xclusv2bhung said:
how the hell do you do that ?
Pardon? Oh, ref to title...
So anyway, if this is essentially asking for a pretty general proof, here:
Newton's First and Second Laws of Motion state, "blah, blah, blah" and "yadda, yadda, yadda", therefore a force must be acting on an object moving in a circle; the vector component of this acceleration is towards the centre of the circle, and this acceleration is centripetal acceleration. The force required to produce such an acceleration is defined by F
c = ma = mv
2/r, where m is the mass of the object, v is the velocity, and r is the radius.
Then Law 2 plays its role; Newton calculated that:
F = m
sv
2/|r
sBAO|, where:
m
s is the mass of the satellite;
v is the velocity at which it orbits;
r
sBAO is the distance between the satellite and a "BAO" ("Big Ass Object")
Newton, knowing Kepler's work, knew that the square of the orbital period for a satellite is proportional to the cube f its orbital radius.
V → (I can't find the "is proportional to" symbol) R/T
(der. from T = 2πr {two-pi-r, in case it doesn't show up properly; circumference} / v)
Putting these two equations (F = m
sv
2/|r
sBAO and V → R/T) together, you may observe that V
2 → R
-1, and therefore the force the BAO (Bad Ass Object, e.g. Sun) exerts on a satellite is:
F = m
sv
2/|r
sBAO| → R/T
Then Newton's Third Law of Motion states, "For every..."; this symmetry means that the two forces of gravitation depend on the masses of both objects in the same way, giving the form of the equation as:
F → m
sm
BAO/|r
sBAO|
2
And then, Newton adds the constant which we know as capital G and gets rid of that (right now it's a wannabe) proportionality sign.
F = Gm
sm
BAO/|r
sBAO|
2
Solved? Validated?
My bad if I make errors, heh.
Oh fucking shit, beaten to the punch... but with non-theory answers. It's waaay beyond high school Physics, 15-whatever the numbers are (edit: 15330). It's not in the syllabus. You better ask teachers for answers and explanations, xclusv2bhung.
Tell us about results, if any.
