This set of Spaceflight Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Minimum Energy Trajectory”.

1. What path of the trajectory is followed if the injection speed is infinity?

a) Elliptical

b) Straight line

c) Hyperbolic

d) Circular

View Answer

Explanation: The injection speed into the lunar trajectory determines the path of the trajectory. When the injection speed of satellite is infinite, the path followed is a straight line.

2. If the satellite’s injection speed in a lunar orbit is infinite, then what is the time of flight?

a) Zero

b) Infinite

c) T/2

d) T/4

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Explanation: If the satellite’s injection speed in a lunar orbit is infinite, the time of flight is zero since the satellite follows a straight line path. There is no conic orbit formation. When this speed is lowered it enters a hyperbolic, parabolic or elliptical orbit.

3. When the velocity at the injection is lowered, the orbit goes from elliptical, parabolic to finally hyperbolic.

a) True

b) False

View Answer

Explanation: When we lower the injection speed for entering the lunar orbit at the perigee of the Earth, the orbit decreases from hyperbolic to parabolic to elliptical in shape. This results in an increased time-of-flight.

4. Which of these criteria for injection speed must be followed to enter the lunar orbit if it is assumed that the injection altitude is 0.05 Earth’s radius?

a) Injection speed = 9.32 km/s

b) Injection speed = 10.82 km/s

c) 1.23 < Injection speed < 5.45 km/s

d) Injection speed = 8.89 km/s

View Answer

Explanation: The injection speed must be qual to or more than the minimum injection speed which is 10.82 km/s for injection altitude of 0.05 Earth’s radius. If the injection speed is any lesser than this, then it does not reach the lunar orbit.

5. What is the time-of-flight for the minimum energy lunar trajectory?

a) 100 hours

b) 110 hours

c) 20 hours

d) 150 hours

View Answer

Explanation: The time-of-flight for the minimum energy lunar trajectory is 7,172 minutes or 120 hours. Thus, in order to reach the lunar orbit, the time of flight must be below 120 hours only. If it exceeds this duration, then the spacecraft is unable to reach the lunar orbit.

6. What is the eccentricity of the minimum energy elliptical trajectory to reach moon?

a) 0.966

b) 0.5

c) 0.740

d) 1

View Answer

Explanation: The eccentricity of the elliptical orbit for minimum energy trajectory condition, the eccentricity is 0.966 which is enough to reach the moon. Eccentricity of 1 represent a parabolic orbit.

7. If there is an assumption of no lunar gravity, then what is the arrival speed for minimum energy trajectory?

a) 0.100 km/s

b) 0.188 km/s

c) 0.231 km/s

d) 0.451 km/s

View Answer

Explanation: For a minimum energy lunar trajectory, and it is assumed that there is no lunar gravity present then the speed of spacecraft’s arrival at the lunar orbit is 0.188 km/s.

8. If there is an increase in sweep angle, there’s a decrease in the injection speed.

a) True

b) False

View Answer

Explanation: The injection speed is a function of the angle swept. When the injection speed decreases, the geocentric sweep angle increases from 0 deg to 180 deg for minimum energy trajectory case.

9. What the sweep angle a function of provided the injection altitude and flight-path angle are fixed?

a) True Anomaly

b) Minimum energy

c) Injection speed

d) Eccentricity

View Answer

Explanation: Sweep angle is a function of injection speed provided the injection attitude and flight-path angle are kept constant. When the injection speed decreases, the geocentric sweep angle increases from 0 deg to 180 deg.

10. For minimizing the injection speed, what should be the suitable sweep angle?

a) 0 deg

b) 90 deg

c) 180 deg

d) 270 deg

View Answer

Explanation: In order to minimize the injection speed, the orbit should be selected in such a way that the sweep angle should be approximately 180 deg. As the injection speed for the satellite is reduced, the sweep angle increases from 0 deg to 180 deg.

**Sanfoundry Global Education & Learning Series – Spaceflight Mechanics**.

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