How Small Must Earth's Mass Be Compressed to Form a Black Hole?

  • Thread starter Thread starter ticels
  • Start date Start date
  • Tags Tags
    Gravitation
AI Thread Summary
To determine how small Earth's mass must be compressed to form a black hole, the escape velocity must equal the speed of light, leading to the calculation of the Schwarzschild radius. Using Newtonian mechanics, the limiting radius can be derived by setting the escape velocity formula to the speed of light and solving for radius. Additionally, once the radius is established, the weight of a mass of 4.26μg at the surface of this super-dense sphere can be calculated using the gravitational force formula. The discussion emphasizes the application of gravitational equations to understand black hole formation. This problem illustrates the intersection of mass, gravity, and the fundamental principles of physics.
ticels
Messages
1
Reaction score
0
a black hole is an object so heavy that neither matter nor even light can secape the influence of its gravitational field. Since no light can scape from it, it appears black. Suppose a mass apporxmiately the size of the Earth's mass 5.56x10^24 kg is packed into a small unifrom sphere of radius r.

*Use speed of light c=3.0x10^8 and Universal Gravitation G
*Escape speed must be the speed of light
*Relative equation
g=sq(G/r2); F=GMm/r^2; escape velocity=sq(2GM/r)

1) based on Newtonian mechanics, determine the limiting radius r0 where this mass (approximately the size of the Earth's mass) becomes a black hole. Answer in units of m.

2)Using Newtonian mechanics, how much would a mass of 4.26μg weigh at the surface of this super-dense sphere? Answer in units of N.

thx for help in advance.
 
Physics news on Phys.org
Hey hey. This is a pretty cool problem I think. What you're doing is calculating the Schwartzchild radius. You can get more info on that from Wikipedia: http://en.wikipedia.org/wiki/Schwarzschild_radius

Basically, you set the escape velocity to be the speed of light and then solve for "r".

You plug in c for the velocity, the given mass for M, and G for G and voila you've got the Schwartzchild radius.

For the 2nd problem, now that you have "r", you can solve for F from Newton's law of universal gravitation: F=GMm/r^2
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

How Small Must Mars Be Compressed to Become a Black Hole?
Replies
4
Views
2K
B A photon always travels in a black hole
Replies
9
Views
1K
Why does the gravitational force decrease below the Earth's surface?
Replies
10
Views
3K
I The initial density of an object and its compression into a black hole
Replies
17
Views
4K
Stargazing Merger of two black holes (video)
Replies
7
Views
3K
B How can a black hole absorb matter?
Replies
31
Views
577
Calculating the Maximum Mass of a Black Hole at a Given Distance
Replies
8
Views
3K
Relating Newton's Force to Black Holes (Calculation?)
Replies
4
Views
2K
Calculate Schwarzschild Radius of Earth-Sized Mass
Replies
2
Views
4K
I Escape velocity near a black hole: Newtonian or Special Relativity?
Replies
17
Views
2K

Hot Threads

Recent Insights

Back
Top