Gravity and Orbits

Most of the universe is empty space.
Our perception of physics is warped by living on a planet.
On Earth, objects thrown return due to gravity, which is not the natural state in space.
Gravity from an object extends infinitely but weakens with distance.

Historically, gravity was a fact of life, not well understood.
In the mid-1600s, scientists like Robert Hooke and Isaac Newton began to investigate gravity mathematically.
They had a feud over who discovered what first.
Now there is a much better understanding of how gravity works.

Everything with mass has gravity and exerts a gravitational force on other objects.
The gravitational force depends on:
- The mass of the object exerting the force.
- The mass of the object experiencing the force.
- The distance between the objects.
Distance is the dominating factor.
The force of gravity weakens with the square of the distance.
- F \propto \frac{1}{d^2}
- Double the distance, gravity is four times weaker.
- Ten times the distance, gravity is 100 times weaker.
Gravity is always attractive, never repulsive.

The simplest orbit is a straight line (dropping a rock).
Throwing a rock introduces sideways motion.
If you throw a ball hard enough sideways, it will fall at the same rate the Earth curves away.
Orbiting is essentially falling and missing the ground.
A rock thrown hard enough will continuously fall toward the Earth but miss, creating a circular orbit.
The speed of an orbiting satellite depends on the mass of the object it's orbiting and its distance from it.
Farther distance means weaker gravity, requiring less speed to maintain orbit.

Johannes Kepler discovered planets orbit the sun on ellipses, not perfect circles.
Elliptical orbits occur when an object is thrown sideways harder than required for a circular orbit.
The orbit becomes more elongated with increased force.
These orbits are closed and bound by gravity.

At a certain velocity, an object can escape gravity.
Gravity weakens with distance and may not be able to stop a fast-moving object.
Escape Velocity: The speed required to escape the gravitational pull of an object.
Escape velocity depends on mass and size.
- Earth: Approximately 11 km/s.
- Jupiter: Approximately 58 km/s.
- Sun: Approximately 600 km/s.
An object launched at escape velocity slows down but never stops completely.
Conversely, an object dropped from far away will hit a planet at its escape velocity.
Escape orbits are open and shaped like parabolas.

Throwing an object even harder than escape velocity results in a hyperbolic orbit.
The object moves away faster and never stops, even at infinity.

Gravity never quite reaches zero, it only gets smaller with increasing distance.
Astronauts in space stations are weightless because they are in orbit, falling around the Earth.
At the height of the space station, gravity is still about 90% as strong as on Earth's surface.
Weight: The force of a surface pushing back on a mass. In freefall, there is no such force.
NASA calls this condition "microgravity" due to subtle forces still acting on the astronauts.
In space, mass remains the same as on Earth, but weight is zero.