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?