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# taking the natural lof a circular motion equation watch

1. I've got this formula:

v=(GM/r)^1/2

where v=velocity
G=gravitational constant and M is the mass of the sun.

the question states: by taking the natural logs of both sides rearrange the equation in the form of y=mx+c, identify the gradient and y intercept.

then it goes on to say draw a graph of ln(v) against ln(r) and estimate the mass of the Sun.

im assuming the gradient would have been the mass of the sun, but i have no idea how to rearrange the equation to get that, ive tried many ways then tried to see if i got the mass of the sun and it didnt work, any suggestions?

2. equation of the line is

ln v= -0.5ln r + 0.5 ln GM
3. (Original post by SdotK)
I've got this formula:

v=(GM/r)^1/2

where v=velocity
G=gravitational constant and M is the mass of the sun.

the question states: by taking the natural logs of both sides rearrange the equation in the form of y=mx+c, identify the gradient and y intercept.

then it goes on to say draw a graph of ln(v) against ln(r) and estimate the mass of the Sun.

im assuming the gradient would have been the mass of the sun, but i have no idea how to rearrange the equation to get that, ive tried many ways then tried to see if i got the mass of the sun and it didnt work, any suggestions?

Just outa interest, ru doing physics/engineering at QMUL ?
4. nope, how comes?
5. (Original post by equinox3o0o)
equation of the line is

ln v= -0.5ln r + 0.5 ln GM
that was one of the things i got buy, isnt ln(r) meant to be x? in terms of y =mx +c
6. y = ln v
m = -0.5
x = ln r
+c = 0.5ln GM
7. yeah that makes sense, so you meant to put in values for r and v, cause i have a table as well which tells me the distance and speed of each planet from the sun, put set of those in and u can find M, right?
8. yep yep
9. nice one, i appriciate that. thanks alot.

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