Earth vs Moon Free-Fall Simulator – Gravity, Weight & Projectiles

Earth vs Moon: the physics of falling objects

Does a heavy ball fall faster than a feather? Drop them side by side on Earth and on the Moon and find out. Then weigh yourself on both, and launch a ball sideways to see how gravity shapes its path.

Under 15If you drop a heavy ball and a light ball together, which lands first? Most people guess the heavy one, but without air they land at the same time! On Earth a feather falls slowly only because the air holds it up. The Moon has no air, so there a feather drops like a stone. Gravity on the Moon is about 6 times weaker, so everything falls more slowly and you'd weigh much less.

20+ · going deeperWith quadratic drag, m dv/dt = mg − ½ρC_dAv², the velocity approaches the terminal speed v_t = √(2mg/(ρC_dA)) as v(t) = v_t tanh(gt/v_t). The equality of inertial and gravitational mass (tested to 1 part in 10¹⁵ by the MICROSCOPE satellite) is the weak equivalence principle, the foundation of general relativity. g also varies with height (g ∝ 1/r²), latitude and local geology; the constant-g model is accurate to about 0.3% over 10 km of altitude.

1 · Drop test 2 · Compare gravity 3 · Motion graphs 4 · Mass vs weight 5 · Projectiles 6 · Predict 7 · Apollo 15

1Drop test

🌍 Eartht = 0.00 s

🌕 Moont = 0.00 s

Objects to drop

Drop height:

Right-hand world

Options Air resistance on Earth Slow motion (¼ speed)

The Moon has no air, so there is never drag there. On Earth with air resistance off, objects fall as if in a vacuum. With it on, each object feels a drag force ½ρC_dAv², using rough real values for its size and shape, so the feather drifts down while the metal ball barely notices the air.

2Compare gravity

Near a planet's surface, everything in free fall speeds up at the same rate g, whatever its mass. Released from rest, taking downward as positive:

v = g t

s = ½ g t²

t_fall = √(2h / g)

Why doesn't mass matter? A heavier object is pulled harder (W = mg), but it is also harder to speed up (a = F/m). The two effects cancel: a = mg/m = g.

3Motion graphs

Live during each drop, for the stone: ● Earth ● Moon. In ideal free fall the acceleration is a flat line (constant g), velocity is a straight line (slope g) and distance is a parabola.

4Mass vs weight

Your mass:

Mass is how much matter you contain, measured in kilograms. It is the same everywhere. Weight is the force of gravity on you, W = m g, measured in newtons. It changes from world to world.

5Projectile motion

Launch speed (horizontal):

Cliff height:

Gravity

Show velocity components

Time in the air √(2h/g)

Range R = u·t

Landing speed

Horizontally there is no force (no air), so the ball keeps its launch speed u: x = u t. Vertically it falls exactly like a dropped ball: y = ½ g t². The two motions are independent: a ball dropped straight down from the same height lands at the same moment. The dots are drawn every 0.25 s; their equal horizontal spacing shows the constant horizontal speed.

6Prediction challenge

Predict first, then press Test it to set up the drop and watch.

7The Apollo 15 hammer and feather

On 2 August 1971, astronaut David Scott stood on the Moon holding a 1.32 kg geological hammer and a 30 g falcon feather, and dropped them together from about 1.6 m. With no air to slow the feather, they hit the ground at the same moment, just as Galileo had predicted. On Earth the feather would flutter down far behind, but only because of the air, not because gravity pulls it differently.

(the metal ball plays the hammer)