and everything in the denominator inversely proportional?

Also how does the proportionality constants work? I know you have to introduce them with I believe every relationship. Do they go with the inverse relationships as well? And with equations with numerator and denominator is there a constant on both top and bottom or is it made into one value.

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# Orbital Velocity vs Mass and Orbital Velocity vs Radius

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