How "Bright" is a Star? | Smart Science Projects

Project Overview:

When you look up at the night sky, have you ever wondered why some stars are brighter than others?

This project will teach you how to build a scaled model to understand the relation between brightness(magnitude), distance and luminosity. Then you will implement the theory by making a 3d constellation with different star brightness based on real star data.

Background Knowledge:

Astronomers define star brightness in terms of apparent Magnitude, which depends on:

- Luminosity: how bright it is physically.

- Distance: how far away it is from the earth.

Build the Model : Explanatory Model

In this model, a LED represents an individual "Star", the brightness and position can be varied. On the "Earth" side, there is an ambient light sensor to get the light intensity, and an ultrasonic sensor to detect the distance. The model connects to a microcontroller then visualize the data in Mind+.

Materials:

1 Wide Cardboard Box

1 Cardboard Sheet

1 Straw

1 Bottle Cap

2 Wires

Hardwares:

1 Arduino Uno with Extension Shield

1 Ultrasonic Sensor

1 Ambient Light Sensor

1 LED

220Ω Resisitor

Activity 1.1 : Brightness-Distance Relationship

When the star's luminosity is fixed, we can study how the brightness of a star changes with distance by gently moving the LED and seeing the data visualize simultaneously in Mind+.

Download the sample program 1 and open it, switch to offline mode, and Upload the code to your microcontroller(Arduino Uno). In this program, the LED is set to maximum brightness(255), and the sensor data is constantly read and sent to the serial port.

Switch to Online mode, where we can visualize the received data on the stage.

First, connect the device to start receiving upload(offline) mode data.

Second, click the green flag to draw the data on the stage. Pull or push the straw to change the LED position, here we translate the star distance into cm, at a scale of 1cm = 10 lightyears.

*Please note the distance reading would be unstable within 2cm (ultrasonic measurement range: 2cm～500cm)

This program sets a default max-brightness to be 3000, but if you find the graph is too big or small due to different lighting conditions, you can change this value according to the actual highest reading from the ambient light sensor (when the LED gets to the closest position).

Result:

It is clear to see that brightness decreases with distance, and the graph looks like a curve rather than a straight line, which follows the inverse-square law：

（Source: https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit1/bright.html）

Therefore, we can draw a conclusion that the brightness of a star depends on its distance from us.

Activity 1.2 : The Big Dipper Magnitude

The Big Dipper is one of the most famous and recognizable asterisms in the northern sky. It consists of seven stars: Dubhe, Merak, Phecda, Megrez, Alioth, Mizar, and Alkaid. Let's test out our hypothesis that they appear brighter or dimmer as a comprehensive result of distance and luminosity.

We can get the fundamental parameters of given stars from the internet:

**Alkaid luminosity varies with different data sources. “...revealed by probes Tycho and Hipparcos...the absolute V luminosity of Alkaid is not 630 suns but 154 suns. ” We use 154 in the project because it is more consistent with other parameters. For more information, please check: https://www.omnicalculator.com/physics/luminosity

Once we get the distance and luminosity data of the stars, we can measure their relative magnitudes with the model.

Download sample program 2 and open it, switch to offline mode, and Upload the code to your microcontroller(Arduino Uno). In this program, we will send the luminosity value from online mode to change the LED brightness.

Switch to Online mode, and connect the device to start receiving upload(offline) mode data. You'll see the stage with the star names and distances, the dist reading at the top indicates the current LED position.

The distance and luminosity data of seven stars are pre-imported as lists.

Measure each star individually:

Now you can set the star distance and luminosity data and measure their magnitude.

1) Move the LED to match the dist with the star distance/10 rounded down (eg: Merak 79 - dist 7).

2) Press keyboard 1-7 to set the luminosity and get the magnitude for each star

3) Compare the graph

Result:

From the graph, we can find out: Dubhe, Alioth and Alkaid are the three bright stars in The Big Dipper, and Megrez is the least visible one. It is consistent with astronomical observations.

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Build the Model : 3D Constellation with LEDs

You already know that luminosity and distance are the two main factors that effects star's visual brightness. In this model, we will use straws to give the stars depth. Then use resistors to change the LED brightness, simulating the real luminosity difference of the seven stars.

Translate Straw Length from Distance:

Translate the star distance data it into a reasonable scale for the model. Please note, since the model will be seen from a distance, the further the viewing distance will lead to the shorter straw length. In the example:

Length = 300 - (Distance x 2)

Calculate Resistance from Luminosity:

To change the LED brightness is to control the voltage that go through the LED. Connecting a resistor with higher resistance will make the LED dimmer. To get an accurate combination of resistors, you can use a Voltage Divider Calculator to help.

Vs - 3.3V (from Arduino)

R1 - Resistor

R2 - LED Resistance (from datasheet)

For example, let's arbitrarily connect the brightest star (Dubhe) with a resistor of 220Ω, from the data sheet you can find the LED resistance (e.g, 160Ω), then the output voltage through the LED will be 1.389V.

Use this value as baseline, you can map the luminosity to a voltage for each LED, then calculate R1 and get the closest resistor.

Materials & Hardwares:

1 Cardboard Box

1 Constellation Print

7 Straws

7 LEDs

7 Resistors (220, 820, 820, 4.7k, 470, 680, 270)

14 Wires