course Phy 231
So I was a bit confused about G on a question (copied and pasted below the dots) when I was studying:if v = +-sqrt(GM/r) and G is in J*s, then
J*s = N*m*s = kg * m/s^2 * m * s =
kg * m^2/s
and then when I multiply that by M, which is in kg, I get kg^2 * m^2/s, and when I divide by r, which is in m, I get kg^2 * m/s, so the units end up being sqrt (kg^2 *m/s)?
How do you get units of velocity from that?
Thanks!
Here's the actual question:
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Derive the expression for v(r), the velocity of a satellite orbiting at distance r from a planet of mass
M. Find dv / dr.
* Given that the mass of the Earth is about 6 * 10^24 kg and G = 6.67 * 10^-34 J s, what is the
velocity of a circular orbit at a distance of 18 * 10^6 km from the center of the Earth?
* What is dv / dr at this distance?
* Use these results to make a differential estimate of the velocity of an orbit at a distance of 18
* 10^6 + 20.5 km from the center of the Earth.
The statement of that probem was in error. G is given in kg m^2 / s^2. The value given on the test is incorrect. Unfortunately the computer that generates the tests is in delicate shape (scheduled for upgrade in a few weeks) and I'm not able to 'operate' on it without risking shutdown of the entire process.
J * s are the units of Planck's constant; the problem generator apparently 'spit out' an incorrect unit.
Your analysis of the units is correct.