1. During lecture we discussed that an elliptical orbit is not necessarily helpful to escape Earth, and we said we would not investigate that further (but you are welcome on your own). However, it is useful to investigate the radius of the "best" (ie, lowest Av) circular parking orbit. For this problem consider the following "steps" to Escape Earth: 1. A Hohmann transfer from the surface to the parking orbit (i.e., 2 Av's). Assumptions: a. launch exactly from the equator with zero velocity relative to the ground b. there is no atmosphere, mountains, obstacles, etc - the Av can happen in the tangential direction from the ground c. Simplify for now and use the Earth rotation = 1 revolution in 24 hours 2. A Av from the parking orbit to escape Earth 3. The target velocity is exactly Vesc (i.e., there is no v... for a specific destination, we just want to escape Earth) For all Av's you can ignore the direction, only consider magnitude. a. Develop an equation (or function in Matlab or a spreadsheet) which takes as input the altitude of the parking orbit and calculates the total Av required from launch to escape. Start with a parking altitude of 0 (no parking). Choose a reasonable value for the maximum altitude. Plot the result. (Tip: a logarithmic plot will help visualize things better.) b. What is the minimum Av required? (Answer: 10.716 km/s) c. Where is the maximum Av required? (Answer: 12.694 km/s)
During lecture we discussed that an elliptical orbit is not necessarily helpful to escape
Earth, and we said we would not investigate that further (but you are welcome on your
own).
However, it is useful to investigate the radius of the “best” (ie, lowest Δv) circular parking
orbit. For this problem consider the following “steps” to Escape Earth:
1. A Hohmann transfer from the surface to the parking orbit (i.e., 2 Δv’s).
Assumptions:
a. launch exactly from the equator with zero velocity relative to the
ground
b. there is no atmosphere, mountains, obstacles, etc - the Δv can
happen in the tangential direction from the ground
c. Simplify for now and use the Earth rotation = 1 revolution in 24
hours
2. A Δv from the parking orbit to escape Earth
3. The target velocity is exactly vesc (i.e., there is no v∞ for a specific
destination, we just want to escape Earth)
For all Δv’s you can ignore the direction, only consider magnitude.
a. Develop an equation (or function in Matlab or a spreadsheet) which takes as
input the altitude of the parking orbit and calculates the total Δv required from
launch to escape. Start with a parking altitude of 0 (no parking). Choose a
reasonable value for the maximum altitude. Plot the result. (Tip: a logarithmic plot
will help visualize things better.)
b. What is the minimum Δv required? (Answer: 10.716 km/s)
c. Where is the maximum Δv required? (Answer: 12.694 km/s)
d. What would be your recommendation? SOLVE b, c and d step by step
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