HOLECALC.DOC

HOLECALC.COM IS A COMPILED S-BASIC PROGRAM THAT CALCULATES THE
PROPERTIES OF A BLACK HOLE GIVEN RADIUS, DENSITY OR MASS.

HOLECALC.BAS IS THE SOURCE CODE FOR HOLECALC.COM AND HOLECALC.PRN 

HOLECALC.PRN IS THE PRINT FILE OF THE COMPILED PROGRAM
HOLECALC.BAS TO HOLECALC.COM. 
WE ARE NOW IN VERSION 2 BECAUSE I DISCOVERED THAT MICRO C'S ZCPR 
NEW VERSION DOESN'T LIKE TO CHANGE MODES FOR PERFECT WRITER. WE
NEED NORMAL MODE FOR THE HOLECALC.BAS PROGRAM.

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HOLECALC.* IS AN SBASIC PROGRAM CORRECTING PREVIOUS EFFORTS AT
ASSESSING THE CHARACTERISTICS OF BLACK HOLES. BLACK HOLES WERE
ORIGINALLY PREDICTED BY REV MR. JOHN MICHELL IN 1784 (SEE SKY AND
TELESCOPE, OCTOBER 1984, P 313) MR MICHELL'S PAPER APPEARED IN
THE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY (LONDON,
1784). HE COUCHED HIS ARGUEMENT IN GEOMETRIC TERMS, AND IT IS FROM
THIS DOCUMENT THAT THE MISCONCEPTION OF A BLACK HOLE IS DERIVED.

     MR MICHELL'S ARGUEMENT IS THAT THERE IS A MAXIMUM SIZE TO
LUMINOUS STARS, BASED ON THEIR ESCAPE VELOCITY. IF THE ESCAPE
VELOCITY IS THE VELOCITY OF LIGHT (SIC), THE BODY WILL BE
INVISIBLE. THUS HE PREDICTED BLACK HOLES 200 YEARS AGO; HOWEVER,
THERE IS A MISTAKE IN HIS REASONING:

     ESCAPE VELOCITY FROM EARTH'S GRAVITY IS APPROXIMATELY 25,000
MPH. WE ARE ALL WITNESSES TO THE FACT THAT SUB ESCAPE VELOCITY
PACKAGES CAN ORBIT THE EARTH WITH NO TROUBLE. ORBITAL VELOCITY IS
APPROXIMATELY 17,670 MPH UP TO ESCAPE VELOCITY. SO IT IS THAT
OBJECTS MAY ORBIT A MASS AT WHOSE SURFACE THE ESCAPE VELOCITY IS
THE VELOCITY OF LIGHT, (THAT IS OBJECTS TRAVELING AT SUBLUMINAL
VELOCITIES.) 

     LAPLACE MADE THE SAME MISTAKE (OR MORE PROBABLY SIMPLY
FOLLOWED MICHELL IN HIS). THE VELOCITY OF ESCAPE THAT THEY WERE
LOOKING FOR IS APPROXIMATELY 4.24264 X TEN TO THE 10TH POWER
CM/SEC. THIS IS THE ROOT OF 2 TIMES 3 X TEN TO THE 10TH POWER,
THE LATTER OF WHICH (3E10) IS THE VELOCITY OF LIGHT IN VACUUM IN
CENTEMETERS PER SECOND. 

    THE SCHWARTZCHILD RADIUS OF BLACK HOLES IS ALSO IN ERROR,
BEING CALCULATED FROM LEPLACE'S EQUATIONS. CORRECT VALUES ARE
GIVEN BY THE PROGRAM, BEING EXACTLY ONE HALF THE RADIUS
PREVIOUSLY PREDICTED. 

    AT THE HEART OF IT ALL LIE TWO FUNCTIONAL RELATIONSHIPS

    D*R^2 = K = 3.22E+27 GRAMS/CC*CM^2 = 3.22E+27 GRAMS/CM

AND

   M = (4*Pi*R^3/3)*D			(A)
 
WITH THESE TWO RELATIONSHIPS, ALL OF THE OTHER RELATIONSHIPS CAN
BE CALCULATED.

     THE CONSTANT, "K," IS SIMPLY THE RESULT OF SOLVING THE
EQUATION:
 
           2*C^2 = 2*G*M/R, SUBSTITUTING RELATION (A) FOR M
 
AND SOLVING FOR THE PAIR (D*R^2). THE VALUE OF K IS
APPROXIMATELY:

          K = 3.22127 TEN(27) GM/CM

IT IS A CRITICAL VALUE: GIVEN ONE CONSTANT SAY DENSITY, THERE IS
ONE RADIUS THAT A SPHERE WITH THAT AVERAGE DENSITY BECOMES A
BLACK HOLE. ANY BODY LARGER THAN THAT AT THAT DENSITY OR ANY BODY
DENSER THAN THAT AT THAT RADIUS WILL BE A BLACK HOLE. THE
CRITICAL MASS FOR THAT DENSITY AND RADIUS IS ALSO CALCULATED. IT
IS ALSO A CRITICAL VALUE. AT THAT RADIUS ANY MASS GREATER THAN M
OR AT THAT AVERAGE DENSITY ANY MASS GREATER THAN M WILL COLLAPSE
INTO A NEWTONIAN BLACK HOLE. THIS DOES NOT NECESSARILY MEAN THAT
THE OBJECT WILL COLLAPSE INTO SINGUARITY, THAT DEPENDS ON
TEMPERATURE AND DENSITY. THE REMAINDER OF PROPERTIES, DRAWN FROM
GENERAL RELATIVITY, I AM NOT PREPARED TO DISCUSS A THIS TIME.
THERE ARE PLENTY OF ARGUEMENTS IN THE MAGAZINES AS TO WHETHER OR
NOT SUPERMASSIVE BALCK HOLES EXIST. I SUSPECT THAT THEY DO AND
THAT OUR X-RAY SOURCES, PARTICUALRLY X-RAY BURSTERS, ARE
SUPERMASSIVE BLACK HOLES (QUASARS TOO). THIS PROGRAM WAS WRITTEN
FOR PEOPLE WHO WANT TO EXPLORE THOSE POSSIBILITIES. SORRY BUT THE
LARGEST MASS ALLOWED BY S-BASIC IS 1E34 GMS. IF YOU WANT TO GET
BIGGER, REPROGRAM WITH INPUTTING MLOG/L (THE LOGARITHM BASE 10 OF
THE MASS) AND WORK OUT THE RELATIONSHIPS FOR THAT (QUANT =
MLOG/L). IT IS SIMPLEST TO DO THIS ON A SCIENTIFIC HAND
CALCULATOR, JUST USE THE LOG FUNCTION ON THE SCIENTIFIC NUMBER OF
THE MASS IN GRAMS. 

    THE UNIVERSE AS WE KNOW IT IS APPROXIMATELY 14 BILLION LIGHT
YEARS (BEVALYS) = 1.325 TEN(28) CM IN RADIUS. YOU CAN CALCULATE
ITS MAXIMUM MASS USING THE PROGRAM. USING THE REALTIONSHIP

     #OF MASSIVE PARTICLES = 2*REST MASS*6.23 TEN(23)

YOU CAN CALCULATE THE MAXIMUM NUMBER OF PROTONS, ELECTRONS AND
NEUTRONS IN THE VISIBLE UNIVERSE. IT SHOULD BE SOMEWHERE AROUND
TEN (81) PARTICLES. AND THAT'S ALL THERE IS!

   				MIKE FINERTY
				2358 E PARKSIDE DR
   				TUCSON, ARIZONA 85713

COMMENTS APPRECIATED!