Physics · Gravity and Orbits

Gravitational Fields

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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: Gravitational Potential and Potential EnergyTurn the same field idea into an energy view.

Key takeaway

A gravitational field is force per kilogram at a point, so it exists before you choose a particular probe mass.
Around one source mass, the field points inward and its magnitude follows the inverse-square rule |g| = GM/r^2.
Changing probe mass changes the force F = m_test g, but it does not change the field created by the source mass and distance.

Common misconception

A heavier probe does not make the field stronger in this bounded model. It feels more force because the same field is multiplied by a larger probe mass.

At a point, the gravitational field is set by the source mass and the source-to-probe distance, not by the probe mass.

Bridge this into orbits

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Energy viewGravity and Orbits

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.

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.

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Reference and support

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Equation snapshotField from one source mass · Inverse-square trendShow 3 equations

Read these in order: the source creates the inward field, distance gives the inverse-square size, and probe mass converts field into force.

Field from one source mass
$g = - G \frac{M}{r ^{3}} r$
The minus sign shows that the field points inward toward the source mass.
Inverse-square trend
$∣ g ∣ = G \frac{M}{r ^{2}}$
At fixed source mass, doubling distance reduces the field to one quarter.
Force on the probe mass
$F = m_{test} g$
Probe mass converts the field into force without changing the field itself.

Why it behaves this way

Explanation

A gravitational field tells you the force per kilogram that a tiny test mass would feel at a point. The field exists because of the source mass, whether or not you place a probe there, so field comes before force.

In this lab one source mass sits at the origin, so every live field arrow points inward toward it. Moving the probe changes distance and direction, changing the source mass changes the field itself, and changing the probe mass changes only the force response through F = m_test g. That keeps the stage, graphs, and equations tied to one live model.

Key ideas

01The source mass creates the field. At one chosen point, the probe mass does not change the field direction or strength.

02For one source mass, the field points toward the source and its magnitude follows the inverse-square rule |g| = GM/r^2, so doubling distance gives one quarter of the field.

03The probe mass turns the existing field into force through F = m_test g, so changing only the probe mass rescales force without rewriting the field.

Worked examples

Solve the live field

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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 the field vector from the live distance and inward direction. Then use that same field to calculate the force on the chosen probe mass, keeping the field-versus-force distinction explicit.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current source mass and probe position, what gravitational field vector acts at the probe?

M

Source mass

2 kg

x_{p}

Probe x-position

1.6 m

y_{p}

Probe y-position

1.2 m

1. Find the source-to-probe distance

From the origin to the probe,

r = x_{p}^{2} + y_{p}^{2} = 2 m

, so

r^{2} = 4

and

r^{3} = 8

2. Substitute into the one-source field rule

With this bounded lab using

G = 1

in the displayed units,

g = - M r / r^{3} = - 2 (1.6, 1.2) /8

3. Resolve the field components

That gives

g_{x} = - 0.4

and

g_{y} = - 0.3

, so the inward field magnitude is

∣ g ∣ = 0.5

Field at the probe

g = (- 0.4, - 0.3), ∣ g ∣ = 0.5

Off the axis the inward pull splits into horizontal and vertical components, but the net field still points directly toward the source mass.

Quick test

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Accessibility

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The simulation shows one source mass fixed at the origin, a movable probe mass in a bounded two-dimensional region, and optional overlays for a coarse field grid, the live field arrow at the probe, the force arrow on the probe, equal-distance rings, and the horizontal scan line used by the graphs.

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

Very near the source, the display uses a minimum sampling radius so the drawn arrows and graphs stay finite and readable. This keeps the visualization bounded while preserving the correct trend that field strength rises sharply near the source.

Graph summary

The field-components graph plots the horizontal and vertical gravitational field components along the current horizontal scan line. Hovering or scrubbing the graph previews the same x-location on the stage.

The strength-response graph plots field magnitude and probe-force magnitude along that same scan line. Changing probe mass rescales only the force curve, while changing source mass or distance changes the field curve itself.

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Gravity and Orbits

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