Question

In this problem we will explore how modifying
the gravitational force law changes orbits. In
order to do this problem, you will need to
understand how elliptic orbits result from
Newton's gravitational force
F=-GmM/12
Imagine that the gravitational potential was
modified from U(r) = -k/r to
U(r)
=
E-kerla
where k = GmM and a is a constant with
units of length. Bounded orbits, i.e. circular
and elliptic orbits, occur for large enough a-
the easiest way to see this is to take
a → and we recover Newton's law.
(a) In our world (a = 00 U = -k/r),
the closest and furthest points that the Earth​

Answer 1

Answer:

Law of Falling Bodies (Galileo)

All falling bodies experience the same gravitational acceleration

Law of Universal Gravitation (Newton)

Gravity is an attractive force between all pairs of massive objects

Gravitational force is proportional to the masses, and inversely proportional to the square of the distance between them.

Newton generalized Kepler's laws to apply to any two bodies orbiting each other

First Law: Orbits are conic sections with the center-of-mass of the two bodies at the focus.

Second Law: angular momentum conservation.

Generalized Third Law that depends on the masses of the two bodies.

Orbital Speed determines the orbit shape:

Circular Speed

Escape Speed