HP Prime: Black Hole Characteristics – Hawking Radiation

01052018, 03:32 AM
(This post was last modified: 01232018 03:02 PM by Eddie W. Shore.)
Post: #1




HP Prime: Black Hole Characteristics – Hawking Radiation
HP Prime: Black Hole Characteristics – Hawking Radiation
Equations Used Given the mass (either in kg or solar masses), the following equations can estimate these black hole characteristics: Swartzchild Radius (in m): R = M * G/c^2 Life time left as the black hole slowly radiates (in s): t = M^3 * 5120 * π * G^2 / (hbar * c^4) The HP Prime uses the conversion for seconds to years: 1 year ≈ 31556925.9747 s Average temperature of the black hole (K): temp = (hbar * c^3)/(M * 8 * k * π * G) If you need to convert to °C subtract 273.15 from this result. Surface area of the black hole (m^2): sa = (M^2 * 16 * π * G^2)/c^4 Surface gravity of the black hole (m/s^2), as you can imagine, this will be a huge number: gr = c^4 / (M * 4 * G) Constants Used Values are taken from the HP Prime Universal Gravitation Constant G = 6.67384 * 10^11 m^3/(kg * s^2) Speed of Light c = 299792458 m/s Plank Constant Divided by 2*π hbar = 1.054571726 * 10^34 J*s Boltzmann Constant k = 1.3806488 * 10^23 J/K HP Prime Program BLACKHOLE Code: EXPORT BLACKHOLE() (edited 1/23/2018, see thread below) Examples Cygnus X1: 14.8 solar masses Schwartzchild Radius: 43705.6410566 m Life: 6.79261706057 * 10^70 years Temperature: 4.16932978074 * 10^9 K (near absolute zero, very cold!) Surface Area: 24004068275.4 m^2 Surface Gravity: 1.02819127807 * 10^12 m/s^2 Sagittarius A*, the center of our Milky Way Galaxy: 4.31 million solar masses Schwartzchild Radius: 12727791415.8 m Life: 1.67758214773 * 10^87 years Temperature: 1.43169560917 * 10^14 K Surface Area: 2.03571024785 * 10^21 m^2 Surface Gravity: 3530680.02679 m/s^2 Source: Jim Wisniewski. “Hawking Radition Calcualtor” Xaonon. January 3, 2017. http://xaonon.dyndns.org/hawking/ Retrieved December 26, 2017 

01052018, 09:05 AM
Post: #2




RE: HP Prime: Black Hole Characteristics – Hawking Radiation
Thanks!
Very useful program. Salvo ∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C  DM42, DM41X  WP34s Prime Soft. Lib 

01202018, 12:23 PM
Post: #3




RE: HP Prime: Black Hole Characteristics – Hawking Radiation
(01052018 03:32 AM)Eddie W. Shore Wrote: HP Prime: Black Hole Characteristics – Hawking Radiation Hello, nice program  had to try it immediately with my brand new HP Prime Yet  it has a small error: If you try to change the input units to [kg], instead of [solar masses], the the check goes wrong: Code: IF ch:=2 THEN should read Code: IF ch=2 THEN With this small change it works nicely and delivers good results. The bug is in IF ch:=2, this sets ch to 2, instead of comparing it. 

01232018, 03:01 PM
Post: #4




RE: HP Prime: Black Hole Characteristics – Hawking Radiation
I think the line should be
IF ch==2 THEN since two equal signs are used for comparison. It seems to work either way with the one or two equal signs. The code on the original thread is now corrected. Much appreciation! Eddie 

03122024, 10:55 AM
Post: #5




RE: HP Prime: Black Hole Characteristics – Hawking Radiation
Bonjour,
Je prends connaissance de ce très intéressant programme ASTROLAB pour HP PRIME que je vais proposer à mon petit fils. Quelqu'un pourraitil me renseigner du nom de l'auteur? de ses coordonnées? J'ai pris connaissance du "Guide" mais ne trouve pas le nom de ce génial astronome. Merci d'avance. 

03122024, 12:08 PM
Post: #6




RE: HP Prime: Black Hole Characteristics – Hawking Radiation
Please use English, even if just a simple online translation, so most readers can understand. Fee free to also include your original language as well, as often there are subtle nuances that are better expressed in the native language.
For your post, google provided this, which seems clear: "I am learning about this very interesting ASTROLAB program for HP PRIME that I am going to offer to my grandson. Can anyone tell me the name of the author? his contact details? I read the “Guide” but cannot find the name of this brilliant astronomer." Bob Prosperi 

03122024, 12:50 PM
Post: #7




RE: HP Prime: Black Hole Characteristics – Hawking Radiation
Good morning,
I am learning about this very interesting ASTROLAB program for HP PRIME which I am going to offer to my grandson. Can anyone tell me the name of the author? his contact details? I read the “Guide” but cannot find the name of this brilliant astronomer. Thanks in advance 

03122024, 02:42 PM
(This post was last modified: 03122024 02:42 PM by KeithB.)
Post: #8




RE: HP Prime: Black Hole Characteristics – Hawking Radiation  
03122024, 03:22 PM
(This post was last modified: 03122024 06:21 PM by carey.)
Post: #9




RE: HP Prime: Black Hole Characteristics – Hawking Radiation
(01052018 03:32 AM)Eddie W. Shore Wrote: HP Prime: Black Hole Characteristics – Hawking Radiation While this is a 2018 post, I just noticed it due to the new comments. Two comments: 1) The code included in the original post is neatly written and motivates me to want to learn Prime programming! 2) An issue regarding precision of the calculated results. A cardinal result in error propagation is that the result of a calculation can be no more precise than the precision of the least precise number that went into the calculation. Otherwise, precision could be gained by calculation, which it can't, but only by more precise measurements. The four equations used (Schwarzschild radius, lifetime, surface area, and surface gravity) all depend on G (the universal gravitational constant) which, unfortunately, is known to only 6 digits of precision (while it's value was recently updated, the known precision is still 6 digits). Hence, calculated results using the four equations can only justifiably be expressed to no more than 6 digits of precision, but appear to be expressed to 12 digits of precision. Actually, the restriction on the number of justifiable digits of precision in the calculated results is even more severe because the four equations also all depend on M. However, M, in the example of Cygnus X1, is known to only 3 digits of precision (recently updated, but still only 3 digits of precision). Black hole masses (M) are typically known to no more than 3 digits of precision. Hence, at a minimum, digits 712 (digits 412 for most examples) of the calculated results would be commonly referred to as "false precision," i.e., while 12digit results may look more "precise," additional digits of precision beyond the number of digits of precision of the least precise number used in a calculation are meaningless and can detract from this excellent program. 

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