This set of Spaceflight Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Perturbations due to Atmospheric Drag”.

1. If the density is doubled by entering a lower altitude, how will the satellite’s atmospheric drag be affected, provided the other components remain same?

a) Remains same

b) Becomes half

c) Becomes doubled

d) Becomes square

View Answer

Explanation: The spacecraft when entering the low-earth orbit, experienced atmospheric drag. This is proportional to the density as shown in the formula below:

a

_{D}= \(\frac{1}{2}\) ρv

^{2}\(\frac{C_D S}{m}\)

2. If two spacecrafts, A and B are entering the atmosphere having cross-sectional areas ratio of \(\frac{S_A}{S_B}\) = 4, then what will be the ratio of the atmospheric drags of A and B provided the other components remain the same?

a) 4

b) 16

c) 2

d) 8

View Answer

Explanation: Given, \(\frac{S_A}{S_B}\) = 4

The spacecraft when entering the low-earth orbit, experienced atmospheric drag. This is proportional to the cross-sectional area of the spacecraft.

The formula to compute the atmospheric drag is:

a

_{D}= \(\frac{1}{2}\) ρv

^{2}\(\frac{C_D S}{m}\)

\(\frac{a_{D{_A}}}{a_{D{_B}}} = \frac{S_A}{S_B}\) = 4 (Since all the other components are same, they get cancelled out).

3. If two spacecrafts, A and B are entering the atmosphere having velocity ratio of \(\frac{v_A}{v_B}\) = 8, then what will be the ratio of the atmospheric drags of A and B provided the other components remain the same?

a) 4

b) 16

c) 64

d) 8

View Answer

Explanation: Given, \(\frac{v_A}{v_B}\) = 8

The spacecraft when entering the low-earth orbit, experienced atmospheric drag. This is proportional to square of velocity of the spacecraft entering the atmosphere.

The formula to compute the atmospheric drag is:

a

_{D}= \(\frac{1}{2}\) ρv

^{2}\(\frac{C_D S}{m}\)

\(\frac{a_{D{_A}}}{a_{D{_B}}}\) = \((\frac{v_A}{v_B})^2\) = 8

^{2}= 64 (Since all the other components are same, they get cancelled out).

4. In which direction does the drag force point relative to the satellite’s relative velocity vector entering the atmosphere?

a) Same direction

b) Opposite direction

c) Perpendicular

d) At an angle theta

View Answer

Explanation: The drag force always opposes the satellite’s relative velocity vector that is relative to the Earth’s atmosphere. Where v

_{rel}= v – ω

_{E}× r

In this formula, v is satellite’s inertial velocity

ω

_{E}is the angular velocity vector of Earth

r is the satellite’s position vector

(All these are in ECI frame of reference).

5. Which exponential function can also be used to model the atmospheric density?

a) ρ = ρ_{0}^{2} exp [-β (h – h_{0}]

b) ρ = ρ_{0}/exp [-β (h – h_{0}]

c) ρ = ρ_{0}exp [-β (h – h_{0}]

d) ρ = ρ_{0}exp – β

View Answer

Explanation: The atmospheric density is also modelled using an exponential function since sometimes it’s hard to find al the terms (cross—sectional area, drag coefficient and density) to compute the drag. The exponential function is: ρ = ρ

_{0}exp [-β (h – h

_{0}]

Where, ρ

_{0}is the atmospheric density at the reference altitude h

_{0}

β is the inverse scale height.

6. Solar flux also has a impact in the atmospheric drag.

a) True

b) False

View Answer

Explanation: Density plays a role in increasing or decreasing the atmospheric drag. This density varies by the high solar flux that occurs during 11- year solar cycle. When the solar flux is high, the density of the upper atmosphere can increase up to 5 times from the mean value thus increasing the atmospheric drag.

7. What is the formular of ballistic coefficient?

a) C_{B} = \(\frac{SC_D}{m}\)

b) C_{B} = \(\frac{Sm}{C_D}\)

c) C_{B} = mSC_{D}

d) C_{B} = \(\frac{m}{SC_D}\)

View Answer

Explanation: Usually to compute the aerodynamic drag, it is difficult to determine drag- coefficient and cross-sectional area at it depends on the satellite’s orientation relative to velocity vector. Thus, these terms are grouped together to form a parameter called ballistic coefficient. The formula is: C

_{B}= \(\frac{m}{SC_D}\). The unit of this parameter is kilogram per meter squared. This value ranges from 10-100 \(\frac{kg}{m^2}\).

8. Drag due to third-body acceleration is greater than atmospheric drag for a LEO satellite.

a) True

b) False

View Answer

Explanation: Atmospheric drag is greater than the third-body gravitational acceleration for Low-Earth orbit satellite with altitudes less than 350 km. The frag acceleration varies by 5 orders of magnitude for circular orbits between 200 to 1000 km altitude.

9. If a satellite is orbiting at 250 km altitude having mass m = 75,000 kg and having a cross sectional area of 350 m^{2}, then what is the approximate value of satellite’s ballistic coefficient?

a) 50 \(\frac{kg}{m^2}\)

b) 107 \(\frac{kg}{m^2}\)

c) 200 \(\frac{kg}{m^2}\)

d) 350 \(\frac{kg}{m^2}\)

View Answer

Explanation- Given, a = 250 km, m = 75,000 kg, S = 350 m

^{2}

Ballistic missile coefficient is given by: C

_{B}= \(\frac{m}{SC_D} = \frac{75,000}{350×2}\) = 107.14 \(\frac{kg}{m^2}\)

(The value of C

_{D}is always taken as 2 when computing drag acceleration unless external values are provided to calculate it).

10. If the satellite is acted upon by the atmospheric drag, then what happens to its orbit with time?

a) Remains same

b) Spirals inward

c) Spirals outward

d) Apogee radius increases

View Answer

Explanation: When the satellite is under the influence of atmospheric drag in low-earth orbit, the drag reduces satellite’s speed and reduces the apogee radius with each consecutive revolution. This leads to the satellite’s eccentricity reduction with each orbital revolution until it is circular and within upper atmosphere.

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