This post describes the paper “Ein Analogieexperiment zur Suche nach Exomonden” (An Analogy Experiment for the Search for Exomoons), published in MNU Journal in 2023 together with Alexander Küpper.
The Gap in the Curriculum
Most physics and astronomy teaching units that address the search for extraterrestrial life focus on exoplanets. The transit method gets visualised, a light curve gets plotted, and the lesson ends with: some exoplanets are in the habitable zone. The end.
What tends to get omitted: moons of exoplanets — exomoons — could equally be candidates for extraterrestrial life, particularly if the exoplanet itself sits in the habitable zone. The moon would then be in the habitable zone too, and a large moon could maintain the atmospheric conditions necessary for liquid water. The possibility is taken seriously in the astrophysics community, and survey data consistently shows that students find the question of life in the universe among the most interesting topics in all of science.
The pedagogical gap is this: the transit method is routinely demonstrated in analogy experiments, but the extension to exomoon detection is almost never treated experimentally, even though it is a natural continuation of the same experiment with only minor modifications. This paper is an attempt to close that gap.
What an Exomoon Signal Looks Like
When only a planet transits a star, the resulting light curve shows a characteristic symmetric dip: flux drops as the planet moves in front of the star, holds at a reduced level during full transit, and recovers as the planet exits. The normalised flux during the flat-bottomed phase is:
$$I(t) = \frac{A_s - A_p}{A_s} = 1 - \frac{A_p}{A_s}$$where the dip depth $\delta = A_p / A_s$ is determined by the ratio of the planet’s cross-sectional area to the star’s.
When the planet has a moon, the situation is more complex. The light curve is now governed by:
$$I(t) = \frac{A_s - (A_p + A_m - A_{pm}(t))}{A_s}$$where $A_m$ is the moon’s cross-sectional area and $A_{pm}(t)$ is the time-dependent overlap between the planet’s and moon’s projected disks (the moon is orbiting the planet, so this overlap changes during the transit).
The consequence: additional dips and asymmetries appear in the light curve. The moon can transit slightly before the planet (causing a small flux dip before the main transit begins), or slide in front of the planet during the transit (temporarily reducing the combined occulting area, causing a brief flux recovery in the middle of the dip), or emerge from behind the planet on the exit side (causing a small dip after the main transit ends). The exact signature depends on the relative sizes of planet and moon, their orbital period ratio, and the geometry of the particular transit.
These signatures are small. In real astrophysics, this is why no exomoon has been unambiguously confirmed. In a classroom analogy experiment, the signals are large enough to see clearly — which is exactly what makes the experiment pedagogically useful.
The Experimental Setup
The starting point is a standard transit analogy experiment: a sphere (the planet) on a rod, moved slowly around a lamp (the star) by a slowly rotating motor. A light sensor — an Android smartphone running phyphox, or an Arduino with a suitable sensor — records the illuminance over time. The resulting light curve shows the characteristic symmetric transit dip.
The modification is straightforward: attach a small battery-powered motor to the planet sphere, with a smaller sphere (the moon) on the motor’s arm. The motor we used is a disco ball motor — inexpensive, widely available, and with a rotation speed that works well relative to the transit timescale if you choose the geometry appropriately.
The result is a physical system with two independent circular motions:
- The planet orbiting the star (driven by the main slow-rotation motor)
- The moon orbiting the planet (driven by the disco ball motor)
When this system transits the “star” (the lamp), the light sensor records a compound light curve with the exomoon signatures described above.
One technical note on sensors: High sample rate matters here. The exomoon signatures are brief features on top of the transit dip, and a sensor that samples too slowly will average them out. We found that the TI SensorTag CC2650, despite being a reasonable choice for the basic transit experiment, has a light sensor sample rate of only 1.25 Hz — too slow to resolve exomoon signatures reliably. Android smartphones and Arduinos both achieve adequate sample rates. The Pasco light sensor used in the paper samples at up to 20 Hz and resolves the features clearly.
