Hello c.l.f.,

I embraced the transit of venus with some enthusiasm, and I wonder 
whether that enthusiasm got the better of my scientific judgment.

I've been doing napkin calculations after the fact and believe that I 
must have been engaging in wishful thinking while I was looking at it. 
I had gone to sears and bought a welder's helmet, because that's all 
they had, but instead of having #14 glass, it had #10.

Everyone's sold out of #14 after the eclipse, which was unbelievable 
here.  Let's take a look at what we know:

R_s = 109 ! a.u.
Ratio_earth_venus = .95 !comparison of radii
D_v = 0.723 332 AU ! mean distance of venus from sun

I have to be on my other operating system to process that, but I'll do 
so in fortran.  I find many aspects of my latest ubuntu install strange, 
so I'll get to know it through the language of my instruction: fortran.

Cheers,
-- 
Twain

On 06/12/2012 12:16 AM, Twain Benson wrote:
> Hello c.l.f.,
>
> I embraced the transit of venus with some enthusiasm, and I wonder
> whether that enthusiasm got the better of my scientific judgment.
>
> I've been doing napkin calculations after the fact and believe that I
> must have been engaging in wishful thinking while I was looking at it. I
> had gone to sears and bought a welder's helmet, because that's all they
> had, but instead of having #14 glass, it had #10.
>
> Everyone's sold out of #14 after the eclipse, which was unbelievable
> here. Let's take a look at what we know:
>
> R_s = 109 ! a.u.
> Ratio_earth_venus = .95 !comparison of radii
> D_v = 0.723 332 AU ! mean distance of venus from sun
>
> I have to be on my other operating system to process that, but I'll do
> so in fortran. I find many aspects of my latest ubuntu install strange,
> so I'll get to know it through the language of my instruction: fortran.
>
> Cheers,

$  gfortran   -Wall -Wextra i2.f90  -o out
$ ./out
  V_nought =   5.23598810E+17 m**3.
  M_nought =   1.04719760E+21 kg.
  I was    4.5070372     per cent off.
  surface gravity of minimal necessarily-round object is   0.27951801 
   m/s**2.
  P nought is   1.39759008E+08 newtons.
$

aha, I can fortran.
--

On 06/12/2012 12:31 AM, Cal Dershowitz wrote:
> R_s = 109 ! a.u.
> Ratio_earth_venus = .95 !comparison of radii
> D_v = 0.723 332 AU ! mean distance of venus from sun

I think the above three data are the only ones we need to determine the 
apparent size of venus versus the sun:


$ gfortran   -Wall -Wextra venus3.f90  -o out
$ ./out
  pi is =    3.1415927
  as is =    37325.262
  av is =    2.8352873
  ratiois =    13164.543
  complement  is =   0.27666801
$ cat venus3.f90
implicit none
real :: pi, venus_au, complement
real :: radius_sun, radius_venus
real :: area_sun, area_venus, ratio

pi = 4.0 * atan(1.0)
print *,"pi is = ", pi

venus_au =  0.723332 ! AU mean distance of venus from sun
radius_sun = 109 ! earths
radius_venus = .95 ! earths

area_sun = pi * radius_sun ** 2  ! earths^2
area_venus = pi * radius_venus ** 2  ! earths^2
ratio = area_sun / area_venus
complement = 1.0 - venus_au

print *,"as is = ", area_sun
print *,"av is = ", area_venus
print *,"ratio is = ", ratio
print *,"complement  is = ", complement


end program
! gfortran   -Wall -Wextra venus3.f90  -o out
$

A little stuck here.  I think I've got all the parts there, but I don't 
know how to punctuate it.  Again, I just may have been staring into that 
son of a gun too long.
-- 
Cal

