HomeConcept libraryPhysicsMechanicsGravity and Orbits

Physics MechanicsIntermediateStarter track

Concept module

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.

Interactive lab

Loading the live simulation bench.

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Jump to a named bench state or copy the one you are looking at now. Shared links reopen the same controls, graph, overlays, and compare context.

Saved setups

Premium keeps named exact-state study setups in your account while stable concept links stay public below.

Checking saved setup access.

This concept can keep using stable links while the saved-setups capability resolves for this browser.

Copy current setup

Stable concept and section links stay public below while exact-state setup sharing stays behind premium.

Stable links

Starter track

Step 5 of 50 / 5 complete

Gravity and Orbits

Earlier steps still set up Escape Velocity.

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: Kepler's Third Law and Orbital Periods.

Start from track beginning

Why it behaves this way

Explanation

Escape velocity is the minimum outward launch speed from one chosen radius that makes the total specific energy reach zero. Above that threshold, gravity still pulls inward and slows the launch, but there is no finite turnaround radius. Below it, even a very high outward trip is still bound and eventually returns.

This bounded lab keeps one source mass, one launch radius, one speed factor, one live radial path, and the linked radius, speed-threshold, and specific-energy graphs on the same state. The local circular-speed comparison stays visible too, so going far away is not confused with escape or with circular orbit balance.

Key ideas

01Escape is an energy threshold, not a place where gravity turns off.

02With displayed units using G = 1, the escape speed from radius r_0 is v_esc = sqrt(2M/r_0), so a heavier source raises the threshold while a larger launch radius lowers it.

03A launch can be faster than the local circular speed and still remain bound if it stays below escape speed and keeps negative total specific energy.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the same source mass, launch radius, speed factor, live time, and graphs already on screen.

Premium unlocks saved study tools, exact-state sharing, and the richer review surfaces that support this guided flow.

View plans

Frozen valuesUsing frozen parameters

For the current source mass and launch radius, what outward launch speed makes the total specific energy exactly zero?

M

Source mass

4 kg

r_{0}

Launch radius

1.6 m

1. Set the threshold condition

At escape threshold,

0 = df r a c v_{t e x t esc}^{2} 2 - df r a c M r_{0}

2. Solve for the threshold speed

v_{t e x t esc} = s q r t 2 M / r_{0} = s q r t 2 (4) /1.6

in the displayed

G = 1

units.

3. Compute the live value

That gives

v_{t e x t esc} = 2.24, ma t h r m m / s

, while the circular-speed comparison is

v_{c} = 1.58, ma t h r m m / s

at the same radius.

Escape speed

v_{t e x t esc} = 2.24, ma t h r m m / s

The escape threshold comes straight from setting the total energy to zero at the launch point.

Escape-threshold checkpoint

Start from High but bound. Without changing the source mass or launch radius, what single control change removes the finite turnaround radius?

Make a prediction before you reveal the next step.

Decide what should happen to the total-energy line and the turnaround marker when the launch just reaches escape threshold.

Check your reasoning against the live bench.

Raise the launch speed until the speed factor reaches 1.00, so the total specific energy reaches zero and the finite turnaround radius disappears.

At fixed source mass and launch radius, changing the speed factor changes the kinetic term at launch. The threshold case happens when

E / m = v_{0}^{2} /2 - M / r_{0} = 0

Common misconception

If a launch gets far enough from the source, it has escaped, and escape means gravity is basically gone.

Distance alone does not decide escape. The deciding quantity is the sign of E/m. Zero or positive total specific energy means there is no finite turnaround radius; negative total specific energy means the launch is still bound.

Gravity does not vanish after escape. It keeps acting and keeps reducing the speed. The difference is that the object never has to reverse direction.

Quick test

Reasoning

Question 1 of 4

Answer from the live launch-and-energy logic, not from detached formulas.

A launch begins faster than the local circular-speed comparison but still below the escape speed from the same radius. What must be true in this lab?

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

Accessibility

The simulation shows one source mass on the left side of a compact radial launch axis, a launched mass moving outward or inward along that axis, and optional overlays for the launch marker, finite turnaround marker, current velocity vector, inward gravity vector, and visited trajectory trail.

Changing source mass, launch radius, or speed factor updates the same trajectory, readout card, and linked graphs together. Compare mode overlays a second launch on a separate dashed track instead of switching to a different model.

The displayed units use a bounded one-source gravity model with G = 1. The stage has a finite maximum visible radius, and bound launches whose turnaround sits beyond that view are labeled explicitly rather than being faked into the visible window.

Graph summary

The radius-history graph compares the live radius with the starting launch radius over the same time window. Hovering or scrubbing the graph previews the same instant on the launch stage.

The speed-thresholds graph compares the live speed with the local escape-speed and circular-speed benchmarks, and the specific-energy graph shows the live kinetic, potential, and total specific energies together with the zero-energy threshold.

Keep the gravity launch story moving

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Bound-orbit timingMechanics