Angular Measurements

1
Angular Measurements
Linear size D
Angular size a
Small angle formula D ad/206,265 D
linear size of object, d distance to object A
angular size of object in arc seconds.
Example, on July 26, 2003, Jupiter was 943
million km from earth and Had an angular diameter
of 31.2 arc seconds. From this information, Calcul
ate the diameter of Jupiter in km. D 31.2
9.43 108 km/206,265 1.43 105 km 143,000
km. Note that the diameter of the earth 2
6,378 km 12,756 km.
2
Angular measurements, continued

• With very good seeing conditions, a telescope
  on earth can see details with an angular size as
  small as 1 arc sec.
• What is the greatest distance at which you can
  see details as small as 1.7 m (the height of a
  typical person).
• d 206,265 D/a 206,2651.7 m/1 350,000 m
  350 km.
• A spy satellite orbits at an altitude of 500 km
  500,000 m. Given that its telescope can see
  (resolving power) angles
• small as 5.1610-2 arc secs, how small an
  object can be seen on earth ?
• D ad/206,265 5.1610-2500,000/206,275
  0.125 m 12.5 cm 12.5 cm 1 inch/2.54 cm
  4.9 inches.

3
Powers of 10, scientific or exponential notation

• We use scientific notation because of the large
  range of number sizes used in physics and
  astronomy.
• Example, 100 1,000 100,000
• But convert to exponential notation
• 102 103 1023 105
• To divide numbers expressed in terms of powers of
  ten, remember that 1/10 10-1 1/100 10-2
• More generally, 1/10n 10-n
• For example, 104/106 104-6 10-2

4
Units of length, time and mass

• We use the MKS system meters, kilograms, second
• Units of length
• 1 millimeter 10-3 m .001 m
• 1 centimeter 10-2 m .01 m
• 1 kilometer 103 m 1000 m
• 1 inch 2.54 cm
• 1 ft 0.3048 m
• 1 mile 1.609 km
• Units of mass
• 1 kg 1000 grams
• 1 Msolar 1.99 1030 kg
• 1 kg is about equal to 2.2 lbs.
• Units of time
• 1 minute 60 seconds
• 1 day 86,400 seconds
• 1 year 3.156 107 seconds.