$ gfortran   -Wall -Wextra venus4.f90  -o out
$ ./out
  pi is =    3.1415927
  complement  is =   0.27666801
  venus_earth  is =    41389052.
  alpha_sun is =   4.64908499E-03
  alpha_venus  is =   1.46217411E-04
$ cat venus4.f90
implicit none
real :: pi, venus_au, complement
real :: radius_sun, radius_venus
real :: alpha_venus, alpha_sun
real :: earth_sma, venus_earth

pi = 4.0 * atan(1.0)
print *,"pi is = ", pi

! values
venus_au =  0.723332 ! AU mean distance of venus from sun
earth_sma = 149598261 ! km semi-major axis
radius_sun = 6.955e05 ! km
radius_venus = 6051.8 ! km

! computations
complement = 1.0 - venus_au
venus_earth = complement * earth_sma
alpha_sun = atan( radius_sun / earth_sma) ! radians
alpha_venus = atan( radius_venus / venus_earth) ! radians

print *,"complement  is = ", complement
print *,"venus_earth  is = ", venus_earth
print *,"alpha_sun is = ", alpha_sun
print *,"alpha_venus  is = ", alpha_venus

!print *,"ratio is = ", ratio
end program
! gfortran   -Wall -Wextra venus4.f90  -o out
$

Still a little stuck at the end.
--

>
> Still a little stuck at the end.
> --

$ gfortran   -Wall -Wextra venus5.f90  -o out
$ ./out
  pi is =    3.1415927
  complement  is =   0.27666801
  venus_earth  is =    41389052.
  alpha_sun is =   4.64908499E-03
  alpha_venus  is =   1.46217411E-04
  ratio is =    1010.9593
$ cat venus5.f90
implicit none
real :: pi, venus_au, complement
real :: radius_sun, radius_venus
real :: alpha_venus, alpha_sun
real :: earth_sma, venus_earth, ratio

pi = 4.0 * atan(1.0)
print *,"pi is = ", pi

! values
venus_au =  0.723332 ! AU mean distance of venus from sun
earth_sma = 149598261 ! km semi-major axis
radius_sun = 6.955e05 ! km
radius_venus = 6051.8 ! km

! computations
complement = 1.0 - venus_au
venus_earth = complement * earth_sma
alpha_sun = atan( radius_sun / earth_sma) ! radians
alpha_venus = atan( radius_venus / venus_earth) ! radians
ratio =  (sin(alpha_sun) / sin(alpha_venus)) ** 2

print *,"complement  is = ", complement
print *,"venus_earth  is = ", venus_earth
print *,"alpha_sun is = ", alpha_sun
print *,"alpha_venus  is = ", alpha_venus
print *,"ratio is = ", ratio
end program
! gfortran   -Wall -Wextra venus5.f90  -o out
$

I think I've got it there, but it seems low to me.  If you consider the 
area that both angular deflections would have at the distance of venus, 
then that radius will be D /sin (alpha).  We're comparing areas, so 
that's pi r^^2.  in the comparison, the pi's and d's cancel, and we're 
left with quotients of the sin's, squared ... I think ....
-- 
Cal

"Cal Dershowitz" <cal@example.invalid> wrote in message 
news:8-GdnVxGXejnSUXSnZ2dnUVZ_rqdnZ2d@supernews.com...

> alpha_sun = atan( radius_sun / earth_sma) ! radians

Consider a triangle with one vertex at the observer, another
at the center of the sun, and the third where the line of
sight of the observer is tangent to the limb of the sun.
Where is the right angle?

> ratio =  (sin(alpha_sun) / sin(alpha_venus)) ** 2

If solid angle were proportional to sin(alpha)**2, then the
solid angle of the whole celestial sphere would be zero.
Recall, O ye of 1.0e6 names, that the integral from zero to alpha
of sin(theta)*dtheta = -cos(theta) from zero to alpha
= 1-cos(alpha) = 2*sin(alpha/2)**2

-- 
write(*,*) transfer((/17.392111325966148d0,6.5794487871554595D-85, &
6.0134700243160014d-154/),(/'x'/)); end

Note that the transit is not usually along a diameter of the Sun due to
Earth's relatively inclined orbit.
You have to treat the problem as one of the time of crossing an arc with a
particular subtended angle to the Sun's geometric centre. The angle is not
180 degrees and the path is not a diameter.

