1 A star 6.0 * 10 12m away from a black hole is rotating around it at a speed of 2.0 *106m/s. What is the maximum radius r of this possible black hole? (1. The gravitational acceleration provides the solution of centripetal acceleration GM/r 2 = v 2/r, and m = v 2 * r/g 2. The escape velocity of a black hole exceeds the speed of light by 2 gm/r >; R < = c 2 solution; = GM/C 2/2) 2 Read the following information and answer the questions according to the relevant information in the information: ① The energy change of the gravitational field caused by the change of the relative position of two objects (relative to a certain zero position) is called the gravitational potential energy of the pair of objects, and then the gravitational potential energy EP can be calculated by the following formula: EP =-GMM/R (let EP=0 be at infinity) where m and m. (2) The star surface. About 200 years ago, Laplace, a French mathematician and astronomer, predicted that a luminous star with a density of the earth and a diameter of 250 times that of the sun would not allow any light to leave it because of gravity, and its escape speed was faster than the speed of light in vacuum. This strange star is called a black hole; Radius r day = 7×105km =11or Earth mass m day =2× 1030 kg=333000M Earth average density ρ day =1.4×103kg. In the following questions, all stars (including black holes) are regarded as a sphere with uniform mass distribution. (1) If the speed of an object moving in a uniform circle around the earth's surface is 7.9 km/s, what is the escape speed of the object from the earth's gravity? (2) Try to estimate the ratio of gravity acceleration on the surface of the sun to that on the surface of the earth. (3) It is known that the mass of a star when it evolves into a black hole is m, and the critical radius rg when it evolves into a black hole is obtained. (4) If the sun can eventually evolve into a black hole, what is the critical radius rg for it to evolve into a black hole? (g = 6.67×10-1nm2/kg2, m day =2.0× 1030 kg, with two significant figures reserved. ) 3 In the center of the Milky Way, there is a "super black hole" (a special celestial body) that cannot be directly seen by the naked eye. In 2005, Shanghai scientists led an international research team to take the clearest "radio photos" of black holes with radio telescope arrays. It is known that the diameter of a black hole is equivalent to that of the earth, but its mass is at least 400,000 times that of the sun. Look up the table and check the relevant data. What is the mass of the black hole? What is the density of a black hole? (Keep one decimal place in the calculation result) 4 http://218.93.122:1616/smallclass.asp? BigClassID = 38 & ampbig class name = % CD % F2 % D3 % D0 % D2 % FD % c 1% A6 % B6 % A8 % C2 % C9 & amp； small classid = 172 & amp； Class name =% ce% c0% d0% C7% ce% ca% cc% E2 (this question bank is very good).