305 Week 2 Homework Assignment

In preparation for this Homework Assignment, review the information in this Week’s Lesson Readings and Read Chapter 2 of our Textbook, then Respond the Following Questions (Assume the average Earth Radius RE = 6378 km):

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)

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°.

  1. Determine the total specific energy (ξ) for this orbit. Use 2 decimal places. (4 Points)
  2. Determine the semimajor axis (a) for the satellite. Use 2 decimal places. (4 Points)
  3. What is the angular momentum (h) of the satellite? Use 2 decimal places. (4 Points)
  4. Determine the parameter (p) for this orbit. Use 2 decimal places. (4 Points)
  5. Calculate the eccentricity (e) of this orbit and identify the shape of the orbit. Use 4 decimal places. (6 Points)

A low-Earth satellite orbits at an average altitude of alt = 878 km and has a parameter of p = 7204 km.

  1. Determine the total specific energy (ξ) for the orbit. Use 2 decimal places. (4 Points)
  2. Determine the angular momentum (h) of this satellite. Use 2 decimal places. (4 Points)
  3. Determine the eccentricity (e) of this orbit. Use 4 decimal places. (4 Points)
  4. 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)
  5. Calculate the Apogee altitude (alta ) for this orbit. Use 2 decimal places. (5 Points)

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°.

  1. Calculate the semimajor axis (a) for this orbit. (4 Points)
  2. Calculate the eccentricity (e) of this orbit. Use 4 decimal places (4 Points)
  3. Determine the parameter (p) for this orbit. Use 2 decimal places. (4 Points)
  4. Calculate the angular momentum (h) for this satellite. Use 2 decimal places. (4 Points)
  5. Calculate the total specific energy (ξ) for this orbit. Use 2 decimal places. (4 Points)
  6. Determine the current radius (r) of the orbit (at θ = 136°). Use 2 decimal places. (5 Points)
  7. What is current velocity (v)of the satellite (at θ = 136°)? Use 2 decimal places. (5 Points)
  8. What is the current flight path angle (h) of the satellite (at θ = 136°)? Use 2 decimal places. (5 Points)

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.

  1. What is the semimajor axis (a) for this orbit? (4 Points)
  2. What is the eccentricity (e) of this orbit? Use 4 decimal places. (4 Points)
  3. 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)