SCIENCE · INVESTIGATE AND EXPLAIN

Separate a condensation threshold from a formation history

A collapsing star-forming cloud can produce a rotating disk through angular-momentum conservation. Solids collide and accumulate, larger bodies gravitationally influence nearby material, and sufficiently massive cores can acquire gas while disk gas remains. These processes depend on time, density and transport; the final planetary arrangement need not preserve every formation radius.

Learning outcome: Move luminosity and radius independently, reconstruct the threshold and mass inventory, then state two histories compatible with a present-day volatile signal.

Starting recap

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

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Try

At L=1 and r=3 AU, T=280/sqrt(3)≈161.658 K, below the supplied threshold, so the inventory contains 30 solid mass units. The snow line is≈2.71280 AU. At L=4 and the same radius, temperature rises to≈228.619 K and only 10 refractory units count as condensed.

Open the experiment

Predict

Does a planet’s present radius from its star uniquely identify where its material condensed?

Your prediction and reason

Experiment

Move luminosity and radius independently, reconstruct the threshold and mass inventory, then state two histories compatible with a present-day volatile signal.

Separate a condensation boundary from a formation-location claim

Worked teaching model · synthetic values · Original temperature law 280 L^(1/4)/sqrt(r) K with fixed ice threshold 170 K. Gas inventory 1000 mass units contains refractory fraction 0.01 and additional ice-condensable fraction 0.02 if T<=170. Threshold is a supplied idealization, not a pressure-dependent chemical equilibrium or actual disk reconstruction.

Stellar luminosity case: 1,4,9 reference units: 0 case Disk radius: 3 AU

Reset keeps your prediction, captures and practice history.

A temperature-dependent solid inventory can influence growth without fixing a planet’s final address.

Pressure-dependent chemistry, drift, mixing, collisions, disk lifetime and migration are absent. The fixed condensation threshold is an instructional boundary, not evidence that a present orbit uniquely identifies its formation location.

Original conditional model ledger
Quantity	Value	Unit
Stellar luminosity factor	1	reference units
Local supplied disk temperature	161.6581	K
Ideal ice boundary radius	2.712803	AU
Ice threshold met	1	0 no / 1 yes
Refractory condensable inventory	10	mass units
Additional ice condensable inventory	20	mass units
Total stipulated solid inventory	30	mass units

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

A temperature-dependent solid inventory can influence growth without fixing a planet’s final address.

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 disk comparison supplies T=280 L^(1/4)/sqrt(r) K, with luminosity L in reference units and radius r in AU. A stipulated ice-condensation threshold of 170 K gives r_snow=(280/170)²sqrt(L). The threshold is an illustrative equilibrium boundary, not a universal value independent of pressure or chemical species.

For an original gas inventory of 1000 mass units, refractory solids contribute 10 units everywhere. An additional 20 units count as condensed ice where T≤170 K. Crossing the threshold triples this supplied solid inventory from 10 to 30; it does not instantaneously create a planet or specify an accretion timescale.

Disk migration, gravitational scattering, impacts and later atmospheric loss can change orbital and compositional evidence. A volatile-rich body now inside an inferred snow line might have migrated, formed under a different earlier disk state or gained material later. A plausible history must address these alternatives rather than treating a present orbit as a unique birth certificate.

3. Work the supplied case

4. Predict and investigate

Does a planet’s present radius from its star uniquely identify where its material condensed?

Move luminosity and radius independently, reconstruct the threshold and mass inventory, then state two histories compatible with a present-day volatile signal.

Apply the evidence to a changed case

Increase luminosity from one to nine reference units. How does the supplied snow-line radius change?

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

Compare a worked response

It scales as sqrt(L), so the threshold radius triples from≈2.71280 to≈8.13841 AU. None of the supported radii 1–3 AU then reaches the supplied ice threshold.

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.

Increase luminosity from one to nine reference units. How does the supplied snow-line radius change?

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: Close a planet’s two-way radiative exchange Next: Infer a surface history without equating craters with age

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