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Concept module

Gravitational Potential and Potential Energy

See one source mass create a negative potential well, compare how potential and potential energy change with distance, and connect the downhill slope of phi to the gravitational field on the same live model.

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Starter track

Step 2 of 50 / 5 complete

Gravity and Orbits

Earlier steps still set up Gravitational Potential and Potential Energy.

1. Gravitational Fields2. Gravitational Potential and Potential Energy3. Circular Orbits and Orbital Speed4. Kepler's Third Law and Orbital Periods+1 more steps

Previous step: Gravitational Fields.

Start from track beginning

Why it behaves this way

Explanation

Gravitational potential describes how much gravitational potential energy one kilogram of probe mass would have at a point relative to zero at infinity. For one source mass in this bounded lab, the potential is always negative, becomes more negative near the source, and rises back toward zero as the probe moves farther away.

This concept keeps the same one-source geometry as Gravitational Fields so the potential map, contour circles, live readout, scan graphs, worked examples, prediction prompts, and challenge checks all stay tied to one honest model. The field is not a separate rule pasted on top afterward: along the current scan line, the horizontal field component is the downhill slope of the potential graph.

Key ideas

01Gravitational potential phi is a scalar set by the source mass and distance, not by the probe mass.

02With zero defined at infinity, one isolated source mass produces negative potential everywhere in this bounded lab, and the well gets deeper as r gets smaller.

03Potential energy uses U = m_test phi, so changing only the probe mass rescales U and the force without changing phi or the source-set field.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Solve the current probe state directly from the live controls. The same source mass, probe location, and probe mass already on screen drive the map, contour circles, scan graphs, and the substitutions below.

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Frozen valuesUsing frozen parameters

For the current source mass and probe position, what gravitational potential exists at the probe relative to zero at infinity?

M

Source mass

2 kg

x_{p}

Probe x-position

1.6 m

y_{p}

Probe y-position

1.2 m

1. Measure the live source-to-probe distance

From the origin to the probe,

r = s q r t x_{p}^{2} + y_{p}^{2} = 2, ma t h r m m

2. Apply the one-mass potential relation

With

G = 1

in the displayed units,

p hi = - M / r = - 2/2

3. Compute the current potential

That gives

p hi = - 1

at the probe.

Gravitational potential

p hi = - 1

Farther from the source, the potential has risen closer to zero, but it stays negative because zero is defined at infinity in this model.

Potential-well checkpoint

Start from Axis 1 m, then move the probe to Axis 2 m while keeping the source mass and probe mass fixed. Before you drag, predict what should happen to phi, U, and |g|.

Make a prediction before you reveal the next step.

Say the ratios first: which quantities should halve in magnitude, and which should fall to one quarter?

Check your reasoning against the live bench.

At twice the distance, the gravitational potential and the potential energy both drop to about half their original magnitude while staying negative, and the field magnitude drops to about one quarter.

For one source mass,

p hi p r o pt o - 1/ r

and

U = m_{t e x t t es t} p hi

, so doubling

r

halves both potential magnitudes. But

∣ v ec g ∣ p r o pt o 1/ r^{2}

, so the field falls more steeply to one quarter.

Common misconception

A negative gravitational potential means gravity is pointing outward or "backward."

The negative sign comes from the reference choice that potential is zero infinitely far away. Closer to the source, the potential is lower than that reference, so phi is negative.

The field still points inward because gravity follows the downhill direction of the potential landscape. A more negative potential means the probe sits deeper in the same inward gravity well, not that the force flips direction.

Quick test

Variable effect

Question 1 of 5

Answer from the live potential-well logic, not from detached formulas. Each question asks what the map, contours, or scan graphs must mean about gravitational potential and energy.

A probe moves from 1 m to 2 m away from one source mass on the same axis while the masses stay fixed. What must happen to the gravitational potential?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows one source mass fixed at the origin, a movable positive probe mass in a bounded two-dimensional gravity well, and optional overlays for a potential map, equal-potential contour circles, equal-distance rings, the local field arrow, the force arrow on the probe mass, and the horizontal scan line used by the graphs.

Dragging the probe changes the sampled location directly on the stage. The focused probe handle also responds to arrow keys for small position changes, and sliders provide the same controls for source mass, probe position, and probe mass.

Very near the source mass, the display uses a minimum sampling radius so the well depth, arrows, and graphs stay finite and readable. This keeps the visualization bounded while preserving the correct trend that potential becomes more negative and the field grows rapidly near the source.

Graph summary

The potential-energy-scan graph plots gravitational potential and the chosen probe's potential energy along the current horizontal scan line. Hovering the graph previews the same x-location on the stage.

The field-link graph plots the horizontal gravitational field component and the matching negative slope of the potential graph along that same scan line. Changing the probe mass rescales the energy curve, but the field-link graph remains a source-mass and geometry readout.

Connect fields, energy, and orbits

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