Self-Assessment Quiz: Newton's Laws in Space

Twenty questions on Newton's laws, momentum, gravitation, and escape velocity. Answer each before opening the key. Aim for 16 or more. Use $\mu_\oplus = 3.986\times10^{5}\ \text{km}^3/\text{s}^2$ and $R_\oplus = 6{,}371\ \text{km}$ where needed.

Question 1

Newton's first law explains why, in the vacuum of space, a coasting spacecraft:

A) gradually slows down and stops B) keeps moving at constant velocity with no fuel C) needs continuous thrust to maintain speed D) speeds up on its own

Question 2

A satellite in a high, stable orbit runs out of fuel. It will:

A) immediately fall to Earth B) slow down and drift away C) continue orbiting essentially indefinitely D) stop moving

Question 3

An orbit persists (in a vacuum) because:

A) the spacecraft's engine constantly fights gravity B) there is no gravity in orbit C) inertia supplies sideways motion while gravity bends it into a closed loop, with no friction to remove energy D) the spacecraft is beyond Earth's reach

Question 4

In its most general form, Newton's second law is best written:

A) $F = ma$ B) $F = mv$ C) $F = dp/dt$ D) $F = \mu/r^2$

Question 5

Why must a rocket be described by the momentum form of the second law rather than simply $F = ma$?

A) rockets move too fast for $F = ma$ B) a rocket's mass changes as it burns propellant C) gravity is stronger in space D) $F = ma$ only works on Earth

Question 6

The thrust of a rocket is given by:

A) $T = \dot m_p / v_e$ B) $T = \dot m_p\, v_e$ C) $T = v_e / \dot m_p$ D) $T = m\,v_e$

Question 7

In a vacuum, the only way for a spacecraft to change its velocity is to:

A) push against the surrounding space B) push against sunlight C) throw mass in the opposite direction D) use a propeller

Question 8

A rocket works in vacuum because it pushes against:

A) the air B) its own expelled propellant C) the launch pad D) Earth's magnetic field

Question 9

Conservation of momentum states that, with no external force, the total momentum of a system:

A) always increases B) always decreases C) stays constant D) equals zero

Question 10

Conservation of momentum is most directly a consequence of Newton's:

A) first law B) second law C) third law D) law of gravitation

Question 11

The gravitational parameter $\mu$ of a body is defined as:

A) $G/M$ B) $GM$ C) $M/G$ D) $g_0 R$

Question 12

The acceleration gravity gives a falling spacecraft is $a = \mu/r^2$, which does not depend on the spacecraft's own mass because:

A) spacecraft are very light B) the mass cancels: gravitational force is proportional to $m$, and $a = F/m$ C) space has no gravity D) $\mu$ already includes the spacecraft's mass

Question 13

Escape velocity from a body of gravitational parameter $\mu$ and radius $R$ is:

A) $\sqrt{\mu/R}$ B) $\sqrt{2\mu/R}$ C) $2\mu/R$ D) $\mu/R^2$

Question 14

Earth's escape velocity from the surface is about:

A) $7.8\ \text{km/s}$ B) $9.4\ \text{km/s}$ C) $11.2\ \text{km/s}$ D) $25\ \text{km/s}$

Question 15

Escape velocity is related to the circular orbital velocity at the same radius by a factor of:

A) $2$ B) $\sqrt{2}$ C) $1/2$ D) $\pi$

Question 16 (True/False, justify)

"There is no gravity at the International Space Station, which is why the astronauts float." True or false? Justify with the approximate value of $g$ there.

Question 17 (True/False, justify)

"A heavier spacecraft needs a higher speed to escape a planet than a lighter one." True or false? Explain in one sentence.

Question 18 (True/False, justify)

"A rocket with more thrust standing on the pad is producing that thrust by pushing on the ground." True or false? Say what it actually pushes on.

Question 19 (Short answer)

An engine expels $250\ \text{kg/s}$ of propellant at an effective exhaust velocity of $3{,}000\ \text{m/s}$. Compute the thrust, showing units.

Question 20 (Short answer)

In one or two sentences, explain why the weightlessness experienced in orbit is called "free fall" rather than "the absence of gravity," and connect it to why an orbit does not decay in vacuum.

Answer Key

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