**Vis Viva**equation. Start by solving the Vis Viva equation for the radius Re, then plug in the speed of light, C, as a value for the escape velocity, Ve. The resulting radius Re is the so-called “event horizon”, which equals the radius at which light cannot escape from an extremely dense sphere of mass, M. As the calculation on the right-hand side of Figure 2 indicates, if we could somehow compressed the earth down to a radius of 0.35 inches – while preserving its total mass light waves inside the sphere would be unable to escape and, therefore, could not be seen by an observer. The radius of the event horizon associated with a spherical body of mass, M, is directly proportional to the total mass involved. Figure 2: The Vis Viva equation was developed and applied repeatedly by Isaac Newton when he was evaluating various gravity-induced phenomena. Properly applied, the Vis Viva equation predicts that sufficiently dense celestial bodies generate such strong gravitational fields that nothing – not even a beam of light – can escape their clutches. Today’s astronomers are discovering numerous examples of this counterintuitive effect. Black holes are one result. As Figure 3 indicates, an enormous black hole 50 million light years from Earth has been discovered to have a mass equal to 2 billion times the mass of our sun. It is located in the M87 Galaxy in the constellation Virgo. Figure 3: In 1994 the Hubble Space Telescope discovered a huge black hole approximately 300,000,000,000,000,000,000,000 miles from planet Earth nestled among the stars of the M87 galaxy in the Virgo constellation. Astronomers estimate that it is 2,000,000,ooo times heavier than our son. That black hole’s event horizon has a radius of 3,700,000,000 miles or about 40 astronomical units. One astronomical unit being the distance from the earth to our sun.The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons. Notice that both the horizontal and the vertical axes range over 20 orders of magnitude! In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles. The event horizon of a black hole is the maximum radius from which no light can escape. The graph presented in Figure 4 links the masses of various celestial bodies with their corresponding event horizons. Notice that both the horizontal and the vertical axes range over 20 orders of magnitude! In 1942 the Indian-born American astrophysicist, Subrahmanyan Chandrasekhar, demonstrated from theoretical considerations that the smallest black hole that can result from the collapse of a main-sequence star, must have a mass that is equal to approximately 3 suns with a corresponding event horizon of 5.5 miles. The event horizon of a black hole is the maximum radius from which no light can escape.

See all the ATI open-enrollment course schedule

See all the ATI courses on 1 page. What courses would you like to see scheduled as an open-enrollment or on-site course near your facility? ATI is planning its schedule of technical training courses and would like your recommendations of courses that will help your project and/or company. These courses can also be held on-site at your facility.