A satellite or planet stays in a stable orbit because gravity pulls it towards the body it orbits and keeps changing the direction of its motion. For a given orbital radius there is only one speed that gives a stable circular orbit. If the speed is wrong for that radius, the object cannot stay in the same circular orbit.
The pull of gravity is stronger closer to a planet. A satellite in a low orbit therefore needs to travel faster to stay in orbit, and it has a smaller orbital radius. A satellite in a high orbit feels a weaker pull, so it travels more slowly, and it has a larger orbital radius.
So if the orbital speed of an object changes, its orbital radius must change too for the orbit to stay stable. A higher speed goes with a smaller radius, and a lower speed goes with a larger radius. Because a distant satellite travels slower and has further to go, it takes a longer time to complete one orbit. This idea is qualitative only: you do not need to calculate values.