Physics · Gravity and Orbits

Gravitational Potential and Potential Energy

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Circular Orbits and Orbital SpeedUse the same gravity model to set a circular-orbit speed.

Key takeaway

Gravitational potential is a scalar well depth set by source mass and distance, with zero defined at infinity in this model.
Potential energy is U = m_test phi, so changing only the probe mass changes U without changing the potential well.
Doubling distance halves the magnitude of phi and U for a fixed probe, while the field magnitude falls to one quarter.
The gravitational field points downhill on the potential landscape, matching the negative slope of phi on a scan line.

Common misconception

A negative potential does not mean gravity points outward or disappears. It means the point sits below the zero-at-infinity reference; the field still points downhill toward the source.

The negative sign comes from the reference choice φ = 0 at infinity. Closer to the source, the point sits lower in the gravitational well, so φ is negative.

Connect fields, energy, and orbits

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Orbit bridgeGravity and Orbits

Circular Orbits and Orbital Speed

See why a circular orbit needs the right sideways speed, how gravity supplies the centripetal acceleration, and how source mass and radius together set orbital speed and period on one bounded live model.

Escape thresholdGravity and Orbits

Escape Velocity

Launch outward from one bounded gravity source and see how source mass, launch radius, and total specific energy decide whether the object escapes or eventually returns.

Compare potential languageElectricity

Electric Potential

Map how source-charge sign and distance shape electric potential, read voltage as a difference across one shared horizontal scan line, and connect the downhill slope of V to the electric field.

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Reference and support

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Equation snapshotPotential from one source mass · Potential energy of the probe massShow 3 equations

Read these as one chain: the source sets the potential well, the probe mass converts that well into U, and the field points downhill on the same landscape.

Potential from one source mass
$p hi = - G df r a c M r$
With zero defined at infinity, the potential from one source mass is negative and becomes more negative as r gets smaller.
Potential energy of the probe mass
$U = m_{t e x t t es t} p hi$
Probe mass turns the source-set potential into potential energy without changing the potential itself.
Field from potential
$v ec g = - nab l a p hi$
The field points downhill on the potential landscape, from higher φ toward lower φ.

Why it behaves this way

Explanation

Gravitational potential φ tells you the gravitational potential energy per kilogram at a point, measured relative to zero at infinity. For one source mass in this bounded lab, φ is negative everywhere, becomes more negative near the source, and rises back toward zero as the probe moves farther away.

This concept uses the same one-source geometry as Gravitational Fields, so the well map, contour circles, live readout, and scan graphs all describe the same state. That lets you compare three linked ideas without switching models: φ is the well depth, U = m_test φ is the probe's potential energy, and the field points downhill on the same potential landscape. Along the current scan line, the horizontal field component matches the negative slope of the potential graph.

Key ideas

01Gravitational potential φ is a scalar set by source mass and distance. It tells you how deep the well is at a point, not which way the force points.

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

03Potential energy uses U = m_test φ, so changing only the probe mass rescales U, while the field comes from how φ changes with position.

Worked examples

Solve the live well

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the current source mass, probe position, and probe mass as evidence. First calculate φ from the live distance to the source. Then use that same φ to find the probe's potential energy and compare the result with the well map and the field-slope graph.

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Example 1 of 2

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. Find the live 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. Substitute into φ = -M/r

With

G = 1

in the displayed units,

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

3. Read the potential

That gives

p hi = - 1

at the probe.

Potential at the probe

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.

Quick test

Loading saved test state.

Accessibility

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

Dragging the probe changes the sampled location directly on the stage. The same location is used by the readout and the graph cursor, so the map, the arrows, and the graphs always describe the same point.

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.

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Gravity and Orbits

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