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Pick the questions that most interest you and focus on those
In this sheet we will see how accurately we can navigate. To
do this we will need to learn about the difference between mean
time as measured on a watch and solar time as measured by looking
at the sun. This sheet will ask you to do some practical measurements.
1. We start by cheating. Find from an Atlas showing the
Longitude and Latitude where you are. This will allow you to
check the answers to the following questions.
2. We will now use two different methods to find your
Latitude.
This one can't be done in school hours, but some of the preparation
can. The angle that the star Polaris makes to the horizon
is your Latitude. Check that you understand why. Now think
of ways that will allow you to measure this angle as accurately
as you can. Using the best method that you come up with, on a
clear night, measure the angle of Polaris.
You can also find your Latitude from the sun. Set a vertical
stick in the ground. This will cast a shadow which will vary
in length during the day. When the shadow is shortest then the
sun is at its highest point in the sky. This point occurs at
Noon. Think of how you might tell when the shadow is shortest.
(You can also cheat a little and see when the shadow is aligned
along a line which points exactly North-South.) Measure this
length and the length of the stick and use this to find the angle
that the sun makes with the horizon. Suppose that this angle
is q. Then the Latitude f is given
by
- where Z is the declination of the sun which is tabulated
in the notes. Using this information, work out f and compare
this with your answer above and the true Latitude.
Which do you think is the best of these two methods for finding
your Latitude? Can you think of a better method?
3. We will now find your Longitude. To do this you need to
know the time difference between where you are and Greenwich
in London. To do this we will allow you to use your watch and
to cheat a little.
- We each live in a time zone which will be a certain number
of hours different from Greenwich Mean Time. Find out what this
is for where you live.
- In each time zone there is a Meridian of Longitude along
which the time difference between it and Greenwich is exact.
Using an Atlas, find out the Meridian of Longitude of this for
your own time zone.
- Suppose that you live x degrees West of the meridian of Longitude.
Show that if noon occurs at 12:00 at this meridian, then noon
(when the sun's shadow is shortest and points North South) will
occur where you live when the time T is shown on a watch, where
T is given by
4. Life isn't quite this simple. Because the earth goes round
the sun in an ellipse and is at an angle to this ellipse then
noon does not occur at 12:00. Instead, at the Meridian of Longitude
it occurs at a time 12:00 + y shown on a watch, where y is called
the "equation of time" and depends upon the date. Look
at the notes to see what values y takes. This means that the
time shown on a watch when the sun's shadow is shortest and points
north south is given by
- (For English schools) How does this formula change when we
go from Summer time to Winter time or vice versa?
- Using your watch, measure T as accurately as you can. (It
may be a good idea to measure T over several days and take an
average.)
- Now look up y for the dates you made your measurements. There
is a catch - the table only gives y at the beginning of each
month. Think about how you may be able to work out y accurately
for each day in the month.
- From your measurement of T and your calculation of y work
out x and hence work out your Longitude.
5. Hard question: The difference y occurs because the
length of the day measured from noon to noon is not exactly the
same for each day. Can you explain why this might be the case? |
