Sep 18 - Time zones. Scale and angular measure.

Question 1

Finding Latitude - Using North/Celestial Poles

Answer 1

Possible when able to locate the north or south celestial poles in your sky, as latitude is equal to the altitude of the celestial pole

n the NH at night, you can determine your approximate latitude by measuring the altitude of Polaris, which lies within 1 degree of the north celestial pole

EX: Polaris has an altitude of 17 degrees, latitude is between 16-18

Question 2

Finding Latitude - Using Stars

Answer 2

Determine latitude from the altitude of any star as it crosses your meridian

Star’s point of crossing over the meridian MINUS star’s dec.

Then 90 deg. MINUS this number = latitude

Question 3

Finding Latitude in Daytime - Using Sun

Answer 3

you can find your latitude from the Sun’s altitude on your meridian if you know the date and the Sun’s declination on that date.

EX: For example, suppose the date is March 21 and the Sun crosses your meridian at altitude 70° in the north. Because the Sun has dec=0° on March 21, you can conclude that the celestial equator also crosses your meridian in the north at altitude 70°, which means you are at latitude 20°S.

Question 4

Finding Longitude - Using Current Position of an Object in Sky

Answer 4

By comparing the current position of an object in your sky with its position as seen from some known longitude

• Suppose you use a sundial to determine that the apparent solar time is 1:00 P.M., which means the Sun crossed your meridian 1 hour ago
• You immediately call a friend in England and learn that it is 3:00 P.M. in Greenwich (or you carry a clock that keeps Greenwich time). You now know that your local time is 2 hours earlier than the local time in Greenwich, which means you are 2 hours west of Greenwich
• (An earlier time means that you are west of Greenwich, because Earth rotates from west to east.) Each hour corresponds to 15° of longitude, so “2 hours west of Greenwich” means longitude 30°W

Question 5

Finding Longitude At Night - Using Positions of Stars in Local Sky

Answer 5

For example, suppose Vega is on your meridian and a call to your friend reveals that it won’t cross the meridian in Greenwich until 6 hours from now. In this case, your local time is 6 hours later than the local time in Greenwich, which means you are 6 hours east of Greenwich, or at longitude 90°E (because 6×15°=90°).

Question 6

What are the three considerations that make celestial navigation more difficult in practice?

Answer 6

1. Finding either latitude or longitude requires a tool for measuring angles in the sky.

• Tools - astrolabe (difficult/expensive to make), planispheres, cross staff, sextant (allows more precise angle determinations by incorporating a small telescope for sightings - still used for celestial navigation on many ships)
• Most people determine direction with the aid of a compass; however, a compass needle doesn’t actually point to true geographic north - instead, responds to Earth’s magnetic field and points to magnetic north, which can be substantially different from true north

2. Knowing the celestial coordinates of stars and the Sun so that you can determine their paths through local sky

• In addition to knowing the celestial coordinates, you must either know the constellations and bright stars extremely well or carry star charts to help you identify them. For navigating by the Sun in the daytime, you’ll need a table listing the Sun’s celestial coordinates on each day of the year.

3. Determining longitude - you need to know the current position of the Sun in a known location, such as Greenwich, England

It’s more practical to carry a clock set to universal time (the time in Greenwich). In the daytime, the clock makes it easy to determine your longitude. If apparent solar time is 1:00 P.M. in your location and the clock tells you that it is 3:00 P.M. in Greenwich, then you are 2 hours west of Greenwich, or at longitude 30°W

• The task is more difficult at night, because you must compare the position of a star in your sky to its current position in Greenwich.

Question 7

Global Positioning System:

Answer 7

positions relative to earth-orbiting satellites, which function like artificial stars

Their positions at any moment are known from their orbital characteristics, and they transmit radio signals that can be picked up by GPS receivers in cars and other devices

Your GPS receiver locates three or more of the satellites and then does computations to calculate your position on earth

Question 8

Angular Sizes & Distances:

Answer 8

• Our lack of depth perception on the celestial sphere means we have no way to judge the true sizes or separations of the objects we see in the sky.
• However, we can describe the angular sizes or separations of the objects we see in the sky without knowing how far away they are

Question 9

Angular Size:

Answer 9

• the angle an objects appears to span in your field of view
• DOES NOT by itself tell us an object’s true size, as it depends on distance

Question 10

Angular Distance

Answer 10

• angle that appears to separate a pair of objects in the sky
• For greater precision, we subdivide each degree into 60 arcminutes, and each arcminute into 60 arcseconds