Gravity and Stable Elliptical Orbits

The Law of Universal Gravitation

Gravitation is a physical force that pulls bodies towards each other.
First defined by physicist Isaac Newton, the law of universal gravitation states that every particle of matter in the universe attracts every other particle.
The strength of this gravitational force is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between their centres.
This law is aptly summarised in the formula F = G(m1*m2)/r^2, where F is the force of attraction between the bodies, m1 and m2 are the masses of the two bodies, r is the distance between the centres of the two bodies, and G is the gravitational constant.

Planetary motion is driven by the gravitational attraction between a planet and the star it revolves around.
A planet moves in an elliptical orbit due to the gravitational pull of the star, which constantly changes with the planet’s position.
An ellipse (the shape of the orbit) has two focus points; for a planet’s orbit, one of these is the star.
The speed of the planet’s motion varies relative to its distance from the star: it is fastest when it’s closest to the star (at perihelion) and slowest when it’s farthest from the star (at aphelion).
This phenomenon occurs due to the conservation of angular momentum.

Newton’s law of universal gravitation and laws of motion intimately connect with Kepler’s laws of planetary motion.
Kepler’s first law (the law of orbits) states that every planet’s orbit is an ellipse with the star at one of the two foci.
Kepler’s second law (the law of areas) demonstrates that a line that connects a planet to its star sweeps equal areas in equal times.
Kepler’s third law (the law of periods) explains the relationship between the time taken for a planet to orbit its star (period) and the average distance from the star (semi-major axis).
Kepler’s third law is often stated as T^2 = r^3, where T is the period of the orbit and r is the average distance from the star to the planet.

Gravity is the force of attraction that holds astronomical bodies in their orbits.
Stable elliptical orbits occur as a result of the interplay between a planet’s momentum and the gravitational pull of a star.
The shape, size, and speed of a planet’s orbit are influenced by Kepler’s laws of planetary motion.
Newton’s law of gravity was pivotal in underpinning Kepler’s findings and understanding planetary motion.