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.)
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Chapter 11 Solutions
Principles of Physics: A Calculus-Based Text
- A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?arrow_forwardWhat is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?arrow_forwardMuch of the mass of our Milky Way galaxy is concentrated in a central sphere of radius r = 2 kpc, where pc is the abbreviation for the unit parsec; 1 pc = 3.26 ly. Assume the Sun is in a circular orbit of radius r = 8.0 kpc around the central sphere of the Milky Way. The Suns orbital speed is approximately 220 km/s; assume the central sphere is at rest. a. Estimate the mass in the inner Milky Way. Report your answer in kilograms and in solar masses. b. What is the escape speed of the Milky Way? c. CHECK and THINK: Do you believe that stars in the Milky Way have been observed to have speeds of 500 km/s? Explain.arrow_forward
- (a) Show that tidal force on a small object of mass m, defined as the difference in the gravitational force that would be exerted on m at a distance at the near and the far side of the object, due to the gravitational at a distance R from M, is given by Ftidal=2GMmR3r where r is the distance between the near and far side and rR .(b) Assume you are fallijng feet first into the black hole at the center of our galaxy. It has mass of 4 million solar masses. What would be the difference between the force at your head and your feet at the Schwarzschild radius (event horizon)? Assume your feet and head each have mass 5.0 kg and are 2.0 m apart. Would you survive passing through the event horizon?arrow_forwardA neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass twice that of our Sun with a radius of 12.0 km. (a) What would be the weight of a 100-kg astronaut on standing on its surface? (b) What does this tell us about landing on a neutron star?arrow_forwardCalculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?arrow_forward
- As 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_forwardCompute directly the gravitational force on a unit mass at a point exterior to a homogeneous sphere of matter.arrow_forwardNothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 × 108^8 m/sm/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 7.5 times the mass of the sun? This distance is called the Schwarzschild radius.arrow_forward
- A rogue black hole with a mass 39 times the mass of the sun drifts into the solar system on a collision course with earth. How far is the black hole from the center of the earth when objects on the earth's surface begin to lift into the air and "fall" up into the black hole? Give your answer as a multiple of the earth's radius. Express your answer using three significant figures. d = ΑΣΦ ? Rearrow_forwardA spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. It has strayed too close to a black hole having a mass 100 times that of the Sun (as shown). 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_forwardA spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 050 kg. It has strayed too close to a black hole having a mass 103 times that of the Sun. 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. Black hole -100 m 10.0 km (a) Determine the total force on the spacecraft. A black hole can be treated in the same manner as any other point mass and used in the equation for the gravitational force as long as you are outside the Schwarzschild radius. N (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 acceleration grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.) N/kgarrow_forward
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