MAE 2: Introduction to Aerospace Engineering
Assignment 3
Due Thursday, 11/1
1. (10) A spacecraft is on a hyperbolic trajectory with respect to Planet
X. At a closest approach of 700 km above the planet surface, how slow
could the spacecraft speed possibly b e? (Assume the planet radius is
6200 km, and the planet µ=Gm = 325000.0km3/sec2.)
2. (10) At perigee (periapsis in an Earth orbit), a spacecraft has an alti-
tude of 1000 km, and a speed of 9 km/sec. Without any burns, will
the spacecraft reach an altitude of 2000 km? If so, what will its speed
when it reaches that altitude? (Assume a spherical Earth model with
radius re= 6378 km.
3. (10) A spacecraft is in circular orbit around the Earth, with orbit
radius, 30000 km. What is the minimal ∆vrequired to get it into
an escape trajectory (i.e., to an orbit of zero energy)? If the fuel has
Ig0= 3 km/sec, what fraction of the spacecraft mass (including fuel)
will be needed to achieve this? Plot p ercent of vehicle mass needed
versus circular orbit radius for a vehicle in Earth orbit, with this fuel.
Use the simple linear approximation that was obtained in class for
required fuel mass.
4. (5) Perform the same estimates, but with the exponential fuel con-
sumption model given in class.
5. (10) For a vehicle in circular Earth orbit with this same fuel, consider
orbit plane change. Suppose the orbit radius is 7000 km, and that one
wants to change the orbit plane by 0.05 radians. What fraction of the
vehicle mass would be required? (Use the simple linear approximation
that was obtained in class for required fuel mass.) What fraction of
the mass would be required if the radius was 70000 km? How about
for 700000 km?
6. (10) Determine the ∆vfor a Hohmann transfer from circular orbit with
radius 4000 km to circular orbit with radius 6000 km around Planet
X (with µX= 40000 km3/sec2).
