Non-Coplanar Lunar Trajectories Questions and Answers

This set of Spaceflight Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Non-Coplanar Lunar Trajectories”.

1. What is the range of the moon’s orbit’s inclination?
a) 14.2° – 15.4°
b) 18.2° – 28.5°
c) 28.5° – 34.3°
d) 35.2° – 48.2°

Explanation: The arrival orbit, patched conic approximation etc. are all based on the assumption that lunar trajectory is in the plane of moon’s orbit. The inclination of moon’s orbit varies from 18.2° – 28.5° over a span of 18.6 years.

2. What is the latitude of the launch site at Cape Kennedy for coplanar trajectories?
a) 28.5°
b) 40°
c) 115°
d) 18.2°

Explanation: Since it is not possible to launch satellite from Earth into an orbit whose inclination is less than the launch site, there is a possibility of coplanar trajectory launch from Cape Kennedy whose latitude 28.5° and moon is at maximum inclination of 28.5° as well.

3. What is the launch azimuth specified by Eastern Test Range safety for lunar missions?
a) < 40°
b) > 115°
c) 40° – 115°
d) 28.5°

Explanation: In case of lunar missions, there are specifics mentioned by the Eastern Test Range for safety requirements. According to them, the launch azimuth β° must lie between 40° and 115°. Where launch azimuth is the angle formed between the north direction of the projection of the initial orbital plane onto the launch location.

4. What is the formula to compute the total geocentric angle?
a) ψff + ψc
b) 2ψc
c) 2(ψff + ψc)
d) 2ψff

Explanation: The total geocentric sweep angle consists of free flight sweep angle ψff and geocentric angular travel from launch to injection ψc.
Thus, the formula is: ψt = ψff + ψc

5. Both free flight sweep angle and geocentric angular travel are arbitrarily chosen.
a) True
b) False

Explanation: Geocentric angular travel ψc is arbitrarily chosen whereas free-flight angle ψff is selected based on the initial injection conditions i.e., r0, v0 and Φ0.

6. How is the free-flight sweep angle computed?
a) Product of true anomaly between injection and lunar intercept
b) Difference between true anomaly between injection and lunar intercept
c) Sum of true anomaly between injection and lunar intercept
d) Square of difference between true anomaly between injection and lunar intercept

Explanation: We know that the geocentric angular travel ψc is arbitrarily chosen whereas free-flight ψff is selected based on the initial injection conditions. This free-flight is just difference between true anomaly between injection and lunar intercept.

7. American Ephemeris and Nautical Almanaclists the correct ascension and declination of moon for selecting launch date.
a) True
b) False

Explanation: in order to carry out a launch, it is essential to find the time when moon is at the perfect declination and the phase is correct. This is done by American Ephemeris and Nautical Almanac who list the right ascension and declination and phase of the moon for every hour.

8. What is the right ascension of launch point equal to?
a) East longitude
b) Greenwich sidereal time
c) Local sidereal time
d) Synodic time

Explanation: Right ascension of the launch point for lunar mission α0 is same as the local sidereal time θ at the launch point or the sum of Greenwich Sidereal Time θg at time t0 and east longitude of launch site λE.
α0 = θ = θg + λE

9. Which of these is not a constraint on lunar trajectories?
a) Launch site location
b) Phase of the moon
c) Accuracy tolerance
d) Rotation speed of the earth

Explanation: There are several constraints which carrying out lunar missions. These include-launch site location, accuracy tolerance, limited range of injection conditions, phase of the moon determining the lighting condition, direction of launch from a site.

10. What kind of trajectory is obtained if the satellite is launched from a place whose latitude is 30 deg
a) Coplanar trajectory
b) Non-coplanar trajectory
c) Co-axial trajectory
d) Arc trajectory

Explanation: Coplanar trajectory only occurs when the launch is at a suitable condition where launch latitude matches the moon’s orbital inclination. This is a rare condition which occurs only at Cape Kennedy whose latitude for launch is 28.5 deg. When launches are done at any other location or when the suitable conditions is not met, it results in non-coplanar trajectory.

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