---
title: "A dark planet bends starlight"
description: "Follow bent light into finite stellar images, derive their changing brightness, and independently fit published microlensing observations."
canonical_url: "https://sandboxphysics.com/stories/microlensing-planets/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/microlensing-planets/"
last_modified: "2026-11-03"
---

AC23

# A dark planet bends starlight

Sandbox Physics · 2026-11-03

Start with a star that briefly brightens. Draw its images, give the star a finite disk, then ask which properties a real light curve can constrain.

1. L1

   ## [How a dark planet makes a distant star brighten](https://sandboxphysics.com/stories/microlensing-planets/a-dark-planet-brightens-a-star/)

   A planet bends the images of a background star. Follow their changing area to understand planetary microlensing and a brief brightening.

2. L1

   ## [From a bent light ray to two stellar images](https://sandboxphysics.com/stories/microlensing-planets/from-bent-light-to-two-images/)

   Derive the point-mass lens equation, locate its two images, and calculate their parity and combined magnification.

3. L2

   ## [What happens when a stellar disk crosses a caustic?](https://sandboxphysics.com/stories/microlensing-planets/a-stellar-disk-crosses-a-caustic/)

   Add two deflections, find critical image directions, and integrate a finite, limb-darkened stellar disk into its light curve.

4. L3

   ## [What can a microlensing light curve tell us about its lens?](https://sandboxphysics.com/stories/microlensing-planets/read-a-light-curve-without-weighing-too-soon/)

   Build a blended-light likelihood, distinguish fitted geometry from physical mass, and see how source size and parallax supply missing scales.

5. L4

   ## [Read a dark planet’s mass from Earth and space](https://sandboxphysics.com/stories/microlensing-planets/read-ground-space-and-roman-evidence/)

   Read the finite-source and Gaia-parallax evidence, inspect a separate host-star search, and distinguish Roman forecasts from detections.

6. L4

   ## [Fit the published OGLE-2005-BLG-390 photometry](https://sandboxphysics.com/stories/microlensing-planets/refit-the-published-ogle390-files/)

   Download five original files, fit finite-source planetary models, and test which conclusions survive alternative solutions and weak parallax.

[Drag the star through a planetary lens](https://sandboxphysics.com/labs/gravitational-lens-telescope/?mode=binary)

## Sources and calculation scope

1. [Beaulieu et al. (2006), OGLE-2005-BLG-390 discovery, astro-ph/0601563v1](https://arxiv.org/abs/astro-ph/0601563v1)

   Read the main text, Table 1 and Figure 1: finite-source planetary anomaly, source limb coefficients, 650 original points and population-conditioned physical mass. Our independently rerun five-file subset contains 308 points.

2. [Bozza et al. (2018), VBBinaryLensing finite-source methods](https://doi.org/10.1093/mnras/sty1791)

   Sections 2–4 and equations 14–20, 25–26 explain contour area, error refinement and radial source profiles. The pinned LGPL code remains a separately downloaded offline reference.

3. [Bozza et al., VBMicroLensing, arXiv:2410.13660v1; A&A 694 A219 (2025)](https://arxiv.org/abs/2410.13660v1)

   Read equations 1–16 and section 6 before interpreting binary roots, parity, critical curves or a missing image pair. This is a methods reading, not a replication of its benchmark suite.

4. [OGLE published OGLE-2005-BLG-390 project files](https://ogle.astrouw.edu.pl/cont/4_main/epl/blg390/)

   Five fixed photometry URLs are named in observation-sources.json. The tutorial fetches them from the author project and verifies byte counts and SHA256. An explicit redistribution license was not found; they are not mirrored here.

5. [Dong et al., A Saturn-mass microlensing object, arXiv:2601.00057v1; Science](https://arxiv.org/abs/2601.00057v1)

   Fixed author version, Figure 2 and supplement S5–S11: finite-source scale, ground/Gaia parallax, alternative blending and solution weights. arXiv identifies the paper as published in Science. This guide reads the evidence; it does not rerun that event.

6. [Johnson et al. (2020), Roman free-floating-planet forecast, arXiv:2006.10760v2](https://arxiv.org/abs/2006.10760v2)

   Sections 2 and 5, Figures 3–5 and Appendix A: Cycle 7 survey assumptions, finite-source light curves, detection cuts and mass-function-conditioned yields. These are the fixed 2020 predictions.

7. [Mróz et al., host-star limits, arXiv:2609.12743v1, submitted to A&A](https://arxiv.org/abs/2609.12743v1)

   Read Figures 2–3, sections 4–5 and Appendix B for interferometric contrast, correlated noise and conversion to a conditional host limit. The fixed version remains a submitted preprint in the metadata checked on 2026-11-03.

8. [NASA Roman Galactic Bulge Time-Domain Survey](https://science.nasa.gov/mission/roman-space-telescope/galactic-bulge-time-domain-survey/)

   Official microlensing survey context checked on 2026-11-03. The cited programme observes the bulge repeatedly with the Wide Field Instrument.

9. [JPL Horizons vector ephemeris documentation](https://ssd.jpl.nasa.gov/horizons/manual.html)

   The exercise retains a fixed 161-node DE441 geometric ICRF Earth vector response, positions in AU, velocities in AU/day and TDB epochs. The headerless photometry keeps its separate timing qualification.