## Introduction: An Accurate Model of a Cepheid Variable Star

Space is big. Very big. Astronomically so, one might even say. That has no bearing on this project, I just wanted to use the pun.

It comes as no surprise that there are many stars in the night sky. It may however, surprise some who are new to the realms of Astrophysics or Astronomy to learn that there are many different types of stars. One particular type is called a Cepheid Variable Star and these are beautiful, interesting and useful all in one. At a glance Cepheids look just like any other star, but if you observe a Cepheid for a few nights in a row, you will notice that it seems to pulsate, its brightness changing to dimmer then brighter states over the course of a few days. Observe for long enough and you'll notice that these 'pulsation periods' don't change. This is what makes Cepheids unique and useful - it turns out their pulsation period is directly related to their size so if we count the time it takes the star to go from bright to dim and back again, we can tell how big it is. We can then use this to figure out more information about the star like how far it is, its actual brightness (Luminosity), etc. That's about all you need to know to understand what is going on with this project, but if you are interested in leaning more, go check out this Wikipedia page on Cepheids.

Also, just for fun, can you figure out which Cepheid I am modelling in this project? (The clue is in the image above and the answer is in the last section)

## Supplies

- Paper (18x54cm or 7.1x21.3")

- Arduino UNO & its Cable

- White LED x3

- 220 Ω resistors x3

- A 2x16 segment LCD

- A 10 kΩ Potentiometer

- A 9v Battery and a power connector

- Some cardboard

- A 500ml Plastic Bottle

- Black Paint & Sharpie

- Superglue & Hot glue (The glue gun will also be needed here)

- Scissors

## Step 1: The Star

The first problem to solve was the star itself: How do we make a roughly spherical object that is both aesthetically pleasing and lets through light? I decided origami would do the job and so looked online for origami spheres. I found quite a few but they were either extremely difficult or falsely advertised (seriously, the amount of cuboid 'spheres' I found across Google was unsettling). However, after a while I found one that I liked, and which was relatively simple to pull off after a few practice goes. The instructions are as follows, and there is a template for folding in the images above.

1. Fold your paper into 24 equal strips. I would recommend dividing it into 3 then folding each section in half. Continue halving until there are 24 rectangular sections in total. The folds should make little valleys in the paper. (See the red lines in image 2).

2. Flip the paper over and make a mark in the top right corner of the paper. Then count 4 folds over and make another mark at the bottom of the fourth fold. Make a diagonal fold between these two marks. Then move the marks two straight folds over and make another diagonal fold there. Continue this until you have reached the end of the paper. (See the green lines in the second image).

3. After reaching the end of the paper, make the same folds but slanted in the opposite direction. (i.e. start in the top left corner and repeat the diagonal folds from step 2 in the opposite direction). See the blue lines in the second image above.

4. Find the centre of the right edge and mark it. Then make a diagonal fold to the bottom of the straight fold two folds over. Then make another fold from the top of this straight fold to the middle of the edge. Repeat this for the left edge, again to the top and bottom of the straight fold two folds over. (See the brown lines in the second image for guidance).

5. Finally you will need to fold the paper to make the sphere. I recommend going over every fold you have made to ensure they are all well-defined. Looking at the last image for guidance, fold the paper so that the faces of the triangles labelled as A are touching the faces of the B triangles. After the very first set of folds, the short edge should curve into a semi-circle and when you have folded everything, the result should unfurl to be the bridge shape in image 4.

6. To get from the bridge to the sphere, connect the ends of the bridge. I did this by placing the faces of the first diamonds from each end onto each other and gluing them together. Hold the two faces together and put a few drops of superglue between them to hold them in place. Lastly, secure all the points at the top of the star by placing a drop of superglue on the star's tip. I would recommend superglue for this as you won’t have to hold the paper together for ages while the glue slowly dries and you begin to question your life choices. The bottom point is where the wires come in so leave it open.

I found making the star to be the most complex part of this project, however it was not so bad once I got the hang of how to fold the paper together. I would personally rate this ball at a difficulty of 3 paper sheets. Have fun and try not to scream in frustration.

## Step 2: The Base

To make my base I started with the little cradle thing I found inside the Easter egg box I got a few weeks back. I simply turned it inside out, trimmed it down to size so that it was 7cm (2.8") tall and then painted it black. You may not have this oddly specific item to hand so I made a rough template for you to make your own out of cardboard (See image 2). Once you have made it, cut a circular hole in the thin end of the top face with a diameter of 4cm (1.6"), centre point about 3.5cm (1.4") away from the top edge (Image 4). Next cut a rectangular hole 7x2.5cm (2.8x0.1") centred at 0.5cm (0.2") away from the bottom edge. The lights will go through the circular hole and the LCD in the rectangular one.

