University:
College
Course:
College Physics
Academic year:

2022
Views:

14

Pages:

2
Author:

anon

IB Physics: Orbital Motion Orbital Motion State that gravitation provides the centripetal force for circular orbital motion. When a satellite orbits the Earth, the gravitation force between the two objects (Newton’s Law of Gravitation) provides a centripetal force to keep the satellite in orbit. The mathematics behind this: GMm / r2 = mv2/r GM /r = v2 v = √ GM/r Please note, ‘M’ is the mass of the object being orbited around. Derive Kepler’s third law. Kepler’s Third Law states that The square of an orbits period is proportional to the cube of radius of its orbit (We will assume the orbit is circular here) Mathematically, this is described as: Velocity around an orbit. This is basically v = d/t (Unit 2), but then the distance travelled here is the circumference 2πr, over time (which is the period) v =2πr /T We learned earlier that GM = v2r So if we substitute v =2πr /T into the above equation GM = (2πr /T)2r GM = (4π2r2/T2 ) r GM = (4π2r3/T2 ) GM /4π2 =r3/T2 Therefore, we proved that r3 / T2 is constant.