Mechanics
Escape trajectory
Launch faster than escape speed — the body leaves M's grip and flies away.
Escape trajectory — interactive Mechanics simulation. Launch faster than escape speed — the body leaves M's grip and flies away. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Escape speed
If speed at a given radius exceeds the escape velocity, the object’s total energy is positive and it never returns.
Escape speed v_esc = √(2GM/r) is √2 times circular orbit speed at the same radius. Above that threshold the trajectory is unbound — a hyperbola or straight departure.
- v_esc = √(2GM/r)
- E ≥ 0 → unbound
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A satellite is launched sideways past a central mass at just above the escape speed for its distance. Does it fall back into orbit, circle forever, or leave and never return?
Predictions to weigh
- It escapes — its distance keeps growing and it never comes back.
- It settles into a closed orbit around the central mass.
- It slows, turns around, and falls back toward the central mass.
Variable roles
What you set:
- Central-mass parameter GM (m³/s²)
- Launch distance r (m)
What you measure:
- Escape speed v_esc (m/s)
- Measured launch speed v (m/s)
How the investigation runs
- Open the Gravitational Escape preset and press Reset. Note the central-mass parameter GM and the satellite's starting distance r from the centre.
- Confirm the speed probe is attached to the satellite — it reports the satellite's speed relative to the central mass in m/s.
- For each trial below, set GM and the launch distance r to the listed values, press Play, and record the satellite's speed at the instant of launch.
Governing equation
Escape Speed — v_esc = √(2GM / r)
The minimum speed at which a body's kinetic energy equals the depth of the gravitational well at distance r, so its total energy is exactly zero and it can coast to infinity. Any faster and it escapes with energy to spare.
Circular-Orbit Speed — v = √(GM / r)
The speed needed to hold a circular orbit at the same distance r. The escape speed is exactly √2 times this — a useful benchmark for judging how far above 'staying in orbit' each launch really is.
What the printable worksheet asks students to work out
- For each row, divide the measured launch speed v by the computed escape speed v_esc. What do you notice about this ratio across all three trials, and what does a ratio greater than 1 tell you about whether the satellite escapes?
- The specific orbital energy is ε = v²/2 − GM/r. Compute ε for your first trial using the measured launch speed. Show that it is positive, and explain why a positive ε means the satellite is unbound.
Where this shows up beyond the lab
- Predict what path the satellite would follow if it were launched at exactly the escape speed (ratio = 1.00) instead of 1.08×. Would it ever truly stop, and at what distance? Explain using ε.
- A real spacecraft launched from a planet's surface must also climb out through atmospheric drag before reaching space. Would that make the speed actually needed to escape larger or smaller than the ideal v_esc = √(2GM/r) computed here? Why?
- AP Physics 1 — Unit 6: Energy and Momentum of Rotating Systems
- AP Physics C: Mechanics — Unit 2: Force and Translational Dynamics
- IB Physics — A.4 Rigid body mechanics
- IB Physics — D.1 Gravitational fields
- General High School Physics — Rotation, gravitation & orbits
- NGSS High School Physics — Gravitational and electrostatic forces
- Welcome to Grav Escape
- Select the satellite
- Press Play
- Leaving forever
- Open the data
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.
Newton's Law of Universal Gravitation