HomeConcept libraryPhysicsMechanicsGravity and Orbits

Concept module

Gravitational Fields

See how one source mass creates an inward gravitational field, how source mass and distance set the field strength, and how a probe mass turns that field into force without changing the field itself.

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Starter track

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Gravity and Orbits

Next after this: 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

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Why it behaves this way

Explanation

A gravitational field tells you what one kilogram of probe mass would feel at a point before you imagine any actual probe there. In this bounded lab, one source mass sits at the origin, the field always points inward toward that mass, and the size of the field follows the inverse-square distance trend.

The same source mass, probe position, and probe mass drive the stage arrows, scan graphs, compare mode, prediction prompts, worked examples, challenge checks, and quick test. That keeps field direction, field strength, and force on a test mass attached to one honest live model instead of drifting into separate rules.

Key ideas

01The source mass creates the gravitational field. The probe mass does not decide the field direction or strength at that location.

02The gravitational field from one mass points toward the source and grows with source mass while dropping quickly with distance.

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

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Solve the current probe state directly from the live controls. The substitutions use the same source mass, probe position, and probe mass now on screen, and the applied examples keep the graph and the stage tied to that same state.

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View plans

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. Measure the live 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. Apply the one-mass field relation

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 current field components

That gives

g_{x} = - 0.4

and

g_{y} = - 0.3

, so the inward field magnitude is

∣ g ∣ = 0.5

Gravitational field

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.

Inverse-square checkpoint

Start from Axis near, then move the probe to twice the distance on the same horizontal line. Before you drag, predict what should happen to the inward field magnitude and to the force if the probe mass stays fixed.

Make a prediction before you reveal the next step.

Say the ratio first: should the field become half, one quarter, or unchanged?

Check your reasoning against the live bench.

At twice the distance on the same radial line, the field magnitude and the force both drop to about one quarter of their original values.

For one source mass,

∣ g ∣ \propto 1/ r^{2}

. Doubling

r

multiplies the denominator by four, so the field drops to one quarter. With the same probe mass,

∣ F ∣ = m_{test} ∣ g ∣

falls by the same factor.

Common misconception

A heavier probe mass makes the gravitational field at that point stronger.

The gravitational field at a point is set by the source mass and the source-to-probe distance. The probe mass is only responding to that field.

Making the probe mass larger increases the force because F = m_test g, but the inward field arrow and the field graph stay the same until you change the source mass or the probe position.

Quick test

Reasoning

Question 1 of 4

Answer from field logic, not from isolated formulas. Each question asks what the stage and graphs must mean about field direction, inverse-square scaling, or force on the probe mass.

A probe is directly above the source mass. Which description best matches the gravitational field there?

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

Accessibility

The simulation shows one source mass fixed at the origin, a movable probe mass in a bounded two-dimensional field region, and optional overlays for a coarse field grid, the live field arrow at the probe, the force arrow on the probe mass, 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 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 field display uses a minimum sampling radius so the drawn arrows and response graphs stay finite and readable. This keeps the visualization bounded while preserving the correct trend that gravitational field strength grows rapidly near the source.

Graph summary

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

The strength-response graph plots the field magnitude and the probe-force magnitude along that same scan line. Changing the probe mass rescales the force curve, but the field curve remains a source-mass and distance readout.

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