Make a 3D Constellation and Measure Star Brightness

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.

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

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 an Arduino then visualize the data in Mind+.

Make the Base:

Make the Slider and Fix the Sensors:

Activity 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. The program is created with Mind+ (mindplus.cc). Please install Mind+ and download the sample program 1.

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：

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

Activity 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:

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

Download sample program 2. 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.

Activity 3: Make 3D Constellation with LEDs and Resistors

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.

Make the 3D Constellation:

Result:

Power up the Arduino. The LEDs light up in different brightness, which looks exactly like what we've seen from the earth.