On 06/13/2012 02:57 PM, James Van Buskirk wrote:
> "Cal Dershowitz"<cal@example.invalid>  wrote in message
> news:8-GdnVxGXejnSUXSnZ2dnUVZ_rqdnZ2d@supernews.com...
>
>> alpha_sun = atan( radius_sun / earth_sma) ! radians
>
> Consider a triangle with one vertex at the observer, another
> at the center of the sun, and the third where the line of
> sight of the observer is tangent to the limb of the sun.
> Where is the right angle?

I have a response for that involving Riemann's stereographic projection, 
but I'd better stick to the things that I'm struggling with most first.

$ gfortran   -Wall -Wextra venus6.f90  -o out
$ ./out
  pi is =    3.1415927
  alpha_sun is =   4.64908499E-03
  rad_to_degrees is =    57.295776
  arc_sun in radians is =   9.29816999E-03
  arc_sun in seconds is =    63.929504
  arc_venus in seconds is =    2.0106337
  ratioin radians is =    31.795700
$ gfortran   -Wall -Wextra venus6.f90  -o out
$ ./out
  pi is =    3.1415927
  alpha_sun is =   4.64908499E-03
  rad_to_degrees is =    57.295776
  arc_sun in radians is =   9.29816999E-03
  arc_sun in seconds is =    63.929504
  arc_venus in seconds is =    2.0106337
  ratio is =    31.795700
$ cat venus6.pl
cat: venus6.pl: No such file or directory
$ cat venus6.f90
implicit none
real :: pi, venus_au, complement
real :: radius_sun, radius_venus
real :: alpha_venus, alpha_sun
real :: earth_sma, venus_earth, ratio
real :: radius_purple, arc_sun, arc_venus
real :: rad_to_degrees, rad_to_seconds

pi = 4.0 * atan(1.0)
print *,"pi is = ", pi

! values
venus_au =  0.723332 ! AU mean distance of venus from sun
earth_sma = 149598261 ! km semi-major axis
radius_sun = 6.955e05 ! km
radius_venus = 6051.8 ! km

! computations
complement = 1.0 - venus_au
venus_earth = complement * earth_sma
alpha_sun = atan( radius_sun / earth_sma) ! radians
alpha_venus = atan( radius_venus / venus_earth) ! radians
! ratio =  (sin(alpha_sun) / sin(alpha_venus)) ** 2
radius_purple = 4 * radius_venus
arc_sun = 2 * alpha_sun
rad_to_degrees = 180.0 / pi
rad_to_seconds = 6 * 60 * 60 / pi

print *,"alpha_sun is = ", alpha_sun
print *,"rad_to_degrees is = ", rad_to_degrees
print *,"arc_sun in radians is = ", arc_sun

!! further computations
arc_sun = arc_sun * rad_to_seconds ! seconds
arc_venus = 2 * alpha_venus
arc_venus = arc_venus * rad_to_seconds  ! seconds
ratio = arc_sun / arc_venus

print *,"arc_sun in seconds is = ", arc_sun
print *,"arc_venus in seconds is = ", arc_venus
print *,"ratio is = ", ratio

end program
! gfortran   -Wall -Wextra venus6.f90  -o out
$



>
>> ratio =  (sin(alpha_sun) / sin(alpha_venus)) ** 2
>
> If solid angle were proportional to sin(alpha)**2, then the
> solid angle of the whole celestial sphere would be zero.
> Recall, O ye of 1.0e6 names, that the integral from zero to alpha
> of sin(theta)*dtheta = -cos(theta) from zero to alpha
> = 1-cos(alpha) = 2*sin(alpha/2)**2
>

We were always taught 3 D's first, at least by the time we reached 
college.  I have images uploaded to define the parameters of this 
consideration but have failed to link them correctly.  Tja.

