Engineering
(Assume
the average Earth Radius RE = 6378 km):
1. Using Newton’s Law of Universal Gravitation (G = 6.67 x 10–11 N·m2
/kg2 ) Calculate the average
gravitational pull between the Earth and the Sun. The mass of the Sun is M Sun = 1.9891 x 10 30
kg and the mass of the Earth is m Earth = 5.9737 x 10 24 kg . 1 AU = 149,597,871 km. (6 Points)
2. A satellite is orbiting the Earth at an altitude of alt = 242 km . Its inertial velocity of v = 8.95 km/s
and its flight-path angle is γ = 14°.
a. Determine the total specific energy (ξ) for this orbit. Use 2 decimal places. (4 Points)
b. Determine the semimajor axis (a) for the satellite. Use 2 decimal places. (4 Points)
c. What is the angular momentum (h) of the satellite? Use 2 decimal places. (4 Points)
d. Determine the parameter (p) for this orbit. Use 2 decimal places. (4 Points)
e. Calculate the eccentricity (e) of this orbit and identify the shape of the orbit. Use 4
decimal places. (6 Points)
3. A low-Earth satellite orbits at an average altitude of alt = 878 km and has a parameter of p =
7204 km.
a. Determine the total specific energy (ξ) for the orbit. Use 2 decimal places. (4 Points)
b. Determine the angular momentum (h) of this satellite. Use 2 decimal places. (4 Points)
c. Determine the eccentricity (e) of this orbit. Use 4 decimal places. (4 Points)
d. Calculate the Perigee radius (r p ) for this orbit. Will this satellite pass through any
noticeable part of the Earth’s atmosphere? Use 2 decimal places. (6 Points)
e. Calculate the Apogee altitude (alta ) for this orbit. Use 2 decimal places. (5 Points)
4. A satellite has an apogee altitude of alt a = 4500 km and a perigee altitude of alt p = 500 km. The
true anomaly is currently θ = 136°.
a. Calculate the semimajor axis (a) for this orbit. (4 Points)
b. Calculate the eccentricity (e) of this orbit. Use 4 decimal places (4 Points)
c. Determine the parameter (p) for this orbit. Use 2 decimal places. (4 Points)
d. Calculate the angular momentum (h) for this satellite. Use 2 decimal places. (4 Points)
e. Calculate the total specific energy (ξ) for this orbit. Use 2 decimal places. (4 Points)
f. Determine the current radius (r) of the orbit (at θ = 136°). Use 2 decimal places. (5
Points)
g. What is current velocity (v)of the satellite (at θ = 136°)? Use 2 decimal places. (5 Points)
h. What is the current flight path angle (h) of the satellite (at θ = 136°)? Use 2 decimal
places. (5 Points)
5. A satellite has a very elliptical orbit with an apogee altitude of alt a = 265622 km and a perigee
altitude of alt p = 222 km.
a. What is the semimajor axis (a) for this orbit? (4 Points)
b. What is the eccentricity (e) of this orbit? Use 4 decimal places. (4 Points)
c. Calculate the orbital period (Tperiod ) for this orbit. Express your final answer in days,
minutes, and seconds. Express your answer in hours, minutes, and seconds (i.e.,
(2:25:23 or (2 hr, 25 min, 23 sec). Use 2 decimal places in your calculations (none
required in the final answer). (6 Points)
The points for each problem are noted next to each part (100 Points Total for the Assignment)
