Question

How does gravity work in space?

Answer 1

The same as anywhere else.

Explanation:

Every particle in the universe has a bit of gravity. The amount of gravity is relative to the mass of the particle in question. Or, in the case of large objects, billions and billions of particles acting in concert.

In the case of the earth, its gravitational influence extends well beyond the moon, which is why the moon stays in its orbit.

In the case of the sun, the sun's gravity extends somewhere past the Kuyper Belt, beyond the orbit of Pluto.

In the case of the Milky Way Galaxy, the black hole's gravity at the center of the galaxy extends past the most distant star associated with the galaxy.

In essence, the earth is effected by both the sun's gravity and the black hole's gravity. That means, anywhere you go in the galaxy you are effected by several gravitational forces at once and in varying degrees according to the mass of the objects effecting you.

Answer 2

Gravitation curves space-time

Explanation:

Peter gave you the classical answer. In case you meant to ask in the relativistic sense, here is the General Relativity answer.

Gravity makes itself felt by curving spacetime. A particle subject to gravity is following a "straight" path, that is the shortest path in a space where straight lines are no longer straight. What curves them is the presence of a mass such as the sun.

To find out how much space is curved is to solve Einstein's equations. These are the usual coupled equation:

Matter generates curvature
Curvature affects matter

The first equation is of the form

Stress-Energy Matter Tensor = curvature

which you need to integrate to get the geometry of space modified by the presence of matter. Integrating gives you the metrics. The metrics is a tensor which describes the difference between one meter in the x direction and one meter in the y direction, or one meter near the sun and one meter far away. These differences are coded in the form of coefficients which you stick into the equation describing a straight line et voila, the equation now describes a curved line.

In reality, things are more complicated, Because the sun cannot affect the earth at a distance but through the exchange of energy and momentum, that exchange being made by the emission and reception of gravitational waves, of, in quantum language, of gravitons.