We consider the universe as solar-system for flatlanders.  The 
flatlanders all live on the disc described by one's middle finger with 
the right-hand rule, when your thumb points to polaris and the motion of 
your hand is counter to the advancing ecliptic. We're at O, the point 
source that is the arbitrary observer.  we keep track of distant objects 
in seconds.  Out there is 6 hours worth of seconds.  Some have posited a 
dual on the other half of the clock, but that's silly 
ueberdimension-talk.  That's just when we sleep.  Rush Limbaugh says 
they took 12 hours from our day.  He can say what he wants: he's the 
sexiest man in this universe: he's so ... round.

Forget the spin and motion of everything.  These are just co-linear 
spheres in a usenet thread. The consideration ends at the closeness of 
the radius of a sphere to its observer.  That's when the rest of us 
said, "it hit you."

But there are not really spheres in flatland, so we'll keep our rumors 
of higher dimensions to ourselves.  My suspicion is that literature will 
go back as far as literature goes on how big the travelers in the sky are.

How many seconds is venus, to someone who looks through a telescope?
-- 
Cal

On 06/14/2012 12:18 AM, Terence wrote:
> Note that the transit is not usually along a diameter of the Sun due to
> Earth's relatively inclined orbit.
> You have to treat the problem as one of the time of crossing an arc with a
> particular subtended angle to the Sun's geometric centre. The angle is not
> 180 degrees and the path is not a diameter.
>
>

Yeah, but we'll define our universe to be co-linear with respect to the 
actors, such that all the big local things get skewered on the same 
shishkabob.

Looking one way, you see, venus the sun then everything else.  Looking 
the other, we see the indomitable mars, jupiter, then outer space.

If I had a nickel to bet on who sees the next transit of venus, I'd put 
it on you, Terence: you'll be lapping us all at 200.
-- 
Cal

"Cal Dershowitz" <cal@example.invalid> wrote in message 
news:RrCdnRA5A6X-JUfSnZ2dnUVZ_sWdnZ2d@supernews.com...

>  arc_sun in seconds is =    63.929504

How do you get such a rapid turnaround time for your messages from
Sirius B?

-- 
write(*,*) transfer((/17.392111325966148d0,6.5794487871554595D-85, &
6.0134700243160014d-154/),(/'x'/)); end

On 2012-06-15 2:28 PM, Cal Dershowitz wrote:
> If I had a nickel to bet on who sees the next transit of venus, I'd put
> it on you, Terence: you'll be lapping us all at 200.

....and still using F77...

Ian Harvey <ian_harvey@bigpond.com> wrote:

> On 2012-06-15 2:28 PM, Cal Dershowitz wrote:
> > If I had a nickel to bet on who sees the next transit of venus, I'd put
> > it on you, Terence: you'll be lapping us all at 200.
> 
> ...and still using F77...

F77 subset, remember, which is almost more like f66 than f77 full
language in many ways. :-)

-- 
Richard Maine                    | Good judgment comes from experience;
email: last name at domain . net | experience comes from bad judgment.
domain: summertriangle           |  -- Mark Twain

Yeah, but I added my own additional link library which adds all the screen,
colours, and full keyboard and (simultaneous) mouse control. And this lets
me compile the same source in F77 and in F90/95 compilers using the
appropriate link library.    :o)>

On 06/14/2012 10:51 PM, James Van Buskirk wrote:
> "Cal Dershowitz"<cal@example.invalid>  wrote in message
> news:RrCdnRA5A6X-JUfSnZ2dnUVZ_sWdnZ2d@supernews.com...
>
>>   arc_sun in seconds is =    63.929504
>
> How do you get such a rapid turnaround time for your messages from
> Sirius B?
>

I'm working on that one, james.

