HP Prime: Black Hole Characteristics – Hawking Radiation
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01-05-2018, 03:32 AM
(This post was last modified: 01-23-2018 03:02 PM by Eddie W. Shore.)
Post: #1
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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 X-1: 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 |
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01-05-2018, 09:05 AM
Post: #2
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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 |
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01-20-2018, 12:23 PM
Post: #3
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RE: HP Prime: Black Hole Characteristics – Hawking Radiation
(01-05-2018 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. |
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01-23-2018, 03:01 PM
Post: #4
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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 |
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