HomeConcept libraryMechanicsGravity and Orbits

MechanicsIntroStarter track

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.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Drag the probe to any point in the bounded field region. The inward field arrow, force arrow, scan-line graphs, compare state, and worked examples all read the same live mass-and-distance model.

Graphs

Switch graph views without breaking the live stage and time link.

Field components on the scan line

Shows how the inward field splits into horizontal and vertical components along the current horizontal scan line.

probe x-position (m): -3.2 to 3.2gravitational field component: -2 to 2

g_xg_y

Hover or scrub to link the graph back to the stage.probe x-position (m) / gravitational field component

Controls

Adjust the physical parameters and watch the motion respond.

Source mass

M

2 kg

Changes the mass creating the field, so both the inward field and the force scale with M at every point.

Probe x-position

x_{p}

1.6 m

Moves the probe left or right across both the stage and the linked scan graphs.

Probe y-position

y_{p}

1.2 m

Moves the probe to a new horizontal scan line so the graphs sample a different field slice.

Probe mass

m_{test}

1 kg

Changes only the force on the probe. It does not change the gravitational field created by the source mass.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 1

Field direction comes first: the gravitational field always points toward the source mass, not away from it.

Try this

Drag the probe around the source and keep the teal field arrow visible. The direction should keep rotating inward toward the center.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

M

Source mass

2 kg

Changes the mass creating the field, so both the inward field and the probe force scale directly with M at every point.

Graph: Field components on the scan lineGraph: Field and force magnitudesOverlay: Field gridOverlay: Field vectorOverlay: Distance rings

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use the current prompt as a compact investigation cue. Each one points at a pattern the stage and graphs already show in the live source-mass model.

ObservationPrompt 1 of 1

Graph: Field components on the scan line

Field direction comes first: the gravitational field always points toward the source mass, not away from it.

Try this

Drag the probe around the source and keep the teal field arrow visible. The direction should keep rotating inward toward the center.

Why it matters

This is the field version of gravity, so direction should be read geometrically before you start thinking about force magnitude.

Control: Probe x-positionControl: Probe y-positionGraph: Field components on the scan lineOverlay: Field gridOverlay: Field vectorEquation

x_{p}

Equation

y_{p}

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

5 visible

Overlay focus

Field grid

Shows a coarse sample of the inward field direction across the stage.

What to notice

Every arrow points toward the source mass, but the arrows shorten quickly as the distance grows.

Why it matters

It makes gravitational field direction a whole-region pattern instead of something you only infer from one probe point.

Control: Source massControl: Probe x-positionControl: Probe y-positionGraph: Field components on the scan lineGraph: Field and force magnitudesEquation

M

Equation

x_{p}

Equation

y_{p}

Challenge mode

Tune the same one-mass field into compact targets. The checks read the live inverse-square model instead of a detached answer key.

0/2 solved

TargetCore

4 of 7 checks

Quarter the field by distance

Starting from Axis near, move the probe to the doubled-distance case on the same horizontal line so the field magnitude falls to about one quarter of the 1 m reference.

Graph-linkedGuided start2 hints

Suggested start

Keep the source mass and probe mass fixed. Use the rings and the response graph together.

Pending

Open the Field and force magnitudes graph.

Field components on the scan line

Matched

Keep the Distance rings visible.

Matched

Keep the Graph scan line visible.

Pending

Keep probe x between 1.95 m and 2.05 m.

1.6 m

Pending

Keep probe y between -0.05 m and 0.05 m.

1.2 m

Matched

Keep field magnitude between 0.48 and 0.52.

0.5

Matched

Keep force magnitude between 0.48 and 0.52.

0.5

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

A source mass of 2 kg at the origin produces a gravitational field of (-0.4, -0.3) at the probe (1.6 m, 1.2 m). The probe is 2 m from the source, so |g| is 0.5 in field units and points down-left. A test mass of 1 kg feels a force of 0.5 in force units toward the source. On the same radial line, doubling the distance would reduce the field strength to about one quarter.

Equation detailsDeeper interpretation, notes, and worked variable context.

Source-to-probe distance

The probe distance from the source mass sets the field strength in the one-mass lab.

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

x_{p}

Probe x-position 1.6 m

y_{p}

Probe y-position 1.2 m

Field from one source mass

The gravitational field points toward the source mass and weakens with distance.

g = - G \frac{M}{r ^{3}} r

This bounded lab fixes G = 1 in the displayed units so the readouts emphasize direction and scaling.

M

Source mass 2 kg

x_{p}

Probe x-position 1.6 m

y_{p}

Probe y-position 1.2 m

Inverse-square trend

Doubling source mass doubles the field, while doubling distance reduces it to one quarter.

∣ g ∣ = G \frac{M}{r ^{2}}

M

Source mass 2 kg

Force on the probe mass

The probe mass scales the force it feels without creating a second field in this model.

F = m_{test} g

m_{test}

Probe mass 1 kg

Progress

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Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

Starter track

Step 1 of 50 / 5 complete

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

This concept is the track start.

See next concept

Short explanation

What the system is doing

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.

Live gravity checks

Solve the exact state on screen.

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.

Live valuesFollowing current 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.

Prediction prompt

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

Check your reasoning

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?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

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.

Bridge this into orbits

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Energy viewMechanics

Gravitational Fields

See each variable before you move it.

Field grid

Quarter the field by distance

Gravity and Orbits

What the system is doing

Solve the exact state on screen.

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

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

Keep moving through the concept map.

Gravitational Potential and Potential Energy

Circular Orbits and Orbital Speed

Escape Velocity