$ gfortran   -Wall -Wextra flatland2.f90  -o out
flatland2.f90: In function �MAIN__�:
flatland2.f90:22:0: warning: �arc_sun� is used uninitialized in this 
function [-Wuninitialized]
$ gfortran   -Wall -Wextra flatland2.f90  -o out
flatland2.f90: In function �MAIN__�:
flatland2.f90:22:0: warning: �arc_sun� is used uninitialized in this 
function [-Wuninitialized]
$ ./out
  pi is =    3.1415927
  moon:
  seconds_next is    17.036123
$ cat flatland2.f90
implicit none
real :: pi
real :: radius_sun
real :: earth_sma, d_next, r_next
real :: arc_sun, arc_next
real :: rad_to_degrees, rad_to_seconds, seconds_next

pi = 4.0 * atan(1.0)
print *,"pi is = ", pi

! values

earth_sma = 149598261 ! km semi-major axis
radius_sun = 6.955e05 ! km

! unit transformations  !!!  hugely suspect
rad_to_degrees = pi / 180.0
rad_to_seconds = pi / 6 * 60 * 60 ! half the clockface is
! 6 hours * 60 min * 60 s

!! further computations
arc_sun = 2 *arc_sun * rad_to_seconds ! seconds

!!!!!!

! lets continue with the moon

print *, "moon: "
d_next = 384399 ! km
r_next = 1737.10 ! km
arc_next = 2.0 * atan( r_next / d_next) ! radians
seconds_next = rad_to_seconds * arc_next
print *, "seconds_next is ", seconds_next

end program
! gfortran   -Wall -Wextra flatland2.f90  -o out
$


I'm gonna guess that the real answer for how many seconds the moon and 
sun are in flatland lies between these values.

I don't see how I offended gfortran.exe in the above.

-- 
Cal

On 06/15/2012 06:58 PM, Terence wrote:
> Yeah, but I added my own additional link library which adds all the screen,
> colours, and full keyboard and (simultaneous) mouse control. And this lets
> me compile the same source in F77 and in F90/95 compilers using the
> appropriate link library.    :o)>
>
>

The cloud does pretty well with that now.  Why the heck is uranus bigger 
than the moon from Amiland?

$ gfortran   -Wall -Wextra flatland3.f90  -o out
$ ./out
  pi is =    3.1415927
  moon:
  seconds_next is   9.58955570E-06
  uranus:
  seconds_next is   1.61003205E-03
$ cat flatland3.f90
implicit none
real :: pi, arc_next
real :: radius_sun
real :: earth_sma, d_next, r_next
real :: rad_to_degrees, rad_to_seconds, seconds_next

pi = 4.0 * atan(1.0)
print *,"pi is = ", pi

! values
earth_sma = 149598261 ! km semi-major axis
radius_sun = 6.955e05 ! km

! unit transformations  !!!  hugely suspect
rad_to_degrees = pi / 180.0
rad_to_seconds = pi / 12 * 60 * 60  ! ??
! let's continue with the moon

print *, "moon: "
d_next = 384399 ! km
r_next = 1737.10 ! km
arc_next = 2.0 * atan( r_next / d_next) ! radians
seconds_next = arc_next / rad_to_seconds
print *, "seconds_next is ", seconds_next

! populate d_next and r_next with uranus values
print *, "uranus: "
d_next = 2876679082.0  ! km
r_next = 18.22941195 * earth_sma ! km 19.229 411 95 AU
! source: http://en.wikipedia.org/wiki/Uranus
arc_next = 2.0 * atan( r_next / d_next) ! radians
seconds_next = arc_next / rad_to_seconds
print *, "seconds_next is ", seconds_next


end program
! gfortran   -Wall -Wextra flatland3.f90  -o out
$
-- 
Cal

On 6/17/12 4:42 AM, Cal Dershowitz wrote:
.....
> rad_to_seconds = pi / 6 * 60 * 60 ! half the clockface is
> ! 6 hours * 60 min * 60 s

Did you really mean (pi/6)*(60*60)  (explicit expression equivalent to 
what you wrote) ? Or should it be  pi/(6*60*60) ?

Giorgio

On Saturday, June 16, 2012 7:42:19 PM UTC-7, Cal Dershowitz wrote:
[...]
> I don't see how I offended gfortran.exe in the above.

