At-Home STEM Activities: DIY Sextant

For New Hampshire’s April school vacation week, when none of us is actually going anywhere, we decided to focus on things we could do if we did have some sort of wild vacation adventure and ended up on a deserted island-

Maybe at this point, despite how much fun it might be on a deserted island, you’ve decided you want to go back home again. Whether that’s in a boat that has miraculously appeared (or you decide to accept this week’s Saturday STEM Challenge) or because you’ve finally figured out how the Professor on Gilligan’s Island made a radio out of coconuts and now you can broadcast a message asking for help, you need to know where you are before you can get home.

There are two pieces of information you need to determine that: your longitude and your latitude.

Longitude refers to your position east or west of the Prime Meridian along imaginary lines running between the north and south geographic poles. The Prime Meridian runs through Greenwich in the United Kingdom, so if you’re the kind of always-prepared person who travels with a watch set to Greenwich time just in case you ever need to determine your longitude, this is the day you’ve been waiting for. (Those of you stranded with internet access can check Greenwich time online.) Longitude is usually expressed as degrees, minutes, and seconds ranging between 0 and 180 east (+) or west (-). Since there are 24 hours in a day and 360 degrees of longitude around the Earth, Earth’s rotation turns so that a point on its surface moves 15 degrees to the east every hour. If you have a clock set to Greenwich time, you can calculate your longitude based on the difference in time between Greenwich and noon where you are (when the sun is highest in the sky)- if it’s later in the day where you are, you are east of Greenwich; if it’s earlier then you are to the west. Multiply the time difference in hours by 15 degrees and that’s your longitude.

If you are stranded on a deserted island without the properly set watch, it is possible to determine your longitude, but you will need an astronomical almanac and very accurate clock to compare when certain celestial bodies pass each other, so longitude may not be an option.

But latitude is much more manageable.

Latitude refers to your position north or south of the Equator- it may help to think of it as ladder rungs circling the globe and parallel to the Equator. We’ll concentrate on calculating latitude in the Northern Hemisphere which is made much easier because of a specific star in the night sky- Polaris, the North Star. (The Southern Hemisphere has a pole star, too- Sigma Octantis- but it’s too dim to see easily for navigation.) Polaris keeps its location in the sky as the Earth spins on its axis, meaning that it can be used as a reliable marker because the position does not change (well, because of long-term precession of the Earth’s axis, we’ll need to use a marker midway between Polaris and Gamma Cephei by 3000 AD for north, but that’s another blog post…).

To calculate our latitude we will need to make a sextant and wait for a relatively clear night. Sextants were first developed in the 1700s and are used to calculate the angle between a celestial body and the horizon, especially for sea navigation.

To make our sextant, we will need the following:

-a protractor

-some string (at least 6” for attaching the object, plus possibly more if used to attach protractor to support)

-tape if not using string to attach protractor to support

-some small and relatively heavy object to hang from the string (I used an earring)

-a ruler/long spoon/straight stick

1. Attach 6” of string to the center of the straight edge of the protractor oriented so that the string falls across the face of the protractor- if tape is an option, that works or tie the string around.

*Note: you want the string to be able to swing freely from the line marking 0 degrees- if you are using tape, make sure the tape doesn’t extend past this line.

2. Attach the protractor to the ruler/spoon/stick- you can use string or tape for this.

3. Attach the object to the end of the string hanging from the protractor.

You are now ready to take a measurement:

1. First you’ll need to be in a location with a good view of the northern sky (remember, we already know which way to look because we have the compass from Monday).

2. While some people might already know which star is Polaris, if you are unsure you can use the Big Dipper- find the Big Dipper and then imagine a line continuing out from the edge of the cup part- the star it’s pointing to is Polaris.

Image courtesy of JPL.NASA.gov

3. Hold the ruler/spoon/stick up so that the protractor and string are hanging down, then aim it at Polaris- the string will line up with an angle on the protractor- depending on how you’ve attached the protractor, if the angle is under 90 degrees, this is your latitude- if it is over 90 degrees, subtract it from 180 and the remainder is your latitude.

*If you cannot see Polaris because it is below the horizon, you’re in the Southern Hemisphere

Don’t have a protractor? You can make one from a piece of paper, but it won’t give you as accurate a reading- you’ll have more of a range of angles since only a few values will be calculated. Check out the instructions from the Exploratorium to make one: http://annex.exploratorium.edu/geometryplayground/Activities/GP_OutdoorActivities/PocketProtractor.pdf

How does this help up get home?

If we have a radio and can broadcast our coordinates, help will be able to find us.

If we are trying to navigate our way home, we can use the sextant and compass to navigate to the latitude of our destination and then travel along the line of latitude until we get there. (If we have both latitude and longitude, we could take a more direct route. )