How was the parsec calculated?

[jimmy p]

My physics teacher wasnt sure how the parsec was worked out. I know it is about 3.26 l.y. but how did it come about and how was it worked out?

Thanx

JP

 

[marcus]

My physics teacher wasnt sure how the parsec was worked out. I know it is about 3.26 l.y. but how did it come about and how was it worked out?

Thanx

JP

parallax second

technical jargon: a second (of angle) is one sixtieth of a minute of angle, which is one sixtieth of a degree

the parsec distance arises when distances to nearby stars are being determined by triangulation, using angles

a second (of angle) is 1/3600 of a degree

parallax is the angular shift in the direction to a star which
happens in the course of the year----earth being way over to one side
on its orbit, and later being way over to the other side of its orbit

the Earth moving thisway and thatway creates a "surveyers baseline" for triangulation

the distance of one parsec is the distance to a star whose parallax (angle shift right or left from center) is
1/3600 of a degree

more distant stars have LESS parallax (less angle shift)

most stars are so far away you can't measure any parallax on them at all

maybe someone will produce a link to a webpage with pictures

 

[marcus]

but how did it come about and how was it worked out?

Thanx

JP

Whoah! a historical question!

A Prussian astronomer named Bessel, if I remember right, around 1838
was the first person to measure the distance to a star by parallax

he measured the distance to a star named "61 Cygni"
which is around 11 lightyears away or roughly 3 parsecs

that is he found that over the course of the year it appeared to shift
position by about 1/3 of a second of angle to the right and to the left
for a total of 2/3, but I guess the convention is that the parallax angle
is half the total---how much it shifts to the right and to the left of center

(it goes by reciprocals, if the star shifts by 1/5 of a second, as we change our vantage point for looking at it, then its distance is 5 parsecs)

to be precise we really should have a picture

anyway, next time you see Cygus (a big cross-shape constellation with milkyway as background) you might reflect that one of those stars is the first one our species ever figured out the distance to

besides the sun, it was hard enough finding the distance to the sun

as for who NAMED that unit of distance the parsec, I don't know, maybe somebody else does

 

[marcus]

...and how was it worked out?...

the arithmetic for why one parsec is 3.26 LY is mainly just
conversion of units

Like, the distance to the sun is 1/63,000 LY
You know that light takes 8 minutes or 500 seconds of time to get here from the sun and that turns out to be about 1/63,000 of a year

so the sun is 1/63,000 LY away from us. Horrible looking number but that is how it is, what happens when you do units conversions and get unfamiliar-looking ways of saying familiar stuff.

and how many seconds of angle are in one RADIAN?
Another ugly number

360 x 3600/2pi

360 x 3600/6.28


Well, if you multiply these two numbers together you get 3.26
and that is how many LY are in a parsec

You just have to multiply

360 x 3600/6.28 times 1/63,000

it is not so bad with a calculator, you say 360 x 3600
and then divide by 6.28 and then divide by 63000

or maybe it is better to have canceled zeros first and say 36 x 36
and then divide by 6.28 and then divide by 63

and then, to squeeze out a final infuriating bit of accuracy, it is better to use
63,200 instead of 63,000

and use a better approximation of 2pi, instead of simply the rough 6.28