Self-Assessment Quiz: Atmospheric Re-Entry

Twenty questions to check your grasp of the energy problem, compression heating, thermal protection, ballistic vs. lifting entry, the corridor, g-forces, and blackout. Answer each before opening the key. Aim for 16 or more. Use $g_0 = 9.81\ \text{m/s}^2$ and $c_p \approx 1{,}005\ \text{J/(kg·K)}$.

Question 1

The kinetic energy per kilogram of a spacecraft in low Earth orbit ($\sim 7.8\ \text{km/s}$) is closest to:

A) $3\ \text{MJ/kg}$ B) $30\ \text{MJ/kg}$ C) $300\ \text{MJ/kg}$ D) $3\ \text{kJ/kg}$

Question 2

The dominant source of heating on a blunt re-entry vehicle is:

A) friction of the air rubbing along the skin B) compression of the air in the shock layer ahead of the vehicle C) the vehicle's own engines D) sunlight focused by the atmosphere

Question 3

A re-entering vehicle does not brake with retro-rockets mainly because:

A) rockets don't work in the atmosphere B) cancelling orbital speed propulsively would cost about $7.8\ \text{km/s}$ of delta-v — as much as launch C) the exhaust would melt the heat shield D) it would violate conservation of energy

Question 4

A blunt body is preferred for re-entry because it:

A) has the lowest drag B) pushes the shock wave off the surface and dumps most heat into shock-heated air that blows away C) is lighter than a sharp body D) creates no shock wave at all

Question 5

An ablative heat shield protects a vehicle by:

A) reflecting heat with a mirror finish B) eroding — charring and vaporizing — so departing material carries the heat away C) conducting heat quickly into the structure D) spinning to distribute heat evenly

Question 6

The Space Shuttle used reusable silica tiles rather than an ablator chiefly because it needed to:

A) survive a faster entry than Apollo B) be reused many times without rebuilding its skin C) generate more lift D) reduce its mass to near zero

Question 7

The ballistic coefficient is $\beta = m/(C_d A)$. A low-$\beta$ capsule, compared with a high-$\beta$ one entering identically, decelerates:

A) deeper in the atmosphere, more violently B) higher in the atmosphere, more gently C) at exactly the same altitude D) not at all

Question 8

Compared with a ballistic entry, a lifting entry of the same vehicle generally has:

A) higher peak g and higher peak heat flux B) lower peak g and lower peak heat flux, but a larger total heat load C) no effect on g-forces D) a shorter total flight time

Question 9

The re-entry corridor is bounded on the shallow side by:

A) excessive g-forces B) the vehicle skipping back out of the atmosphere C) melting of the landing gear D) loss of the parachute

Question 10

The re-entry corridor is bounded on the steep side by:

A) excessive deceleration and heating B) skipping back out of the atmosphere C) running out of propellant D) the plasma blackout

Question 11

The Allen–Eggers peak deceleration $a_{\max} = v_E^2 \sin\gamma_E/(2eH)$ depends on all of the following except:

A) entry speed B) entry flight-path angle C) the vehicle's ballistic coefficient D) the atmospheric scale height

Question 12

Communication blackout during re-entry is caused by:

A) the vehicle's antenna melting B) a layer of ionized gas (plasma) that reflects radio waves below its plasma frequency C) the curvature of the Earth D) the heat shield absorbing radio waves

Question 13

The stagnation heating scaling $\dot q \propto \sqrt{\rho/R_n}\,v^3$ implies that heating grows most steeply with:

A) nose radius B) air density C) speed (as its cube) D) vehicle mass

Question 14

A naive stagnation-temperature estimate for a LEO entry gives about $30{,}000\ \text{K}$. The real gas is far cooler because:

A) the heat shield absorbs the difference B) the air dissociates and ionizes, absorbing energy without a proportional temperature rise C) the calculation used the wrong speed D) space is cold

Question 15 (True/False, justify)

"Re-entering vehicles glow because of friction between the vehicle and the air." True or false? Justify in one sentence.

Question 16 (True/False, justify)

"Two capsules entering at the same speed and angle pull the same peak g, even if one is twice as heavy." True or false? Explain briefly.

Question 17 (True/False, justify)

"A shallower entry is always safer because it means lower g-forces." True or false? Say why.

Question 18 (Short answer)

Explain in one or two sentences why re-entry from the Moon ($\sim 11\ \text{km/s}$) is so much more punishing than re-entry from LEO ($\sim 7.8\ \text{km/s}$), referring to both energy and heating.

Question 19 (Short answer)

A ballistic entry has $v_E = 7.8\ \text{km/s}$, $\gamma_E = 3^\circ$, $H = 7{,}000\ \text{m}$. Compute the peak deceleration in g's (show $\sin\gamma_E$ and the arithmetic).

Question 20 (Short answer)

In your own words, state the "free brake" idea of re-entry: what problem are you trading away, what problem are you accepting instead, and roughly what does each cost?

Answer Key

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