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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:

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() BEGIN // EWS 2018-01-04 // Hawking Radiation // Input of mass LOCAL ch,M; INPUT({M,{ch,{"kg","Solar Mass"}}}, "Mass",{"Mass: ","Unit: "}); IF ch=2 THEN M:=1.988435ᴇ30*M; END; LOCAL k,G,c,hbar; // from 4 Constants // Shift, Units, Constant k:=1.3806488ᴇ−23; // Chemistry G:=6.67384ᴇ−11; // Physics c:=299792458; // Physics hbar:=1.054571726ᴇ−34; // Quantum // Swartzchild radius (m) LOCAL R:=(2*G*M)/c^2; // Life (years) LOCAL t:=M^3*5120*π*G^2/ (hbar*c^4*31556925.9747); // Temperature (K) LOCAL temp:=(hbar*c^3)/ (M*8*k*π*G); // Surface Area (m^2) LOCAL sa:=M^2*16*π*G^2/c^4; // Gravity  LOCAL gr:=c^4/(4*G*M); // Results PRINT(); PRINT("Schwartzchild Radius:"); PRINT(R+" m"); PRINT("Life:"); PRINT(t+" years"); PRINT("Temperature:"); PRINT(temp+" K"); PRINT("Surface Area:"); PRINT(sa+" m^2"); PRINT("Surface Gravity:"); PRINT(gr+" m/s^2"); // List RETURN {R,t,temp,sa,gr}; END;```

Examples

Cygnus X-1: 14.8 solar masses

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

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
Thanks!
Very useful program.

Salvo
(01-05-2018 03:32 AM)Eddie W. Shore Wrote: [ -> ]HP Prime: Black Hole Characteristics – Hawking Radiation

<...>
HP Prime Program BLACKHOLE

Code:
```EXPORT BLACKHOLE() BEGIN // EWS 2018-01-04 // Hawking Radiation // Input of mass LOCAL ch,M; INPUT({M,{ch,{"kg","Solar Mass"}}}, "Mass",{"Mass: ","Unit: "}); IF ch:=2 THEN M:=1.988435ᴇ30*M; <...>```
<...>
http://xaonon.dyndns.org/hawking/ Retrieved December 26, 2017

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`

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.
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
Bonjour,
Je prends connaissance de ce très intéressant programme ASTROLAB pour HP PRIME que je vais proposer à mon petit fils.
Quelqu'un pourrait-il 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.
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.

"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."
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.
(01-05-2018 09:05 AM)salvomic Wrote: [ -> ]Thanks!
Very useful program.

Salvo

Wow, what do you do for a living to make this "useful"? 8^)
(01-05-2018 03:32 AM)Eddie W. Shore Wrote: [ -> ]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:

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)

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)

Universal Gravitation Constant
G = 6.67384 * 10^-11 m^3/(kg * s^2)

Examples

Cygnus X-1: 14.8 solar masses

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

While this is a 2018 post, I just noticed it due to the new comments.