Astronauts aboard the International Space Station (ISS), orbiting at about 400 km altitude, experience apparent weightlessness. What is the correct explanation?
AAt 400 km altitude, Earth's gravity is too weak to affect the astronauts measurably
BThe vacuum of space prevents gravitational force from being transmitted to the astronauts
CThe ISS and everything inside it are in free fall together, so astronauts experience no normal force from any surface
DThe astronauts' mass decreases in orbit, reducing the gravitational force to near zero
At 400 km, g is still about 90% of its surface value — gravity absolutely reaches the ISS. Weightlessness occurs because the station and everything inside it are all falling together toward Earth at the same rate. There is no surface pressing up on the astronauts, so they feel no normal force — the sensation of weight. This is the same physics as a falling elevator: all objects inside accelerate together and feel 'weightless.' This directly addresses the misconception that gravity 'turns off' in space; it merely goes undetected because there is nothing to push back against.
Question 2 Multiple Choice
Why do a feather and a bowling ball fall at the same rate in a vacuum (ignoring air resistance)?
AGravity exerts the same force on all objects regardless of mass
BThe more massive object experiences a larger gravitational force, but also has proportionally more inertia — these effects cancel exactly, leaving the same acceleration
CNear Earth's surface, the gravitational constant G adjusts to equalize acceleration across different masses
DGravity is a property of the gravitational field, so object mass is irrelevant to the resulting acceleration
From F = GM_E m / R_E², a more massive object experiences a larger gravitational force. But from Newton's second law, a = F/m. Substituting: a = GM_E m / (R_E² · m) = GM_E / R_E². The mass m cancels completely — heavier objects are pulled harder but are harder to accelerate in exactly equal measure. This is not a coincidence but a consequence of the fact that gravitational mass and inertial mass are equal (the equivalence principle). Option A is wrong: gravity does exert a larger force on the heavier object.
Question 3 True / False
The gravitational acceleration at the Moon's surface is about 1/6 of Earth's because the Moon is approximately 6 times farther from Earth than the Moon's own surface is from Earth's center.
TTrue
FFalse
Answer: False
The Moon's surface gravitational acceleration is g_Moon = GM_Moon / R_Moon², determined by the Moon's own mass and radius — not its distance from Earth. The Moon's mass is about 1/81 of Earth's and its radius is about 1/3.7 of Earth's. Plugging in: g_Moon ≈ (1/81)/(1/3.7)² × 9.8 ≈ 1.6 m/s², roughly 1/6 of g_Earth. The Moon's distance from Earth is irrelevant to what you feel standing on the Moon's surface.
Question 4 True / False
The gravitational force Earth exerts on the Moon is greater than the force the Moon exerts on Earth, because Earth's mass is much larger.
TTrue
FFalse
Answer: False
By Newton's third law, every force has an equal and opposite reaction. The gravitational force Earth exerts on the Moon and the force the Moon exerts on Earth are an action-reaction pair — they are exactly equal in magnitude and opposite in direction. Earth's greater mass means it accelerates much less (a = F/m), but the force magnitudes are identical. This is also visible in the universal law: F = Gm₁m₂/r² is symmetric in the two masses, so swapping which body is 'exerting' the force gives the same numerical result.
Question 5 Short Answer
Derive the expression for surface gravitational acceleration g from Newton's universal law F = Gm₁m₂/r², and explain why this derivation shows that all objects fall at the same rate regardless of mass.
Think about your answer, then reveal below.
Model answer: For an object of mass m at Earth's surface: the gravitational force is F = GM_E m / R_E². By Newton's second law, F = ma, so GM_E m / R_E² = ma. The object's mass m cancels from both sides, giving a = GM_E / R_E² = g. Because m cancels, the acceleration is the same for every mass — a feather and a bowling ball accelerate identically under gravity alone.
The cancellation of m is the key step, and it relies on a deep physical fact: gravitational mass (how strongly gravity pulls on an object) and inertial mass (how much it resists acceleration) are the same quantity. This equivalence is the foundation of general relativity. Newton noticed it empirically; Einstein elevated it to a fundamental principle.