This set of Spaceflight Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Interplanetary Travel Basics”.

1. Which method is employed for interplanetary missions?

a) Patched-conic method

b) Two-body problem method

c) N-body problem method

d) Euler’s method

View Answer

Explanation: For carrying out interplanetary missions, the patched conic method is employed to divide the mission into three parts. The basic aspect of these missions is that they are considered to be Hohmann transfer.

2. In how many parts are the interplanetary mission divided into?

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: Using the patched-conic method, the mission is divided into three parts-hyperbolic departure trajectory which is relative to the home planet, cruise ellipse relative to sun and finally the hyperbolic arrival of the trajectory relative to the target plane.

3. In order to escape from the Earth’s atmosphere to reach another planet for example Venus, which of these orbits it used?

a) Circular

b) Elliptical

c) Parabolic

d) Hyperbolic

View Answer

Explanation: In order to begin an interplanetary cruise, spacecraft first needs to escape the earth’s gravitational pull. The transition from near-earth space to interplanetary space is done using a hyperbolic departure trajectory. This helps the spacecraft in crossing the fictitious boundary known as Earth’s Sphere of Influence (SOI).

4. What is sphere of influence of a planet?

a) Fictitious boundary for 2-body motion about a planet

b) Fictitious boundary where there is presence of gravity

c) Fictitious boundary for N-body motion about a planet

d) Fictitious boundary where there is atmosphere

View Answer

Explanation: Sphere of Influence is a fictitious boundary where when the satellite enters, its orbit can be approximated by the two-body problem with the planet as the central body. It cannot be used to represent the motion of N-body gravity field.

5. According to Laplace, how is the sphere of influence defined?

a) Ratio of central- body acceleration and perturbing acceleration

b) Ratio of perturbing acceleration and central-body acceleration

c) Ratio of gravitational field of the planet to the potential field of the object

d) Ratio of the potential field of the object to the gravitational field of the planet

View Answer

Explanation: According to Laplace, Sphere of Influence (SOI) is described as the ratio of perturbing acceleration and central-body acceleration.

6. In the heliocentric phase of the patched conic method, which orbit is followed by the spacecraft?

a) Circular

b) Elliptic

c) Parabolic

d) Hyperbolic

View Answer

Explanation: In the heliocentric phase of the patched conic method, the spacecraft follows the elliptical transfer orbit where sun is considered as the primary gravitational body. The interplanetary cruise is analyzed by two-body mechanics in heliocentric0ecliptic coordinate frame.

7. In order to arrive from the Earth to the target planet for example Venus, which of these arrival orbits it used?

a) Circular

b) Elliptical

c) Parabolic

d) Hyperbolic

View Answer

Explanation: The arrival trajectory inside the target planet’s sphere of influence is done using a hyperbolic orbit which is analyzed in inertial planet-centered frame. As soon as the spacecraft enters the target planet’s sphere of influence, the sun’s gravity is turned off and planet’s gravity is turned on.

8. What is the value of 1 AU unit?

a) 365,000 km

b) 149,597,871 km

c) 5,022,643 km

d) 132,712,444 km

View Answer

Explanation: Since the distances in heliocentric orbits are very large, the distances are referred in terms of AU (Astronomical unit) rather than kilometers. 1AU = 149,597,871 km.

9. What is the reference velocity used for heliocentric orbits?

a) 1AU/TU

b) 2AU/TU

c) TU/AU

d) TU/3AU

View Answer

Explanation: For heliocentric orbits, the reference velocity used is defined as the circular orbital speed in a heliocentric orbit at 1AU. This is 29.784630 km/s.

v

_{ref}= \(\sqrt{\frac{\mu_s}{r_{ref}}}\) = 29.7847 km/s

Where, μ

_{s}= 1.327124 × 10

^{11}\(\frac{km^3}{s^2} = \frac{1AU^3}{TU^2}\) is the sun’s gravitational parameter.

r

_{ref}= 1AU/TU.

10. Which is the main assumption for the heliocentric transfer orbit?

a) Planetary orbits are coplanar

b) Planetary orbits are circular

c) Planetary orbits are circular and coplanar

d) Planetary orbits are tangential

View Answer

Explanation: For transfers to most of the planets, we consider that the planetary orbits are both circular and coplanar. Hohmann transfer is considered to be the most economical method for transfer between coplanar circular orbits.

11. What is the energy of the Hohmann transfer trajectory for spacecraft travelling from earth to mars? (Given- radius to mars from sun is 1.524 AU, radius to earth from sun is 1 AU).

a) -0.396 \(\frac{AU^2}{TU^2}\)

b) 0.245 \(\frac{AU^2}{TU^2}\)

c) 0.456 \(\frac{AU^2}{TU^2}\)

d) 0.284 \(\frac{AU^2}{TU^2}\)

View Answer

Explanation: r

_{M}= 1.524 AU, r

_{E}= 1 AU

Energy of the Hohmann transfer trajectory is given by:

ε

_{t}= \(\frac{-\mu_s}{r_M + r_E} = \frac{-\frac{1AU^3}{TU^2}}{1.524 AU + AU}\)

Where μ

_{s}= \(\frac{1AU^3}{TU^2}\)

ε

_{t}= -0.396 \(\frac{AU^2}{TU^2}\).

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