Transcript Black Holes
Black Holes Black Holes Escape speed: The minimum speed required for a projectile to escape the gravitational effects of an object. For the earth, the escape speed from the surface is 11 km/sec. Escape Speed Interesting piece of information: IF the earth (magic?) could be collapsed to a radius of 0.008756 m (just about a centimeter) Some numbers: From the surface of the earth, M = 5.97 x 1024 Kg R = 8.756 x 10-3 m vescape, earth = 3.0 x 108 m/sec Hmmmmmmmmmm Black Holes Interesting implication, once the details of General Relativity were understood: If the earth were to collapse to a radius of about 1 cm (a little less, actually), light would not be able to escape the gravitational pull of the earth. The trick is that the earth isn’t going to collapse to a radius of less than 1 cm However…….. Black Holes It is known from physical law that if the starting mass of a star is above 25 solar masses, the core that will remain after the life cycle has been completed will have a mass greater than 3 solar masses. There are no known mechanisms in physical law that can overcome gravity under these circumstances, and the core will continue to collapse FOREVER Escape Speed Recall: vescape = 1/2 ( ) 2GM R Escape Speed If you are looking for a circumstance for which the escape speed will equal the speed of light, then: vescape = c = 1/2 ( ) 2GM R Or, rearranging, R= 2G c2 ( )M or, R M Black Holes IF a core has a mass greater than 3 solar masses, and gravitation collapse cannot be stopped, then it is guaranteed that eventually the core will reach a radius with an escape speed greater than c. Once this happens, nothing, INCLUDING LIGHT, can escape the large gravitational pull of the core. Black Holes Schwarzschild Radius – the radius of a celestial object at which gravitational forces exceed the ability of matter and energy to escape. Event Horizon – A sphere with a radius equal to the Schwarzschild radius. Once the radius of the collapsing core goes below the Schwarzschild radius (ie, the physical object is contained within the event horizon), no form of information can escape. Block Hole – A object which has collapsed to a radius smaller that its Schwarzschild radius. Black Holes Event Horizon Black Holes And from outside, it look like….. Black Holes Are we all going to be eaten by black holes?? Black Holes Earth Sun Black Holes Earth F = G ME M / r2 Sun r Black Holes Earth Sun shrunk to inside Event Horizon Black Holes Earth r Sun shrunk to inside Event Horizon Black Holes Earth F = G ME M / r2 r Sun shrunk to inside Event Horizon Black Holes Earth F = G ME M / r2 r Sun shrunk to inside Event Horizon The earth will experience no unusual effect if the sun were to suddenly shrink to inside of its event horizon !