Self-Assessment Quiz: Getting to Orbit

Twenty questions to check your grasp of orbital velocity, the gravity turn, gravity and drag losses, the ascent trajectory, and the suborbital/orbital distinction. Answer each before opening the key. Aim for 16 or more. Use $g_0 = 9.81\ \text{m/s}^2$ and $\mu = 3.986\times10^5\ \text{km}^3/\text{s}^2$.

Question 1

The single most important idea in this chapter is that orbit is fundamentally about:

A) reaching a great altitude B) sideways (tangential) speed C) escaping Earth's gravity entirely D) high thrust

Question 2

A satellite in low Earth orbit stays up because it is:

A) beyond the reach of Earth's gravity B) held up by the thin remaining atmosphere C) moving sideways fast enough that it falls around the curved Earth D) balanced by centrifugal force from the Sun

Question 3

Circular orbital velocity is given by:

A) $v = \sqrt{2\mu/r}$ B) $v = \sqrt{\mu/r}$ C) $v = \mu/r^2$ D) $v = g r$

Question 4

Orbital speed in low Earth orbit is approximately:

A) $1.4\ \text{km/s}$ B) $7.8\ \text{km/s}$ C) $11.2\ \text{km/s}$ D) $28\ \text{km/s}$

Question 5

In a gravity turn, the rocket bends from vertical toward horizontal because:

A) reaction control thrusters push it sideways the whole way B) the fins deflect the airflow C) gravity rotates the velocity vector while thrust stays aligned with velocity D) the Earth's magnetic field torques it

Question 6

The main reason a launch vehicle keeps its angle of attack near zero in the lower atmosphere is to:

A) improve the specific impulse B) avoid large aerodynamic side loads that could break the vehicle C) increase gravity loss D) point the antenna at the ground station

Question 7

The gravity-loss rate along the flight path is $g\sin\gamma$. It is largest when the vehicle flies:

A) horizontally ($\gamma = 0^\circ$) B) at $\gamma = 45^\circ$ C) straight up ($\gamma = 90^\circ$) D) it does not depend on $\gamma$

Question 8

A typical gravity loss for an ascent to low Earth orbit is about:

A) $0.1\ \text{km/s}$ B) $1.5\ \text{km/s}$ C) $7.8\ \text{km/s}$ D) $11\ \text{km/s}$

Question 9

Drag loss (~$0.1\ \text{km/s}$) is much smaller than gravity loss because:

A) rockets are perfectly streamlined B) air density and vehicle speed are large at opposite times during ascent C) there is no atmosphere below $50\ \text{km}$ D) drag does not depend on speed

Question 10

A rocket lifting off with thrust exactly equal to its weight (thrust-to-weight $= 1$) will:

A) accelerate rapidly upward B) hover, wasting delta-v at rate $g$ while gaining no speed C) tip over immediately D) reach orbit most efficiently

Question 11

Typical lift-off thrust-to-weight for an orbital launch vehicle is about:

A) $0.5$ B) $1.2$–$1.5$ C) $5$–$10$ D) exactly $1.0$

Question 12

The optimal ascent trajectory is a compromise between minimizing:

A) mass and cost B) gravity loss (favours going horizontal early) and drag/loads (favour going up first) C) thrust and specific impulse D) inclination and altitude

Question 13

A suborbital flight to $100\ \text{km}$ needs roughly what ideal launch speed?

A) $0.1\ \text{km/s}$ B) $1.4\ \text{km/s}$ C) $7.8\ \text{km/s}$ D) $11.2\ \text{km/s}$

Question 14

Compared with reaching space ($100\ \text{km}$ hop), reaching orbit requires about:

A) the same energy B) twice the energy C) thirty times the energy D) a hundred times the energy

Question 15 (True/False, justify)

"A rocket that flies straight up all the way to $100\ \text{km}$ and stops thrusting is in orbit." True or false? Justify in one sentence.

Question 16 (True/False, justify)

"An eastward launch from near the equator needs less launch delta-v than the same launch from a high latitude." True or false? Explain briefly.

Question 17 (True/False, justify)

"Because gravity loss ($\sim 1.5\ \text{km/s}$) dwarfs drag loss ($\sim 0.1\ \text{km/s}$), the best trajectory pitches to horizontal immediately after lift-off." True or false? Say why.

Question 18 (Short answer)

Explain, in one or two sentences, why astronauts on the Space Station float, given that gravity at that altitude is about $90\%$ of its surface value.

Question 19 (Short answer)

A launch vehicle must supply $9.4\ \text{km/s}$ with $v_e = 3.0\ \text{km/s}$. Compute the required mass ratio (show the exponent), and state why this forces the vehicle to use more than one stage.

Question 20 (Short answer)

In your own words, why is the launch delta-v ($\sim 9.4\ \text{km/s}$) larger than the orbital speed ($\sim 7.8\ \text{km/s}$)? Name both contributions and their approximate sizes.

Answer Key

Topics to review by question