A satellite maintains an orbit equidistant from the earth at all points along its path of orbit due to centripetal force of earth or force of gravity. 
Explanation 
A centripetal force is a type of force that makes the object follow a closed path. 
The orbits of satellite due to the force of centripetal produced by the gravity of earth. 
As the earth has a bigger size than the satellite, the gravity force pulls the satellite towards earth, else it will move away from earth.