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final velocity

Vm = 631.3481 rB-'*

velocity on transfer orbit at final orbit

VfcB = 631.3481 [2 / rB -1/ <%,]'*

final velocity change

AVa=[Vy+ V^-2VBVmcos

total velocity change

AVt= AVa + AVS

eccentric anomaly at B

E = tan-1[(1 - e2)"2 slnv/(e+cosv)]

time of flight

TOF= 0.001 583 913 a*™ (E- e sin£), Einrads

Table 6-6 compares the total velocity change required and time-of-flight for a Hohmann transfer and a one-tangent burn transfer from a low altitude parking orbit to geosynchronous orbit

Another option for changing the size of the orbit is to use a constant low-thrust burn, which results in a spiral transfer. We can approximate the velocity change for this type of orbit transfer by

where the velocities are the circular velocities of the two orbits. Following the

TABLE 6-6. Comparison of Coplanar Orbit Transfers from LEO to Geosynchronous Orbit.

Variable

Hohmann Transfer

One-Tangent-Burn

rA

6,570 km

6,570 km

rB

42,200 km

42,200 km

a*

24,385 km

28,633 km

AVt

3.935 km/s

4.699 km/s

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