---
title: "Eclipses and Transit Photometry Interactive Lab | Sandbox Physics"
description: "How much can a small dip in starlight tell us about a planet? A transit measures how much stellar light a foreground body blocks."
canonical_url: "https://sandboxphysics.com/labs/shadow-eclipse-lab/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/shadow-eclipse-lab/"
last_modified: "2026-10-28"
---

O014 · A planet crosses a star

# Eclipses and Transit Photometry

**How much can a small dip in starlight tell us about a planet?** A transit measures how much stellar light a foreground body blocks. Converting its depth into a size needs the stellar brightness profile, path, exposure and contaminating light; the planet’s physical radius also needs the star’s radius. The same overlap geometry explains eclipse contacts and shadows.

Drag the planet’s path across a glowing star. Compare full and grazing transits, finite exposures and light from a nearby companion, then return to the eclipse-shadow geometry.

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

Model assumptions

The transit is a synthetic opaque circular planet on a prescribed circular orbit across a spherical star with quadratic radial limb darkening. Annular integration supplies host flux, a uniform time window supplies finite exposures, and a constant unresolved companion dilutes that same flux. The circularly inferred density assumes negligible planet mass; physical planet radius additionally needs stellar radius. Starspots, atmosphere, orbital eccentricity, detector noise and binary validation are outside the interactive model. Shadow and solar views retain exact apparent-disk overlap and common-tangent geometry with compressed axial distances and enlarged bodies. Real TESS observations are fitted only in the separate fixed-input tutorial, with quality flags, supplied errors and conditional assumptions preserved.

Synthetic circular-orbit transit, finite exposure and constant contaminating light.

Cyan: recorded exposure with companion; amber dashed: instantaneous host-only reference.

Integration and display conventions

The stellar disk follows the same radial brightness law as the flux integral. Its color and outer glow are illustrative. Thin planet outlines mark the distance swept during the exposure, not additional planets. The companion’s angular separation and glyph size are schematic; its light ratio is explicit. The replay follows the visible passage; the chart also includes the full exposure wings and their baseline.

The two geometric eclipse views retain apparent-disk overlap and tangent shadow boundaries. They omit topography, atmospheric refraction, coronal radiance and diffraction. Their axial lengths are compressed and bodies enlarged.

Physics tutorial

## Read a dimming star in the right order

**Background** A planet hides part of a stellar disk. The light lost depends on how bright that part was, how long the camera averaged it and how much other light entered.

**Why it matters** The same small depth can accompany several planet sizes when the path or light source changes.

Start with the essentials

- **Focus question**: Does a shallow dip necessarily mean a small planet?
- **One-sentence intuition**: Depth measures blocked brightness; geometry and the source turn it into a size.

### Core mathematical model

#### Uniform centered disk

$$
\delta=p^2,\qquad p=R_{\rm p}/R_\star
$$

This area rule applies to a fully contained planet across a uniformly bright disk.

#### Brightness weighted by the hidden area

$$
F_\star=1-\frac{\int_{\rm blocked}I\,\mathrm dA}{\int_{\rm disk}I\,\mathrm dA}
$$

The stellar center and limb need not contribute equal light per area.

#### Averaging an exposure and blending light

$$
\overline F_{\rm obs}=\frac{\Delta t^{-1}\int F_\star(t)\,\mathrm dt+c}{1+c}
$$

The window spans one exposure, and the constant companion ratio refers to unobscured host light.

### Common difficulties

#### A grazing planet

**Typical misconception** Every planet blocks its full disk area at mid-transit.

**Better mental model** A grazing path leaves part of the planet outside the stellar disk, so even its deepest point can be partial overlap.

#### A successful fit

**Typical misconception** A good planet curve confirms that the signal came from a planet.

**Better mental model** Blended eclipsing stars and stellar structure need separate tests. The curve fit assumes its object and source model.

### Run the experiment

1. 01

   #### Move the chord

   Drag the planet vertically from the stellar center toward its limb.

   **What to observe:** The passage shortens and can become grazing; the same radius need not produce the same depth.

2. 02

   #### Watch a shutter average

   Select A long exposure and compare the cyan curve with the amber instantaneous reference.

   **What to observe:** Ingress and egress are rounded by a time window; the outlined swept path shows the same interval.

3. 03

   #### Add a companion

   Select A bright companion, then reduce its light ratio without changing the planet.

   **What to observe:** The normalized dip deepens as contaminating light falls.

4. 04

   #### Return to eclipse geometry

   Open the shadow and solar views and move the foreground body.

   **What to observe:** The same apparent-disk contacts connect visible flux to tangent shadow boundaries.

Physical conclusion

Measure radius ratio with an explicit brightness, exposure and dilution model, then supply stellar radius for physical size.

## Related experiments and articles

A planet crosses a star · Reading path

### A planet crosses a star

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

1. [Article **What a small bite of starlight tells us**](https://sandboxphysics.com/stories/transit-evidence/a-bite-of-starlight/)
2. [Article **Weigh the light hidden by a planet**](https://sandboxphysics.com/stories/transit-evidence/weigh-the-hidden-light/)
3. [Article **Use the transit clock to measure a chord**](https://sandboxphysics.com/stories/transit-evidence/clocks-chords-and-density/)
4. [Article **Fit a frozen TESS transit without losing its assumptions**](https://sandboxphysics.com/stories/transit-evidence/fit-the-tess-transit/)
5. [Article **Find the star that shapes the transit signal**](https://sandboxphysics.com/stories/transit-evidence/the-star-in-the-signal/)
6. [Article **Read transit duration as an orbital speedometer**](https://sandboxphysics.com/stories/transit-evidence/duration-as-a-speedometer/)

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)