Length of Sidereal Day

Sidereal day is the time taken by the Earth to rotate on its axis relative to the stars. Because star is so far away, this is equivalent to saying that it’s the time for the Earth to rotate 360 degrees, and the solar day is the time that it takes the Sun to go from one noon to the next noon.

These two videos also describe sidereal day:

So to calculate sidereal day we can put a camera on an equatorial mount and point it to Polaris. This is because Polaris is the North Star or Pole Star. In the picture below we exposed the camera for 90 minutes, closed the shutter for 5 minutes, and exposed again for 15 minutes. If you look at any single star trail, you will see a longer bright part (90m), a dark part in between (5m), and the shorter bright part (15m). What is the total time in minutes for the entire star trail?

star trail

Save the image above to your computer then upload it to this Online Protractor website. It should look like this. (If you are on the android or iphone, you can also use any app that can measure the angle.)

star trail

Read the instruction in the website. Move the protractor to the center of the star trails. Pick a star trail and measure the angle. Estimate your answers to the 10th decimal. See the picture below for example. Pick another star trail and measure the angle for the 2nd time. Repeat again for the 3rd time. You should have three angle measurements.

star trail

Take 1 screenshot for proof of work. It should look like the picture above. Give your picture a name like sidereal.jpg and upload this image to your Google Drive in the “Colab Notebooks” folder. 1 picture is good enough.

Log into your Google Colab and Google Drive. Create a new notebook and rename to Lab06.iybnb. Save your notebook

Google Colab Google Colab

Check your “Colab Notebooks” folder in your Google Drive it should have two files like this:

Google Colab

Take the average of your three angle measurements. Remember measurements should be to the 10th decimal. Use this average angle to calculate the sidereal time. Convert your answer to xx hours xx minutes format. Show your calculation. Hint the total time it takes to generate this star trail is also the time it takes the Earth to rotate through this angle. The sidereal time is the time it takes the earth to rotate the whole circle. How many degrees are in a circle?

Insert your sidereal.jpg into Colab. Watch the video below for instruction:

Finally answer this question: Through how arc minutes (‘) does the Moon move in one hour? The Moon completes one orbit (a circle) around the Earth in 27.3 days. Show your calcualtion.

Click on Share and Get shareable link. Copy this link and submit it to Canvas Lab 06.

Google Colab

Here is a tutorial on Google Colab if you need a review. Watch from 1:45 - 9:30 min:

After reading this article, Click and view this Google Colab. Your Colab notebook should follow this sketch.