Example
For the geostationary transfer orbit we have = 42,164 km and e.g. = 6,678 km (altitude 300 km).
In the smaller circular orbit the speed is 7.73 km/s, in the larger one 3.07 km/s. In the elliptical orbit in between the speed varies from 10.15 km/s at the perigee to 1.61 km/s at the apogee.
The delta-v's are 10.15 − 7.73 = 2.42 and 3.07 − 1.61 = 1.46 km/s, together 3.88 km/s.
Compare with the delta-v for an escape orbit: 10.93 − 7.73 = 3.20 km/s. Applying a delta-v at the LEO of only 0.78 km/s more (3.20-2.42) would give the rocket the escape speed, while at the geostationary orbit a delta-v of 1.46 km/s is needed for reaching the escape speed of this circular orbit. This illustrates that at large speeds the same delta-v provides more specific orbital energy, and energy increase is maximized if one spends the delta-v as soon as possible, rather than spending some, being decelerated by gravity, and then spending some more (of course, the objective of a Hohmann transfer orbit is different).
Read more about this topic: Hohmann Transfer Orbit
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