Habitable Zone

Overview

The habitable zone is the range of distances from a star where a planet's surface temperature could allow liquid water. But what is the physical law behind this zone, and how sharply do conditions change with distance? In this experiment, a TI SensorTag (infrared sensor) is mounted on a Bluetooth low-energy (BLE) mouse. The mouse is driven steadily away from an infrared lamp while phyphox plots the IR temperature signal as a function of distance (in arbitrary units) in real time. Students see that the closer the "planet" is to the "star", the higher the radiation, and connect this to the concept of the habitable zone. It is a qualitative analogue, not a quantitative test of the inverse-square law and not a habitable-zone calculator.

Grades	7–10
Subject	Physics, Natural Sciences
Method	Student experiment
Duration	Variable
Language	German, English
Sensor	TI SensorTag (infrared temperature sensor, TMP007) + BLE mouse

Background

A planet's equilibrium temperature depends on how much stellar energy it receives. In the real world this falls off as the inverse square of the distance (the inverse-square law). Double the distance, and the energy per unit area drops to one quarter. The habitable zone boundaries are set by the stellar luminosity and the albedo and greenhouse properties of the target planet.

For the Sun, the habitable zone runs roughly 0.95–1.7 AU, depending on the climate model. Around a dimmer M-dwarf like TRAPPIST-1, the habitable zone is much closer to the star — which is why tidal locking becomes so likely for those planets.

Materials

• Infrared lamp
• Bluetooth Low Energy (BLE) mouse
• TI SensorTag (infrared temperature sensor)
• Attachment to mount the SensorTag on the mouse

The materials listed are examples.

Setup and Procedure

1. Attach the TI SensorTag to the top of the BLE mouse so that the infrared sensor faces the lamp.
2. Place the infrared lamp at one edge of the table.
3. Open ir-dist_habitable.phyphox in phyphox and connect both the mouse and the SensorTag via Bluetooth.
4. Switch on the lamp. Align the mouse and sensor in a straight line with the lamp.
5. Start the measurement. Slowly drive the mouse away from the lamp. The mouse measures the distance in arbitrary units. Do not rotate the mouse, otherwise the total distance can no longer be reconstructed.
6. phyphox plots the IR temperature signal (°C) against distance, plus the ambient temperature. Stop the measurement and discuss the graph. Optionally, drive the mouse back toward the lamp for a second run.

Discussion

• At what distance does the signal drop to half? Why can the distance axis (arbitrary units) not be used to test the inverse-square law quantitatively?
• For a star twice as luminous as the Sun, where would the habitable zone shift to?
• Why is the habitable zone of a red dwarf much narrower in absolute terms, even though the relative width is similar?
• How does this experiment connect to the albedo experiment?

phyphox Files

• SensorTag + BLE mouse: ir-dist_habitable.phyphox
• Earlier version for SensorTag + BLE mouse with lower power use: ir-dist_habitable-sleep.phyphox

The file contains English, German and French texts. The phyphox files are maintained in the curious-signals-phyphox repository.