How are objects kept in orbit?

for a satellite to being in orbit there must the a balance. Gravity is trying to pull the satellite into its parent. The speed of the satellite is trying to take it away. Given the masses of the objects and the speed of the satellite this defines the distance that the satellite must be from its parent.

Once this balance is achieved the satellite will stay in orbit indefinitely. It requires the pull of another body to change that.

If a satellite is travelling too slowly for its distance above the parent it was start to fall under gravity. As it falls it speeds up. Assuming the satellite doesn't collide with the parent, it will reach the distance where gravity and speed are in balance and will be in a lower orbit.

If a satellite is travelling to fast for its height to be in orbit it will start moving away from the parent. This will start to slow the satellite down. Assuming that the satellite isn't travelling faster than escape velocity, t will reach the distance where gravity and speed are in balance and will be in a higher orbit.

Putting a man made satellite in orbit requires getting it to the right height and speed and let gravity do the rest.

If an object comes towards a planet. If it isn't travelling too fast or on a collision course it will get captured when the balance is reached.