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- The distance of a galaxy from our solar system is 10 Mpc. (a) What is the recessional velocity of the galaxy? (b) By what fraction is the starlight from this galaxy red shifted (that is, what is its z value)?A2. A light beam falls radially inwards towards the center of a black hole. First it passes shell A at a distance rA from the center of the black hole. It then passes the shell B at a distance rB from the center of the black the hole. We call the two shell passes event A and event B. Where large is the time interval between these two events and how can did you figure it out? Explain with a maximum of 3 sentences (plus any equations if you wish).The Schwarzschild radius RBH for an object of mass M is defined as (See image.) where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole. 1. The mass of the Sun is about 1.99 × 1030 kg. What would be the radius of a black hole with this mass? 2. The mass of Mars is about 6.42 × 1023 kg. What would be the radius of a black hole with this mass? 3. Suppose you want to make a black hole that is roughly the size of an atom (take RBH = 1.10 x 10-10 m). What would be the mass M of such a black hole?
- Also, Many astronomers believe that the massive object at the center of the Milky Way galaxy is a black hole. If so, what is its Schwarzschild radius Rs?a. Find the acceleration due to gravity at the surface of a neutron star of mass 1.5 solar masses and having a radius of R = 10.0 km. b. Find the weight of a 0.120-kg baseball on the surface of this star. c. Assume the equation U = mgh applies, and calculate the energy that a 70.0-kg person would expend climbing a 1.00-cm-tall mountain on the neutron star. d. Find the speed needed by a small satellite to maintain a circular orbit with a radius of 2R around the neutron star.The Small Magellanic Cloud is a dwarf galay orbiting the Milky Way at a distance of 50 kiloparsecs from its center, on a circular orbit. It is moving at a velocity. rolative to the Milky Way, of 207 km/s. What is the mass of the Milky Way, in units of solar masses, inside the Cloud's orbit? B !! 245 If'a quasar emits 10^(10) times the Sun's luminosity, converting 10% of the mass of the material it eats into radiation, how many stars (ach of the Sun's mans) must it consume per year?
- In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of 1×1021×102 suns and a radius equal to one-half the radius of our moon. A)What is the density of the black hole in g/cm3g/cm3? The radius of our sun is 7.0×105km7.0×105km, and it has an average density of 1.4×103kg/m31.4×103kg/m3. The diameter of the moon is 2.16×1032.16×103 miles. 1km=0.6214mile1km=0.6214mile.?When you throw a ball into the air, it usually falls back down. If you throw it a little harder, it will take it longer to fall back down. You can throw it so hard that it never falls back down to Earth. This launch speed is called the escape velocity. When you are far from Earth, the potential energy of an object with mass m can no longer be written as PE = mgh. Instead, we must use the equation М-т PE = -G .. 1" M is the mass of the planet you launch from. m is the mass of the object being launched. r is the distance from the center of the planet to the object being launched. G is a universal constant called the gravitational constant (6.67-10-" ). kg-s Notice that the potential energy is 0 when you are infinitely far away from the planet, and negative as you get closer.A black hole has an event horizon radius of 5.00××1033 m. a) What is its mass? b) Determine the gravitational acceleration it produces at a distance of 5.01××1033 m from its center. c) Determine the escape speed at a distance of 5.01××1033 m from its center.
- The acceleration of gravity near a black hole is so large that not even light can escape. Which two factors would increase the acceleration of gravity near a black hole? O A black hole with more mass and the same radius A black hole with a larger radius and the same mass A black hole with less mass and the same radius A black hole with a smaller radius and the same mass O O OThe following quotation is taken from the article “Quantum Black Holes”, by Bernard J. Carr and Steven B. Giddings, in the May 2005 issue of Scientific American. "The total time for a black hole to evaporate away is proportional to the cube of its initial mass. For a solar-mass hole, the lifetime is an unobservably long 1064 years." a. Recall that the solar mass is 2 × 10³0 kilograms. Write a formula for the lifetime, L, of a black hole as a function of its mass, m. Start by finding the value of the constant k, then write your function using the letter k (rather than its value in scientific notation). For example, for a direct variation you would write “L(m) = km”. k = a × 10¹ where a = L(m) = b. The present age mass = c × 10ª kg, where c = A and b = = of the universe is about 10¹0 years. What would be the mass of a black hole as old as the universe? ID and d = JCompact objects and black-holes 2. Consider three compact objects in the form of: a white dwarf of 0.5Mo; a neutron star of 1.4Mo and a black-hole of 50 Mo. The radii of the white dwarf and neutron star are: Rwp 5.5 106 m and and RNS 10 Km. (a) Determine the radii of curvature Re = c2/g (where c is the speed of light and g is the local gravitational acceleration) around cach objcct specifying which radius you assume for the BH.