Assignment #4 – Navigation – understanding the movement of the sky

You will require the star charts from the first Assignment for this one as well.

One of the key uses of the night sky has been as a navigation aid. In modern times we rely mostly on GPS (Global Positioning System), but pilots and others are still taught how to navigate by the stars should they need to. Most people understand that the North Star is in the direction north, but much more detailed positioning is possible. By understanding how the sky moves, we can find both latitude and longitude.

Latitude

For a great deal of recorded history we have been able to figure out the latitude we are at by observing what constellations are visible in the sky at specific times of night, and what their altitude and azimuth are. Altitude is the angular height above the horizon, while azimuth is the compass direction we must look. Because the Earth is turning, these will change through the course of the night. Greenwich Observatory, and the U.S. Naval Observatory used to put out extensive tables of star (and constellation) positions and times for navigational uses, particularly for naval use.

Since the night sky is always changing we must be able to figure out how to place a horizon on the star chart we have. The star chart is a complete map of the sky, but now we are interested only in the part that is visible at a particular time on a particular date.

NOTE: When doing these type of exercises, we will be working in Standard time. If you wish to use this sort of chart for observing, you must remember that a conversion to Daylight time may also be necessary.

For the date of interest we start with the position of the meridian. The meridian is the line which starts in the North and passes directly overhead to the South. It will pass through the Zenith, which is the point directly overhead. On your chart the position of the meridian is given by the dates at the bottom of the charts for 8 p.m. Standard time. (it does not matter what time zone you are in).

To find the zenith, we need the latitude of the point we are observing at. The latitude of the point of observation gives us the latitude of the point we are at.

Since Toronto is at 45N latitude, the zenith will be at 45N declination on the meridian line.

For Toronto this gives us a south point of -45S and a north point 12 hours of R.A. away at 45N.

The east point of your horizon will always be 6 hours of R.A. to the east (left) of the meridian on the celestial equator, while the west point will always be 6 hours of R.A. to the west (right) of the meridian, on the celestial equator.

Draw this line on your star chart for Toronto by connecting the points with a gentle curve.

Stars above this line will be visible, while stars below will not. (this applies for the Northern Hemisphere, if you were South of the equator, the stars below the line would be visible, while stars above would not, and your north and south points would be reversed.)

Over the course of a night, the meridian moves, and the horizon line with it. One hour of R.A. corresponds to one hour of movement of the meridian line. Stars appearing in the east will be rising, while stars in the west will be setting.

Using your star chart sketch the Toronto Horizon for 8 p.m. EST on Feb. 10th and on August 21st . Mark the meridian, zenith and N, S, E, W points for both.

Longitude

It is far more difficult to find a position’s longitude. Accurate measurements of longitude were not done (as far as we know) until the 1700’s. The accurate measurement of longitude requires accurate time keeping, and the ability to measure the height of a particular star or the sun (often referred to as ‘shooting the sun’). The angle is then compared to a standard angle at a point of reference. Since the British were the first to correctly measure longitude – the standard reference is the Greenwich Observatory. (As you may know this is also the central location for time zones – the two are related).

If the sun is directly overhead at your standard reference, then as you move around the globe, the position of the sun will change. The greater the difference from you expected reference, the further in degrees you have gone. You must use a clock synchronized to your standard reference.

For example if your clock says noon, but by shooting the sun, you get a position that says 10 a.m., (you would use the table referred to earlier to figure out the sun positions), you have a difference of 2 hours. If we look at the globe, it will take 24 hours to make a complete circle – or 360 degrees. This means that each hour is also equivalent to a change of 15 degrees of longitude. This means you are 2 hours or 30 degrees of longitude away from your standard reference. Here the standard reference would be Greenwich Observatory – which is given as zero degrees longitude.

The other thing to consider of course is whether you have gone east or west. Longitude is measured going west for Greenwich. Toronto for example is at approximately 80 degrees of longitude. This means we are 80 / 15 or 5 hours 20 min time difference from Greenwich (note this is the five hour time difference between England and Ontario)

The time zones into which we divide the globe are also roughly based on the longitude (although other considerations that have nothing to do with longitude also affect it). Each time zone corresponds to about 15 degrees of longitude.

Questions

Latitude

  1. Hand in your star chart with the horizon sketches. Day 1 – Oct. 6th Day 2 –July 6th.
  2. Considering your Toronto horizon, which constellation will be at the Zenith on the two different dates at 8 p.m ?
  3. Considering your Toronto horizon, two hours later which constellations will be at the Zenith for both dates?
  4. On July 6th, what times would the following stars rise at?
  5. Altair
  6. Mira
  1. On what night would the following bright stars be directly overhead, and at what latitude would you be?
  2. Betelgeuse
  3. Arcturus
  4. Sirius
  5. Mira
  6. Antares

Longitude

  1. If the sun is at the standard reference for noon, what would be the following longitudes based on the sun position?
  2. 6.30 am
  3. 4.00 am
  4. 11.00 pm
  5. midnight
  6. 5.15 pm
  1. Given the following longitudes, what is the time difference to the point in question?
  2. 15
  3. 60
  4. 110
  5. 280
  6. 315

Name: Student Number: .

Answer Sheet - Exercise # 3

Latitude

  1. Hand in chart
  1. Constellation at Zenith? Day 1______Day 2______
  1. Constellation at Zenith? Day 1______Day 2______
  1. Rising times?

5. / Latitude / Date
a.
b.
c.
d.
e.

Longitude

1. Longitudes / 2. Times
a.
b.
c.
d.
e.