Preview

Gravity Force Lab: Basics

Q: If you triple the distance between two masses, how does gravity change?

F ∝ 1/r² → tripling r reduces F by factor 9.

Q: Why do you not feel gravitational attraction to the person next to you?

G is tiny (10⁻¹¹); typical person masses give force ~ 10⁻⁷ N.

Q: How does surface gravity g relate to Newton's Law?

At Earth's surface: g = GM_Earth/R_Earth².

Discover how mass and distance affect gravitational force

The story goes that Newton watched an apple fall and asked the outrageous question: does the same pull reach all the way up to the Moon? It does — the apple and the Moon are both falling toward Earth, one hitting the grass, the other endlessly missing because it moves sideways fast enough. One law runs both: F = Gm₁m₂/r². Now the part almost everyone gets wrong. Earth is eighty-one times the Moon's mass — surely Earth pulls harder on the Moon than the Moon pulls back? It does not, and cannot: gravitation is one interaction with two ends, and both ends carry exactly the same force — about 1.986×10²⁰ newtons each way, enough to drag Earth's oceans into tides. Right now you are pulling the entire planet up toward you precisely as hard as it pulls you down; Earth just wears the same force differently, because acceleration is force divided by mass. In this lab the two amber arrows will refuse to differ no matter how you slide the masses apart, the force readout will dive by the square as you stretch the distance, and the same law will hand you Earth's surface gravity, the Moon's 27-day month, and the 11.2 km/s it takes to leave — all from three sliders and one line of seventeenth-century mathematics.

What you'll be able to do

State Newton's third law for gravitation with the sim's own arrows: the force on each body is the same single F = Gm₁m₂/r² — 1.986×10²⁰ N between Earth and Moon at defaults — and doubling either mass doubles that one number while both arrows grow together, never apart
Apply the inverse-square law quantitatively: doubling the separation 3.84 → 7.68 (×10⁸ m) cuts the force to a quarter (1.986×10²⁰ → 4.965×10¹⁹ N), halving it to 1.92 quadruples the force to 7.944×10²⁰ N — and even at the slider's far end (10×10⁸ m) the force is still 2.929×10¹⁹ N, never zero
Read the whole solar system out of one law: surface gravity g = GM/R² (9.82 m/s² with Earth's numbers), orbital speed v = √(GM/r) (1.02 km/s at the Moon's distance), escape velocity √(2GM/R) (11.18 km/s), and the orbital period 2πr/v (27.41 days at defaults — the sidereal month, straight from the panel)

Formulas

F = G\frac{m_1 m_2}{r^2}

Newton's Law of Universal Gravitation (G = 6.674×10⁻¹¹ N·m²/kg²)

g = \frac{GM}{R^2}

Surface gravitational field strength

v_{orbit} = \sqrt{\frac{GM}{r}}

Circular orbital speed at radius r

v_{esc} = \sqrt{\frac{2GM}{R}}

Escape velocity from the surface

T^2 = \frac{4\pi^2}{GM}r^3

Kepler's Third Law — orbital period vs radius

Make a prediction

Default Earth-Moon state: Mass 1 = 5.97×10²⁴ kg, Mass 2 = 7.35×10²² kg, distance 3.84×10⁸ m — the force row reads 1.986×10²⁰ N and the two amber arrows are exactly equal. Now double Mass 2 (the small one) to 14.70×10²² kg. What happens?

No grading here — commit to a guess, then scroll down and test it yourself.

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Explore

Replay the gate live: slide Mass 2 from 7.35 to 14.70 and watch the force row double 1.986×10²⁰ → 3.972×10²⁰ N while both arrows grow in lockstep — then yank Mass 1 instead and see the same doubling. Neither arrow ever outgrows the other. One interaction, two equal ends.
Walk the inverse-square staircase: from 3.84, double the distance to 7.68 — force quarters to 4.965×10¹⁹ N. Come back and halve it to 1.92 — force quadruples to 7.944×10²⁰ N. Twice the road, a quarter the pull; on the chart station the F-vs-r curve dives as 1/r², never a straight line.
Tour the presets and read the solar system off one law: Earth-Moon clocks T = 27.41 days (the sidereal month, straight from 2πr/√(GM/r)); Orbital Mechanics at 2.0×10⁸ m runs closer, faster, shorter — 1.41 km/s and 10.30 days; Surface Gravity pins g = 9.82 m/s² and escape at 11.18 km/s from the same M and R.
Drag the distance to its far end, 10×10⁸ m, and read the force: 2.929×10¹⁹ N — thinned four-hundred-fold from the closest approach, but nowhere near zero. Gravity never switches off; astronauts float because they fall around Earth, not because they've escaped its pull. The faint field lines around the planet stay put through all of it — the field is always there, only its grip thins.

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Check

Did the lab agree with you?

Your prediction

You skipped the prediction — jump back to the preview and commit to a guess first; the comparison is the whole point.

Answer: The one force doubles to 3.972×10²⁰ N and BOTH arrows grow together, still exactly equal — F = Gm₁m₂/r² is one interaction with two equal ends

F = Gm₁m₂/r² is symmetric in the two masses: double either one and the single product m₁m₂ doubles, so the one force doubles — 1.986×10²⁰ → 3.972×10²⁰ N on the panel. And it is one force: Newton's third law says the pull of A on B and the pull of B on A are the same interaction seen from its two ends, 'equal but opposite' in OpenStax's exact words. That is why the sim draws both arrows with one shared length at all times and shows a single force row — there is only one magnitude to show. Option B is the classic 'dominance' misconception the Force Concept Inventory's third-law cluster is built to catch: the heavier body does not pull harder, it only responds less (a = F/m — Earth accelerates 81× less under the same force). Option C confuses the force with its visible effect: the product m₁m₂ weights both masses equally, so the 'small' slider moves the force exactly as powerfully, ratio for ratio, as the big one.

Quiz (0/3)

If you triple the distance between two masses, how does gravity change?

Why do you not feel gravitational attraction to the person next to you?

How does surface gravity g relate to Newton's Law?

You can now

State Newton's third law for gravitation with the sim's own arrows: the force on each body is the same single F = Gm₁m₂/r² — 1.986×10²⁰ N between Earth and Moon at defaults — and doubling either mass doubles that one number while both arrows grow together, never apart
Apply the inverse-square law quantitatively: doubling the separation 3.84 → 7.68 (×10⁸ m) cuts the force to a quarter (1.986×10²⁰ → 4.965×10¹⁹ N), halving it to 1.92 quadruples the force to 7.944×10²⁰ N — and even at the slider's far end (10×10⁸ m) the force is still 2.929×10¹⁹ N, never zero
Read the whole solar system out of one law: surface gravity g = GM/R² (9.82 m/s² with Earth's numbers), orbital speed v = √(GM/r) (1.02 km/s at the Moon's distance), escape velocity √(2GM/R) (11.18 km/s), and the orbital period 2πr/v (27.41 days at defaults — the sidereal month, straight from the panel)