Reading the Light Curves
The paper presents two distinct light curve types that emerge from the experiment, each with a different exomoon orbital configuration.
Type 1: The moon’s orbital period is short relative to the transit duration. Multiple exomoon signatures appear within a single transit. These include:
- A small dip before the main transit begins (moon transiting alone)
- Asymmetric ingress/egress (moon leading or trailing the planet)
- A brief flux recovery midway through the transit (moon passing behind the planet, reducing the total occluding area)
- A small post-transit dip (moon still in front of the star after the planet has exited)
Type 2: Specific orbital phase alignment where the moon moves directly behind the planet at the moment of maximum occultation. In this case, the deepest point of the transit corresponds to planet alone blocking the star (moon hidden behind planet). As the moon emerges from behind the planet, the total occluded area increases again briefly before both planet and moon exit.
This second case is particularly useful for quantitative analysis: if the orbital geometry is right, students can separately determine the planet’s radius from the secondary dip depth and the combined planet-moon radius from the primary dip depth.
Video + Light Curve Together
The paper recommends recording a video of the experiment simultaneously with the light sensor measurement, from the perspective of the sensor (i.e., looking up at the lamp from below). This technique — which is also central to the transit method paper — is even more valuable here.
Without the video, the exomoon signatures in the light curve are easy to misread as noise or experimental error. With the video, students can advance frame by frame through the moments corresponding to the unusual features and see exactly what the physical system was doing: the moon sliding in front of the planet, the moon emerging from the planet’s shadow, the moon transiting alone at the start or end of the main event.
The cognitive load of interpreting an unfamiliar, complex signal drops substantially when the signal can be correlated frame by frame with a visual record of what produced it.
Differentiation and Extensions
The paper suggests the exomoon experiment as an extension for higher-ability students at the end of a unit on exoplanet detection, not as the entry point. The transit method should come first; the exomoon experiment builds on it.
For students who are comfortable with quantitative analysis, the formula above allows a full treatment: given the measured light curve and a known lamp radius, students can derive both the planet radius and the moon radius from the dip depths at the appropriate moments.
Possible further extensions:
- Noise floor investigation: systematically vary the moon’s size and determine the smallest moon still detectable. This connects directly to the real astrophysical problem — the reason no exomoon has been confirmed is that the signal is buried in noise.
- Period ratio effects: vary the transit speed (and thus the effective period ratio between moon and planet) to see how the light curve changes.
- Sensor comparison: test different sensor types and compare their ability to resolve exomoon signatures. This turns the instrumental limitation into an explicit investigation.
For the deeper theoretical connections — transit timing variations, the David Kipping approach to exomoon detection — see the transit simulation post, which models these effects in a browser-based tool.
For the secondary school curriculum context and the Direct Imaging pre-experiment that typically precedes the transit unit, see Fremde Welten.
References
Küpper, A., & Spicker, S. J. (2023). Ein Analogieexperiment zur Suche nach Exomonden. MNU Journal, 76(5).
Sato, M., & Asada, H. (2009). Effects of mutual transits by extrasolar planet-companion systems on light curves. Publications of the Astronomical Society of Japan, 61(4), L29–L34.
Tusnski, L. R. M., & Valio, A. (2011). Transit model of planets with moon and ring systems. The Astrophysical Journal, 743(1), 97.
Heller, R. (2018). On the detection of extrasolar moons and rings. In H. J. Deeg & J. A. Belmonte (Eds.), Handbook of Exoplanets (pp. 835–851). Springer.
Küpper, A., Spicker, S. J., & Schadschneider, A. (2022). Analogieexperimente zur Transitmethode für den Physik- und Astronomieunterricht in der Sekundarstufe I. Astronomie+Raumfahrt im Unterricht, 59(188), 46–50.
Changelog
- 2025-10-03: Updated the Tusnski & Valio (2011) reference to use article number 97, replacing the previous page range “1–16.”