program 30, output 2
calculate distance tu a star with trig & apparent position in ski





   Astronomers get the position in the ski av a target star relativ tu
bakground av "fixed" stars 6 months apart.  In 6 months, erth go half
wae round the sun.  Yer position chaenjes bi the diameter av the orbit
round the sun.  This makes a baseline for a triangel.  Astronomers gaej
the difference in the direction tu the star.  This giv the angel opposit
the base.  This define the triangel.  Yukan yuze trig funkshuns tu
find the length av the side from base tu the angel=distance tu star.
Astronomers kall the angel the "parallax".
   In praktis, astronomers yuze half the diameter=the radius, and yuze
half the angel.  But earths orbit is an elipse insted av a serkel.
So yuze the mean distans tween erth & sun...defined tu be 1 astro unit.

        1 AU=149,597,870,660 meters (8.31647 lite-minuts).
   Problems such as klouds mae prevent him from see the star wen him wanna.
So time tween 2 points mae not be 1/2 yeer.  So gotta calculate erth
position in orbit & get reel length av the baseline.  But astronomers
konvert results tu wot it wood be for base=1 AU.
   Distance=base/tangent(angel)=base/tan(x).
Yuze series expanshun...tan(x)=x+(x**3/2)+(2*x**5/315)+...
But the angel x is so small, yuze tan(x)=x.  Plenty good nuff.
x in this equashun must be radians.
   Astronomers invented a nu yunit="parsek"=the distans wen the angel=
1 arc sekond.   serkel=360 degrees with 60 minuts/degree & 60 sekonds/minut.
1 arc sekond=serkel/1296000=2 pi radians/1296000.
1 ark sekond=6.28385306/1296000 radians=4.84813681*10^-6 radians.
1/x=206264.8063 wen angel=1 arc sekond.
Then distans=149,597,870,660*206264.8063=3.08567759*10^16 meters.
1 parsek=3.085677* 10^16 meters=3.26116333 lite-yeers.
   Ground based teleskopes kan gaej the direction av a star tu 0.01 sek.
Tu hav sum akkuracy, the star parallax need tu be 0.05 or bigger.
Thus kan get faer results for stars up tu 20 parseks awae.  Theer R
bout 100 stars kloes nuff so em kan get the distans this wae.
= max number stars em mite get the distans tu.
   Resent...teleskopes in spaes kan gaej star direkshun tu 0.001 arc sek.
Hopefully, in a fyu yeers we will no distans av bout 5,000 stars.

            distans tu neerbi stars
      name          lite-yeers   parseks   angel, arc-sekonds
1.  Proxima Centauri   4.2421      1.31    0.76
2.  Alfa    Centauri   4.3650      1.34    0.75
3.  Barnards star      5.9630      1.83    0.55
4.  Wolf 359           7.7825      2.39    0.42
5.  Lalande 21185      8.2905      2.54    0.39
6.  Sirius (a & b)     8.5828      2.63    0.38
7.  Luyten 726-8       8.7280      2.67    0.37
8.  Ross 154           9.6813      2.97    0.34
9.  Ross 248          10.322       3.17    0.32
10. Epsilon Eridani   10.522       3.23    0.31
11. Lacail 9352       10.742       3.30    0.30
12. Ross 128          10.919       3.35    0.295