---
title: "Planet Survey Selection Interactive Lab | Sandbox Physics"
description: "Does a catalog full of large planets mean small planets are rare? Small planets block less starlight, so many disappear into detector noise."
canonical_url: "https://sandboxphysics.com/labs/planet-survey-selection/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/planet-survey-selection/"
last_modified: "2026-11-03"
---

AC24 · The planets a survey misses

# Planet Survey Selection

**Does a catalog full of large planets mean small planets are rare?** Small planets block less starlight, so many disappear into detector noise. Orbital alignment and observing gaps hide others. To estimate how common planets are, keep every searched star and calculate which planets the survey could have found.

Turn the detector dial and extend an observing season. Watch the same planet population pass through orbital alignment, gaps and noisy transit detection.

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

Model assumptions

Synthetic Poisson planet population on 5000 identical stars with circular, isotropically oriented orbits. Uniform stellar disks and opaque planets produce the same finite-exposure transit templates shown in the scene. The local transit path is a straight chord. A prepared known-period Gaussian template statistic requires at least three completely covered events. Fourteen-day observing cycles have explicit gaps; the exact phase integral already includes them. The Gamma occurrence posterior conditions on the generating period and radius shape, and contains no false events. Shared-host and individual log-radius errors affect the displayed radius catalog. The real DR25 exercise is separate: fixed source data, a conditional empirical response and a propagated family of unknown-selection bounds. Star-field spacing, telescope scale and time speed are schematic.

## The same population before and after the search

Synthetic truth is orange, detections are blue. Only the blue catalog receives the shared-host and individual radius errors.

Period and radius of the generated planets

Radius distribution on the same absolute count scale

The default survey is already complete. Change one setting to rerun it.

Physics tutorial

## Follow one population through a survey

**Background** A transit survey measures brief losses of starlight. Small signals, unfavourable orbital directions and observing gaps leave planets outside the discovery catalog.

**Why it matters** The radius distribution of discovered planets combines the sky population with the search that selected it.

Start with the essentials

- **Focus question**: Can the same planet population produce two very different discovery catalogs?
- **One-sentence intuition**: Keep every searched star and average the complete geometry-and-recovery probability before dividing detections by effective exposure.

### Core mathematical model

#### Projected shadow

$$
\delta=\frac{A_{\rm overlap}}{\pi R_\star^2}
$$

A uniform stellar disk loses light in proportion to the actual blocked area. The finite exposure averages the changing overlap.

#### Whole searched sample

$$
E=\sum_j\int q_j(P,R)h(P,R)\,dP\,dR
$$

The normalized density describes the assumed planet shape inside the chosen period-radius region. Each searched star contributes, including nondetections.

#### Integer discoveries

$$
N_{\rm det}\mid f,E\sim\operatorname{Poisson}(fE)
$$

In this independent synthetic Poisson population, selection thins the planet count. The generating mean is planets per searched star.

### Common difficulties

#### Keep nondetections

**Typical misconception** Only known planet hosts belong in the denominator.

**Better mental model** The search also examined stars whose planets were missed. Removing them changes the question to an already selected host sample.

#### Use a window once

**Typical misconception** Every measured recovery curve needs another duty-cycle penalty.

**Better mental model** A recovery experiment that used the actual interruptions already contains them. Add a factor only for a new requirement absent from that experiment.

### Run the experiment

1. 01

   #### Predict the shallow signals

   Record the orange population, then turn the detector dial toward lower noise.

   **What to observe:** The generated planets stay fixed and more shallow transits pass.

2. 02

   #### Wait for more events

   Restore default noise and extend the observing season.

   **What to observe:** Some long-period planets gain the three complete events the detector rule requires.

3. 03

   #### Compare a real valley with a selected sample

   Choose A true radius valley, then increase radius scatter in the advanced group.

   **What to observe:** The orange bimodal truth remains; measured blue radii move between bins and blur its minimum.

Physical conclusion

A discovery catalog becomes a population measurement only after the searched stars and selection assumptions are specified.

## Related experiments and articles

The planets a survey misses · Reading path

### The planets a survey misses

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

1. [Article **Why do large planets fill a discovery catalog?**](https://sandboxphysics.com/stories/planet-populations/why-big-planets-fill-the-catalog/)
2. [Article **Keep the stars with no detected planet**](https://sandboxphysics.com/stories/planet-populations/keep-stars-without-detections/)
3. [Article **Which transits survive the survey?**](https://sandboxphysics.com/stories/planet-populations/which-transits-survive/)
4. [Article **From a few detections to a population**](https://sandboxphysics.com/stories/planet-populations/from-counts-to-a-population/)
5. [Article **Replay a bounded DR25 parent sample**](https://sandboxphysics.com/stories/planet-populations/replay-a-dr25-parent-sample/)
6. [Article **Read the evidence for the radius valley**](https://sandboxphysics.com/stories/planet-populations/read-radius-valley-evidence/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

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