Problem 1
Table 1: Table of physical constants
Name
\mu_{earth}
Value
Units
3.986004 \times 10^5 km^3/s^2
A
B
Figure 1: Geometry of transfer in Problem 1. Not to scale.
Sometime in the future, a transport spacecraft from the Weyland-Yutani corporation is departing an Earth
orbiting space station with some workers from a geostationary orbit with radius $r_a = 42164$ km to an asteroid
(Small enough that you may ignore its gravitational effect) which has previously been towed into a higher
circular orbit with radius $r_b = 60000$ km. The workers are going to start their month long shift at the mining
rig on the asteroid. The transport spacecraft will execute a Hohmann transfer from orbit A to orbit B. You
may assume the spacecraft and the asteroid are properly aligned for the transfer so you don't have to worry
about phasing yet.
Compute:
a. The semimajor axis of the transfer orbit
b. The initial velocity, before the transfer begins
c. The final velocity, after the transfer ends
d. The magnitude of the initial burn $\Delta v_1$
e. The magnitude of the final burn $\Delta v_2$
f. The total $\Delta v$ for the entire Hohmann transfer from orbit A to orbit B
