Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 68Q
To determine
To explain:
The reason for the requirement of careful piloting to direct a spacecraft into a black hole.
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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?
In 1999 scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun but occupying less space than our moon. Suppose that of these black holes has a mass of 1x10^3 sun's and radius equal to one-half the radius of our moon. What is the density in grams per cubic centimeter? The mass of the sun is 2.0x10^30 kg and the radius of the moon is 2.16x10^3 mi.
Devise a way for the occupants of a spaceship to know whether they are being pulled into a black hole. What can they do if they determine they are within the Schwarzschild radius?
Chapter 21 Solutions
Universe: Stars And Galaxies
Ch. 21 - Prob. 1QCh. 21 - Prob. 2QCh. 21 - Prob. 3QCh. 21 - Prob. 4QCh. 21 - Prob. 5QCh. 21 - Prob. 6QCh. 21 - Prob. 7QCh. 21 - Prob. 8QCh. 21 - Prob. 9QCh. 21 - Prob. 10Q
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- A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. Ii has strayed too close to a black hole having a mass 100 times that of the Sun (Fig. P11.11). The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)arrow_forwardAs an object falls into a black hole, tidal forces increase. Will these tidal forces always tear the object apart as it approaches the Schwarzschild radius? How does the mass of the black hole and size of the object affect your answer?arrow_forwardIn 1999, scientists discovered a new class of black holes with masses 100 to 10000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5km and it has an average density of 1.4x10^3kg/m^3. The diameter of the moon is 2.16x10^3 miles. Note: the volume of a sphere is V=4/3 pie r^3arrow_forward
- As a person approaches the Schwarzschild radius of a black hole, outside observers see all the processes of that person (their clocks, their heart rate, etc.) slowing down, and coming to a halt as they reach the Schwarzschild radius. (The person falling into the black hole sees their own processes unaffected.) But the speed of light is the same everywhere for all observers. What does this say about space as you approach the black hole?arrow_forwardIn 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 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5 km, and it has an average density of 1.4x10^3 kg/m^3. The diameter of the moon is 2.16x10^3 miles.arrow_forwardIn 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.?arrow_forward
- Calculate the Schwarzschild radius for the sun and Earth.arrow_forwardX and Y were born on the same year on planet LOL (event O). On their 60th birthday, X discovered a star explosion that is 70 light years away from LOL (event X). Similarly, on their 70th birthday, Y discovered a different star explosion that is 80 light years away from LOL (event Y). X calculates the proper distance between events O and X while Y calculates the proper distance between events O and Y. Who will obtain the largest proper distance? A. Proper distance cannot be obtained for these pair of events. B. X C. Y D. They will calculate the same proper distancearrow_forwardA particle maintains a circular orbit around a black hole of mass 10 Solar masses at a distance equal to 2 Schwarzschild radii. Calculate the orbital velocity of the particle and express the answer in units of the speed of light.arrow_forward
- The evil team of Ms. Moonstruck and Mr. Luny intend to deflect the Moon from its orbit around Earth by pulling it with a force of 2330 N . They plan to accomplish this by placing a mini black hole 7.71×10^6 m from the center of the Moon and letting gravitation do what gravitation does. What must the mass of the mini black hole be for the evil duo's evil scheme to succeed? The mass of the Moon is 7.36×10^22 kg .arrow_forwardQuestion A5 State the value of the Ricci tensor R on the event horizon of a Schwarzschild black hole, and justify your answer.arrow_forwardA2. 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).arrow_forward
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