Next we need something to hold the star in place. I opted not to put it directly onto the hole as the shape of the star does does not fully cover the hole so we would have been able to see the circuitry inside the base, which is a bit of shoddy workmanship if you ask me. To get around this you will need the dome from the top of a 500ml water bottle (Make the cut about 4 cm from the top, Image 6) and paint it black (Image 8). I left a little window in mine so that I could still see the base of the star. I thought it would look nicer than if the bottom just disappeared into the abyss. I found that the black paint did not stick to the bottle too well so I coated it in primer (Image 7) before adding the colour. Unfortunately I used an oil based primer and the result was pretty much as smooth as before. Don't use an oil based primer.

After painting I made a little tube of paper and coloured it in black. It was then glued into the neck of the bottle as shown in image 9 with hot glue. The purpose of this is to camouflage the wires when they go through the hole and into the star, so the tube needs to be just tall enough to hide all the exposed wiring, but not tall enough to displace the star when we rest it inside the bottle top (for the height I cut my bottle it was 3.5cm / 1.4"). You do not need the tube if you have not left a window in your bottle.

The final step was to secure the support into its hole in the base. Apply the hot glue to the underside of the box to avoid seeing the unsightly mess (Image 10).

Once you have finished assembling the base, use a sharpie for any spots the paint did not reach. Do not overdo the sharpie however, it gives a shinier finish than paint and this will show in large amounts. A few dots here and there is fine however.

## Step 3: The Code

Attached below you should find the code for the electronics. Simply download it and install it on your Arduino. If you do not have the Arduino IDE, you can download the official version here. Just choose the version that best suits your device and OS (I use version 1.8.12 for Windows 7 and up).

Before uploading the program to your board, you need to also have the LiquidCrystal library. If you do not already have this library to hand, I have attached a link to the one I used below. Simply download the .zip file and put it in the same folder as the arduino sketch. There is no need to unzip it. If the program does not run then here is the official arduino guide for installing and running libraries.

LCD Library. (I did not make this library, but it works well with the project. Simply go to the link and download version 1.0.7 from under the Downloads section. Full Credit goes to the Library's author, not me).

## Step 4: The Circuitry

The first image is the Circuit diagram of the project. One thing you should notice is that the LEDs are attached to the ends of wires in order to connect them to the breadboard while inside the star. You should use the M-F wires for this and also for the LCD. However, as you may be able to see in the second image, I did not have enough M-F wires at hand for all the connections, so I improvised with electrical tape and blu-tack. I used electrical tape to hold the wires to the LED legs (Image 3) and I used blu-tack to hold the wires to the LCD pins as they kept falling off, probably because the pins were too small for the tape to stick to well enough to support the weight of the wires. You should use M-F wires, it's a lot less stressful. Also, colour code the wires, it leads to a lot less confusion.

As can be seen in the second image, I used a 9v battery to power the board because it would have been a hassle to power it via the computer cable.

The potentiometer was set at around half way to its max (~5 kΩ), which provided a good level of contrast for the screen.

## Step 5: The Final Assembly

So now we have the star, base and circuitry ready, it is time to assemble everything to create the model. The first thing I did was to place the base over the circuit and put the LCD into the slot we cut for it. To ensure it did not slide out I coated the shorter edges in a strip of blu-tack. This has the dual benefits of hiding the LCD's back-light and holding the screen in place. (Note: Make sure that when you stick it in, the display is facing the correct way, otherwise we run into illegibility issues. That won't be fun.)

Next we need to feed the LEDs through the hole in the top of the base and into the hole we left in the bottom of the star. Try to keep the LEDs in the centre of the star, otherwise you will be able to see bright patches on the surface of the star, which doesn't look too great. Once the LEDs are inside the star, simply rest it on the edge of the bottle and it will sit tight.

Finally, connect the battery and hide it inside the base next to the breadboard. Now you have an accurate model of Polaris Aa, one of the three stars that makes up the North star (Yes, you read that right. The point in space we call the North Star is actually the combined light of three stars: Polaris Aa, Ab and B. Because they are ~433 light-years away they appear to be a single point in the sky).

Also, I should say that the accuracy of this project is in relation to the Luminosity of the LEDs and Polaris as measured in Watts. Each LED had 0.023 W of power (0.069 W total) and the star's luminosity is 1,260 times greater than the sun which is 3.83 x 10^26 W (So Polaris has a luminosity of 4.84 x 10^27 W).