00:02
Our question wants us to convert the distance from the earth to the sun, which is an astronomical unit, or one day you into both units of parsecs and units of light years.
00:14
Eso to relate parsecs to astronomical units.
00:18
We're gonna note that the angle is measured in radiance is equal to the arc length, which is we're gonna call s divided by the radius are so for a very large radius circle a small value of the angle.
00:32
The art may be approximated as a straight line segment of length one a u.
00:37
So we're gonna say that data, which is equal to one arc second arc seconds, um can be converted into units of radiance.
00:53
So one by considering the fact that one arc minute is equal to 60 art seconds.
01:12
Okay, so now in units of arc minute and there is one degree for everyone, excuse me for every 60 art minutes.
01:33
So now we're in degrees and there are two pi radiance for every 360 degrees.
01:46
Oh, so you carry this out.
01:49
We find that the angle is equal to 4.85 times 10 to the minus six.
02:05
The units here are radiance.
02:10
Okay, so therefore, one par sec, which we abbreviate as pc, which is equal to, um which is equal to the arc length, which is s divided by the angle.
02:28
Data is therefore equal to 2.6 since the since s is one, eh? you this is gonna be 2.6 times 10 to the five a u.
02:56
Okay, so now, for part a, we can convert this using the conversion of part with the relationship between parsecs and astronomical units.
03:11
We can, uh we can convert, uh, one a u one astronomical unit into units of parsecs.
03:21
So one a u multiplied by our conversion here, which is, uh, one par sec.
03:30
One p c is equal to 2.6 times 10 to the fifth...