Question

Describe the differences between circular motions and elliptical motions. Explain how Newton’s universal gravitational law can be applied to study the interplanetary motions.

Answer 1

the differences between circular motions and elliptical motions is of rotational axis and radius of gyration

so there are two axis of rotation in the elliptical motion but in case of circular motion

radius of gyration varies in the elliptical motion

since gravitational law is universal law that can be applied to study affect of gravity on interplanetary motion

Rules given by newton and kepler for planetary motion can be applied to study the interplanetary motions

Rules like

1. Since the planets move on ellipses (Kepler's 1st Law), they are continually accelerating, as we have noted above. As we have also noted above, this implies a force acting continuously on the planets.
2. Because the planet-Sun line sweeps out equal areas in equal times (Kepler's 2nd Law), it is possible to show that the force must be directed toward the Sun from the planet.
3. From Kepler's 1st Law the orbit is an ellipse with the Sun at one focus; from Newton's laws it can be shown that this means that the magnitude of the force must vary as one over the square of the distance between the planet and the Sun.
4. Kepler's 3rd Law and Newton's 3rd Law imply that the force must be proportional to the product of the masses for the planet and the Sun.