---
title: "Planetary Atmospheric Escape Interactive Lab | Sandbox Physics"
description: "When does a warm atmosphere become an escaping wind? A strongly bound atmosphere can lose a tiny high-speed tail after collisions become rare."
canonical_url: "https://sandboxphysics.com/labs/planetary-atmospheric-escape/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/planetary-atmospheric-escape/"
last_modified: "2026-10-28"
---

AC13 · From thermal tails to a wind

# Planetary Atmospheric Escape

**When does a warm atmosphere become an escaping wind?** A strongly bound atmosphere can lose a tiny high-speed tail after collisions become rare. A hotter, sufficiently collisional atmosphere can instead carry gas outward collectively through a sonic point. Gravity, particle mass and temperature set the binding; an independent heat budget must still supply the escaping flow. A mathematical wind alone does not establish that heating is available.

Drag the planet and its irradiating star. Compare a Maxwellian escape tail, a transonic isothermal wind and the power needed to sustain it.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Synthetic single-component spherical models with prescribed temperature and a fixed reservoir boundary. Jeans flux is evaluated only at a located hydrostatic local-Knudsen exobase with strong binding; importance-sampled ballistic tracers exaggerate rare escape paths. Parker transport has independently fixed base density and requires a collisional sonic region and a subsonic lower boundary. XUV power is a separate finite-radius budget, not a temperature or heating solution. No ionization, chemistry, cooling, magnetic field, tides, stellar-wind confinement or planet evolution is solved. The apparent planet is the gas reservoir boundary, not a measured rocky surface. The tutorial supplies independent numerical synthetic benchmarks, not observed atmosphere profiles.

Prescribed-temperature Parker wind; collisional sonic region.

Cyan and amber tracers show subsonic and supersonic model flow. A dotted sphere marks the sonic radius for the wind, or the located exobase for Jeans escape. In the Jeans view, returning paths are cyan and rare unbound paths are amber; eight escape paths are deliberately oversampled and carry their correct small flux weights. These are synthetic trajectories, not measured images.

Formal accelerating Parker solution

Wind density and local continuum check

Numerical and display conventions

The planet edge represents the gas-reservoir radius. The scene extends to four base radii; profiles and power extend to twelve. The ambient glow is decorative, not a calibrated optical image. Wind tracer positions follow the computed travel time; time is accelerated. Ballistic paths follow central gravity above the located exobase; their display speeds are enlarged. No atmosphere depletion or radius evolution is integrated.

Physics tutorial

## Three questions before calling it a wind

**Background** Watch the default outflow cross the dotted sonic sphere. Then ask whether its collisions and its heat supply can support that mathematical solution.

**Why it matters** Hot gas can still be bound, and an available heat source can still fail to launch a collisional wind.

Start with the essentials

- **Focus question**: Which assumptions support this escape rate?
- **One-sentence intuition**: Binding, transport and heating answer different questions.

### Core mathematical model

#### Binding

$$
\lambda=\frac{GMm}{rkT}
$$

Binding energy compared with the thermal energy per particle.

#### Continuity

$$
\dot M=4\pi r^2\rho u
$$

A steady spherical flow carries the same mass through every sphere.

#### Critical point

$$
r_{\rm s}=\frac{GM}{2c^2},\qquad c^2=\frac{kT}{m}
$$

The accelerating isothermal wind crosses the sonic point at this radius.

### Common difficulties

#### Power does not prescribe temperature

**Typical misconception** More XUV must change this prescribed-temperature wind rate.

**Better mental model** The wind has a fixed temperature and base density. XUV changes a separate available-power comparison; a full energy equation would couple them.

### Run the experiment

1. 01

   #### Move gravity

   Drag the planet upward. Watch the dotted radius and the speed profile.

   **What to observe:** At fixed temperature, stronger gravity moves the sonic point outward and reduces the base flow.

2. 02

   #### Separate a tail from a wind

   Select A rare escaping tail, then Collisions run out. Read the local continuum warning.

   **What to observe:** A hydrostatic exobase can support an illustrative Jeans calculation while the formal Parker sonic region is collisionless.

3. 03

   #### Ask who pays for the wind

   Choose The missing heating and drag the star upward. Keep temperature fixed.

   **What to observe:** The available power changes; the independently prescribed-temperature transport does not. A real atmosphere would need an energy equation to decide its temperature and rate.

Physical conclusion

Locate the critical point, test collisions, then ask how the flow stays hot.

## Related experiments and articles

Planetary atmospheres from thermal tails to winds · Reading path

### Planetary atmospheres from thermal tails to winds

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How a planet loses its atmosphere**](https://sandboxphysics.com/stories/atmospheric-escape/leaving-a-planet/)
2. [Article **Calculate the escaping thermal tail**](https://sandboxphysics.com/stories/atmospheric-escape/thermal-tails/)
3. [Article **Build a wind through its sonic point**](https://sandboxphysics.com/stories/atmospheric-escape/critical-wind/)
4. [Article **Solve and check a critical atmospheric wind**](https://sandboxphysics.com/stories/atmospheric-escape/solve-a-wind/)
5. [Article **Read the competing explanations of the radius valley**](https://sandboxphysics.com/stories/atmospheric-escape/radius-valley/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)