Gfortran told you, "warning: 'arc_sun' is *used uninitialized* in 
this function", and it is.  The first use of arc_sun is in this
statement:

> !! further computations
> arc_sun = 2 *arc_sun * rad_to_seconds ! seconds

Therefore, you get garbage in arc_sun since it has never been
initialized, it has an indeterminate value on the RHS.

Reading error messages isn't *really* that hard...

   -Ken

On 06/17/2012 06:03 AM, Giorgio Pastore wrote:
> On 6/17/12 4:42 AM, Cal Dershowitz wrote:
> ....
>> rad_to_seconds = pi / 6 * 60 * 60 ! half the clockface is
>> ! 6 hours * 60 min * 60 s
>
> Did you really mean (pi/6)*(60*60) (explicit expression equivalent to
> what you wrote) ? Or should it be pi/(6*60*60) ?
>

Thx, Giorgio, that certainly wasn't helping matters.  I can't at all 
decide whether the seconds that we can count with a wristwatch have 
anything to to with the seconds that derive from the degrees in 
geometrical calculations, so I removed them:

$ gfortran   -Wall -Wextra flatland3.f90  -o out
$ ./out
  pi is =    3.1415927
  moon:
  degrees_next is   0.51783597
  uranus:
  degrees_next is   1.07398548E-03
  jupiter:
  degrees_next is   1.27374576E-02
  degrees_next is    90.000000
$ cat flatland3.f90
implicit none
real :: pi, arc_next
real :: radius_sun
real :: earth_sma, d_next, r_next
real :: rad_to_degrees, degrees_next

pi = 4.0 * atan(1.0)
print *,"pi is = ", pi

! values
earth_sma = 149598261 ! km semi-major axis
radius_sun = 6.955e05 ! km

! unit transformations
rad_to_degrees = 180.0 / pi

print *, "moon: "
d_next = 384399 ! km
r_next = 1737.10 ! km
arc_next = 2.0 * atan( r_next / d_next) ! radians
degrees_next = arc_next * rad_to_degrees
print *, "degrees_next is ", degrees_next

! populate d_next and r_next with uranus values
print *, "uranus: "
d_next = 2876679082.0  - earth_sma! km
r_next = 25559 ! km 25,559
! source: http://en.wikipedia.org/wiki/Uranus
arc_next = 2.0 * atan( r_next / d_next) ! radians
degrees_next = arc_next * rad_to_degrees
print *, "degrees_next is ", degrees_next

! populate d_next and r_next with jupiter values
print *, "jupiter: "
d_next = 778547200.0 - earth_sma ! km
r_next = 69911.0  ! 69,911
arc_next = 2.0 * atan( r_next / d_next) ! radians
degrees_next = arc_next * rad_to_degrees
print *, "degrees_next is ", degrees_next

arc_next = pi / 2.0
degrees_next = arc_next * rad_to_degrees
print *, "degrees_next is ", degrees_next


end program
! gfortran   -Wall -Wextra flatland3.f90  -o out
$

I think, from a flatland perspective, this shows jupiter to be an order 
of magnitude larger than uranus.

Is it possible that the moon takes up less than a degree in the sky?
-- 
Cal

On 06/18/2012 11:01 AM, ken.fairfield@gmail.com wrote:
> On Saturday, June 16, 2012 7:42:19 PM UTC-7, Cal Dershowitz wrote:
> [...]
>> I don't see how I offended gfortran.exe in the above.
>
> Gfortran told you, "warning: 'arc_sun' is *used uninitialized* in
> this function", and it is.  The first use of arc_sun is in this
> statement:
>
>> !! further computations
>> arc_sun = 2 *arc_sun * rad_to_seconds ! seconds
>
> Therefore, you get garbage in arc_sun since it has never been
> initialized, it has an indeterminate value on the RHS.
>
> Reading error messages isn't *really* that hard...
>
>     -Ken

True, true.  I couldn't find this line in my source then, and I couldn't 
now.  Juggling windows on this new ubuntu platform has been problematic, 
but I'm getting the knack.
-- 
Cal