Re: Planet X: SIZE Clarification

On Mon, 28 May 2001 19:12:18 -0500, Nancy Lieder <zetatalk@zetatalk.com> wrote:
> In Article <3B12B51B.B01FA740@tut.fi> John Shakespeare wrote:
> > tholen@AntiSpam.ham wrote:
> >> Pluto is 2300 km in diameter and 0.11 arcsec in angular
> >> diameter.  Given that subarcsecond seeing is possible
> >> from the ground, and quite common at some sites,
> >> let's pick 1 arcsec as making an object not look like a
> >> point source.  You could get that with something only
> >> twice the Earth's size.
> >
> > Nancy's object is claimed to be 9 times further than Pluto, and
> > four times the diameter of the Earth (so it is claimed, anyway).
> > That would make it 0.2 arcsec or thereabouts
> 
> We're dealing with theoreticals here?  We're dealing with David's "lets
> pick" size, and going from there?  We've had (below) the following stabs
> at the viewable arcseconds that P-X would present, if 4 times as large
> as Earth and 9 Sun-Pluto distance at present.  WHERE'S THE MATH WHEN WE
> NEED IT!  (Not being able to do this, I whine and hollar and put the
> burden on someone else, I confess.)
> 
(...snipped...)
>
>

The below is a slightly edited portion of an earlier post I
(JJ) posted on SA and SAA, under the Subject: and Date: as
given, that shows the calculated apparent size of Planet X
with respect to Pluto and shows the math used to obtain the
value:
 
Subject: Re: Planet X: MAY Coordinates
Date...: Thursday, May 10, 2001 3:18 PM

(...snip...)
The apparent size of Planet X at this time is NOT smaller
than the apparent size of Pluto.  In fact it is almost 2
times (1.857) the apparent size of Pluto.  Data stated by
you or your own website indicates this.  This is determined
by calculating and comparing the apparent angular size of
the two objects: (Those of you on this list that know this
stuff better than I, please correct me if I've strayed,
inferred or calculated improperly. Much obliged!)

Using the following formula:

                              Object Linear Width
                              (viewable diameter)
Apparent Angular Size (AAS) = -------------------
    (in radians)               Object Distance

    (see http://www.astronomical.org/astbook/form.html)

PLANET X -- From your own words above, you state that Planet
X is 4 times (in diameter?) the size of earth or 12,756 km
times 4 or 51,024 km.

    (see http://www.nineplanets.org/earth.html)

From your website, the current position of Planet X (at 104
weeks to go) is given as 33.119 billion miles from Earth,
which, times 1.609 km/mile is 53.288 billion kilometers.


    (see http://www.zetatalk.com/theword/Tword03a.htm)


PLUTO -- Pluto's diameter is 2274 km

    (see http://www.nineplanets.org/pluto.html)

and according to Starry Night, Pluto is currently 29.48 AU
from Earth or 29.48 times 1.496*10^8km from Earth or 4.410
billion km.

Summarizing:  

Pluto Diameter...: =          2,274 km
Pluto Distance...: =  4,410,000,000 km
Planet X Diameter: =         51,024 km
Planet X Distance: = 53,288,000,000 km

Calculating:

AAS Pluto...: =  2,274 / 4.410*10^9  = 515.67*10^-9 radians

AAS Planet X: = 51,024 / 53.288*10^9 = 957.51*10^-9 radians

So the apparent angular size of Planet X is greater than the
apparent angular size of Pluto by:

(AAS Planet X) / (AAS Pluto) = 957.51 / 515.67 = 1.857

This indicates to me that if using the same telescope,
Planet X, if it could be seen today, should appear nearly
twice as large (1.857 times) as Pluto.

(...snip...)

JJ