More on degrees and angular sizes
• There are 360 degrees in a circle and the circumference of a circle of radius R is 2piR or 6.282 x radius.
• Each degree can be split into 60 parts called a minute
• Each minute can be split into 60 seconds called a second
• So there are 60x60 seconds in a degree
• How many seconds in a circle?
• The "arc" or part of a circle made up of a 90 degree angle at the center is its circumference times 90/360
• So for a circle of radius 10metres, its circumference is 6.282 x 10 = 62.82m
• For this circle an angle of 1 degree has an arc of (1/360) x 62.82 = 0.175m
• An angle of 1 minute at the centre subtends an arc of (1/360x60) x62.82 = 0.003m
• An angle of 1 second at the centre subtends an arc of (1/360x60x60) x62.82 = 0.00005m
• Latitude measures "angle" at the center of the Earth, so an angle of 90 degrees at the centre corresponds to a distance or arc of 6.282 x Earth's radius x 0.25 km at the surface.
• So the distance between the North Pole and Belem in Brazil (0 degrees latitude) is 6.282 x 6389 x 0.25 = 10033.9km.
• Oswego is at latitude 43.455 degrees N, Syracuse is at latitude 43.04 degrees N, a difference of about 0.42 degrees, so the distance from Syracuse to Oswego is circmference of the Earth x (0.42/360) km.
• An arcminute is the length of arc subtended by an angle of a minute at the center.
• An arcsecond is the length of arc subtended by an angle of a second at the center.
• On Earth, the angular size of the full moon is about 30 minutes of arc.
• The angular size of an object is proportional to its linear size divided by its distance from you.
• Angular size calculator
• So a marble 1cm in diameter has angular size proportional to 0.01/1 at a distance of a metre and an angular size proportional to 0.01/10 degrees at a distance of 10 metres.
• So the angular size of an object goes down as the distance to the object goes up.
• But a marble of diameter 10 cm has an angular size at 1 metre proportional to 0.1/1 degrees and a marble of diameter 100cm has an angular size proportional to 1/1 degrees at a distance of 1 meter.
• So angular size of an object goes up as the size of the object goes up if the distance to the object stays the samep.
• The radius of the moon is 1738km and its distance from Earth is 384400km. What is its angular size?
• The radius of the Sun is 700,000km and its distance from Earth is 1AU. What is its angular size?
• The altitude of Polaris, the north star, is equal to your latitude,
• Oswego's latitude is roughly 44 degrees north. What altitude is the north star in Oswego?
• In a certain city, the altitude of Polaris is 60 degrees. Is this city north or south of Oswego?
• Your friend measures that Polaris is 30 degrees from the zenith and says your measurement of the altitude of Polaris is wrong. Who is right?