SCIENCE · INVESTIGATE AND EXPLAIN

Separate atmospheric thickness from an escape claim

Hydrostatic balance relates pressure decrease with height to the weight of overlying gas. For an isothermal ideal gas with constant gravity, dP/dz=−ρg and P=ρRT/μ combine to give P(z)/P(0)=exp(−z/H), where H=RT/(μg). Molar mass μ must be in kilograms per mole with the stated gas constant.

Learning outcome: Compare two molar masses at the same temperature, keeping hydrostatic height, thermal speed and binding parameter distinct. Name a missing high-altitude or replenishment measurement before making a retention claim.

Starting recap

Keep interior, thermal, surface-history, orbital and detection assumptions distinct before drawing a planetary inference.

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Try

At 400 K with μ=0.044 kg/mol, H≈7.55860 km and the pressure ratio at 20 km is exp(−20/7.55860)≈0.07093. Doubling temperature doubles H at fixed composition and gravity; it does not double pressure at every altitude.

Open the experiment

Predict

Does a larger scale height establish that an atmosphere is escaping?

Your prediction and reason

Experiment

Compare two molar masses at the same temperature, keeping hydrostatic height, thermal speed and binding parameter distinct. Name a missing high-altitude or replenishment measurement before making a retention claim.

Compare hydrostatic scale height with an escape-energy diagnostic

Worked teaching model · synthetic values · Original ideal-gas isothermal layer, gravity 10 m/s², molar masses 2/18/44 g/mol, gas constant 8.314462618. H=RT/(mu g); pressure ratio at 20 km=exp(−z/H). Fixed escape speed 10 km/s gives Jeans energy parameter vesc²mu/(2RT). Bulk temperature is not a measured exobase temperature; no retention/lifetime guarantee or chemistry model.

Isothermal temperature: 400 K Molar mass case: H2 0 / H2O 1 / CO2 2: 2 case

Reset keeps your prediction, captures and practice history.

Temperature, molecular mass and gravity affect atmospheric structure through different physical quantities.

The isothermal hydrostatic layer and escape diagnostic share supplied parameters but are not a full escape model. The actual exobase, high-energy irradiation, collisions and nonthermal loss can change atmospheric evolution.

Original conditional model ledger
Quantity	Value	Unit
Molar mass	0.04400000	kg/mol
Isothermal pressure scale height	7.558602	km
Pressure at 20 km divided by reference pressure	0.07093496	fraction
Thermal root-mean-square speed	476.1912	m/s
Fixed escape speed	10000	m/s
Escape-energy thermal ratio	661.4980	dimensionless

Read exact plotted values

Height / km	Pressure/reference pressure
0	1
2	0.7675135
4	0.5890770
6	0.4521246
8	0.3470117
10	0.2663362
12	0.2044166
14	0.1568925
16	0.1204171
18	0.09242178
20	0.07093496
22	0.05444354
24	0.04178616
26	0.03207144
28	0.02461526
30	0.01889255
32	0.01450029
34	0.01112917
36	0.008541785
38	0.006555936
40	0.005031769

Original supplied models, not actual planet observations or a unique interior, atmosphere or discovery claim.

Temperature, molecular mass and gravity affect atmospheric structure through different physical quantities.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define the planetary evidence

2. Connect mechanism and inference

The original comparison uses gravity 10 m/s², temperatures 200–600 K and idealized molar masses 2, 18 or 44 g/mol. These labels denote gas particles, not a claim that water remains gaseous at every modeled pressure or that a real atmosphere is isothermal. At the same temperature and gravity, lighter gas has a larger scale height.

Thermal motion has rms speed sqrt(3RT/μ). A separate supplied escape speed of 10 km/s produces the dimensionless binding-to-thermal energy parameter vesc²μ/(2RT). This compares energy scales, not the fraction of particles that escape or an atmosphere’s lifetime. The high-altitude exobase temperature and distribution matter for thermal escape, while nonthermal processes can also remove particles.

Actual atmospheric evolution additionally depends on volcanic outgassing, impacts, chemistry, condensation, stellar radiation and replenishment. The bulk-layer temperature used for a hydrostatic demonstration is not automatically the exobase temperature. A large binding parameter therefore cannot certify permanent retention or surface habitability.

3. Work the supplied case

4. Predict and investigate

Does a larger scale height establish that an atmosphere is escaping?

Apply the evidence to a changed case

At fixed composition, double temperature from 200 to 400 K. State the ratios of H, rms speed and binding parameter.

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Scale height doubles, rms speed increases by sqrt(2), and the binding parameter halves. No escape lifetime follows because neither the exobase distribution nor particle supply has been specified.

Source and boundaries

Primary source. Checked 31 October 2026. Original diagrams and supplied model records are not actual planetary observations. No direct solar viewing, instrument operation or physical experiment is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

At fixed composition, double temperature from 200 to 400 K. State the ratios of H, rms speed and binding parameter.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Compare internal production with surface heat loss Next: Close a planet’s two-way radiative exchange

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