Satellites are launched and put into their intended orbit longitude positions, where they normally stay for many years. As time passes and needs change, it can be helpful to move satellites to new orbit longitude positions. During a satellite's lifetime, typically 15 years, it may be moved perhaps a couple of times.
The figure above shows the geostationary orbit as the outer black circle. The satellites are travelling eastwards at 3075 m/sec, to keep up with the earth's rotation below.
When it is required to initiate a orbit repositioning to a further east longitude orbit position, there is a need to advance the position gradually in easterly direction for a while, typically over a few weeks till the new position is reached.
The method described here starts to lower the orbit of a satellite over the pacific, so that the satellite goes round the earth faster for a while, then the orbit is raised up again when the new orbit longitude is reached.
Start by slowing down the satellite at position A. It will now start to drop down, into an elliptical orbit, and if allowed to do so will come back up again to the same height, a day later. Rather than that, wait half a day and slow it down yet more, at B, so that it is now in a circular orbit at lower height, as indicated by the orange line.
Here it is safe from collisions and will be going round the earth in less than a whole day, so it will appear to slowly advance its easterly longitude position as each day passes.
Transfer from slightly lower circular orbit
up to circular geostationary orbit.
I'm assuming you want to move a satellite, initially over the pacific, by 90 deg further east in longitude, so it is over the Americas (position D). Long= 270E or 90W.
At C you need to boost the speed up a bit so that half a day later, the satellite will be higher up (at its apogee) at geostationary height (35786km). After a further half day it will be back down at C, but crucially, it will be orbiting slower than it was in the higher speed orange orbit.
Wait a few weeks till it opposite America, above 90 east, the Bay of Bengal, near India.
At C you need to boost the speed up a bit so that half a day later, the satellite will be higher up (at its apogee) at geostationary height (35786km).
At D you need to speed it up further so that the orbit becomes circularised. The black geo orbit has a slower rotational orbit period than the orange orbit.
At each of the positions, A, B, C and D thrusters need to be fired directly along the direction of the orbit. To slow the satellite down you need to use thrusters facing forwards, to speed up the satellite use thrusters facing backwards.
The height difference in the figures is greatly exaggerated.
The amount of these thruster firings needs to be sufficient to make the required change in speed, called "delta V". For example, two burns of 3.5 m/s are associated with a height change of 186 km and a 2.4 deg per day drift rate.*
If there is a need to move a satellite westwards, the above procedure is modified to raise it temporarily to a higher orbit, so it gradually goes backwards in longitude, for a while.
A whole day refers to a siderial day, 23.93447 hours.