I'm assuming everyone here knows what a black hole is. It is something so dense that even light can't escape. That means the escape velocity is greater than the speed of light.
Therefore the Diameter of Earth would need to be about 1.78 cm with it having the same mass it has now for it to be a black hole.
Wasn't that fun!? =p
The escape velocity of Earth is about 11.2 km/s.
The formula to find that is:
V_esc = sqrt((2*G*Mass of Earth)/Radius of Earth)
The speed of light is C, approximately 3*10^8 m/s.
If we wanted to know what the diameter of Earth would have to be for it to be a black hole (given mass remains constant) we would simply do this:
V_esc = C = sqrt((2*G*Mass of Earth)/Radius of Earth)
C^2 = (2*G*Mass of Earth)/Radius of Earth
Radius of Earth = (2*G*Mass of Earth)/C^2
Diameter of Earth = (4*G*Mass of Earth)/C^2
Now I will plug in the numbers:
Diameter of Earth = (4*(6.67*10^-11)*(5.98*10^24))/((3*10^8)^2)
Diameter of Earth = 0.0178 m = 1.78 cm
The formula to find that is:
V_esc = sqrt((2*G*Mass of Earth)/Radius of Earth)
The speed of light is C, approximately 3*10^8 m/s.
If we wanted to know what the diameter of Earth would have to be for it to be a black hole (given mass remains constant) we would simply do this:
V_esc = C = sqrt((2*G*Mass of Earth)/Radius of Earth)
C^2 = (2*G*Mass of Earth)/Radius of Earth
Radius of Earth = (2*G*Mass of Earth)/C^2
Diameter of Earth = (4*G*Mass of Earth)/C^2
Now I will plug in the numbers:
Diameter of Earth = (4*(6.67*10^-11)*(5.98*10^24))/((3*10^8)^2)
Diameter of Earth = 0.0178 m = 1.78 cm
Therefore the Diameter of Earth would need to be about 1.78 cm with it having the same mass it has now for it to be a black hole.
Wasn't that fun!? =p