Concept explainers
(a)
The proof for the statement that when
(a)
Answer to Problem 69PQ
It is showed that when
Explanation of Solution
Write the equation for the gravitational field for a mass.
Here,
Write the expression for the difference in gravitational field at a distance
Use equation (I) to find the expression for
Use equation (I) to find the expression for
Put the above two equations in equation (II).
Expand the numerator of the above equation.
It is given that
Conclusion:
Neglect
Thus, it is showed that when
(b)
The difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole.
(b)
Answer to Problem 69PQ
The difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is
Explanation of Solution
The expression for the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is derived in part (a).
Write the expression for the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole.
Conclusion:
Given that the mass of the black hole is one solar mass, the length of the person is
Substitute
Therefore, the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is
(c)
Whether the difference in gravitational field found in part (b) large enough to spaghettify the person.
(c)
Answer to Problem 69PQ
The difference in gravitational field found in part (b) is large enough to spaghettify the person.
Explanation of Solution
Spaghettification is the term used by Stephen Hawking to describe what happens to someone who falls feet first into a small but highly massive object. Since the gravitational field at the person’s feet is sufficiently higher than the gravitational field at the head, the person gets stretched out like a spaghetti noodle.
In part (b), it is found that the difference between the gravitational field of the black hole at the feet and the head if the person falls with feet first into the black hole is
Conclusion:
Since the feet of the person are accelerating toward the black hole
Want to see more full solutions like this?
Chapter 7 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- Since 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?arrow_forwardWhich of the following statements are fundamental postulates of the special theory of relativity? More than one statement may be correct. (a) Light moves through a substance called the ether. (b) The speed of light depends on the inertial reference frame in which it is measured. (c) The laws of physics depend on the inertial reference frame in which they are used. (d) The laws of physics are the same in all inertial reference frames. (e) The speed of light is independent of the inertial reference frame in which it is measured.arrow_forwardWhat would be the Schwarzschild radius, in light years, if our Milky Way galaxy of 100 billion stars collapsed into a black hole? Compare this to our distance from the center, about 13,000 light years.arrow_forward
- 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_forwardWhen observed from the sun at a particular instant, Earth and Mars appear to move in opposite directions with speeds 108,000 km/h and 86,871 km/h, respectively. What is the speed of Mars at this instant when observed from Earth?arrow_forwardThe acceleration due to gravity of planet X is 7.80m/s2, and its radius is 5,900 km. The gravitational constant is ?=6.67×10−11m2kg−1s−2. The mass of planet X is close to:arrow_forward
- There is a galactic, royal wedding in El Candrea. Maria Isabela, the princess of andalusia prima maxima, is riding a diamond-studded, pink spacetime motorcycle whose maximum speed is 5x10^2 km/s. The religious princess started her speed at about 5x10^1 km/s and she is to supposed to travel 1.78 x 10^4 km at a straight distance in about 60 seconds to reach the wedding before the galactic church closes. The princess accelerated until her max speed was reached. She then maintains the aforementioned speed till she reached the wedding gates. To reach the church before it closes, what should be her minimum constant acceleration? a. 8.30 km/s^2, b. 7.50 km/s^2, c. 5.29 km/s^2, or d. 6.95 km/s^2arrow_forwardWe sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the planet. It took our probe 3.5x105s to orbit the planet. Calculate the mass of planet Kerbal. Possible Formulas that can be used to answer the question: v=(2πr)/T ac=v2/r ac=(4π2r)/T2 Fc=mac Fg=mg F=(Gm1m2)/d2 g=Gm/r2 T2=(4π2/Gm)r3 v=√(Gm)/r g=9.80m/s2 G=6.67x10-11 (N∙m2)/kg2arrow_forwardI am trying to calculate the gravitational mass (in solar masses) I have the formula M= V^2 R / G (4.31 x 10^-6) The paperwork says our numbers should be big but I am coming up with .002 etc. What am I doing wrong?arrow_forward
- A planet with mass 8.07x1023 kg orbits a star with mass 1.18x1030 kg. The orbit is circular, and the distance from the planet to the sun is 121x106 km. What is the length of a year on this planet? Give your answer in earth years (1 earth year = 31,557,600 seconds).arrow_forwardThe Millennium Falcon is approximately 35.2 m long. There are conflicting reports, but the Falcon made the Kessel Run in approximately 12.27 parsecs. This is an odd unit to measure speed with as a parsec is a unit of length equal to 3.26 light-year. The science FICTION comes in when you consider that ships in Star Wars use hyperdrive to travel faster than the speed of light, so they are able to make jumps through space. Han Solo picked difficult or dangerous points to jump between to make the trip so short. Let's imagine that the Millennium Falcon travels at 0.96c during the 12.27 parsec Kessel Run. What distance, in light-year, does an observer at the finish line measure for the trip? Don't forget to convert parsec to light-year. X light-year What distance, in light-year, does Han Solo measure for the trip as he pilots the ship? light-year Which person measures the proper distance of the trip? Which person would measure the proper length of the Millennium Falcon?arrow_forwardThe Millennium Falcon is approximately 35.8 m long. There are conflicting reports, but the Falcon made the Kessel Run in approximately 12.86 parsecs. This is an odd unit to measure speed with as a parsec is a unit of length equal to 3.26 light-year. The science FICTION comes in when you consider that ships in Star Wars use hyperdrive to travel faster than the speed of light, so they are able to make jumps through space. Han Solo picked difficult or dangerous points to jump between to make the trip so short. Let's imagine that the Millennium Falcon travels at 0.97c during the 12.86 parsec Kessel Run. What distance, in light-year, does an observer at the finish line measure for the trip? Don't forget to convert parsec to light-year. light-year What distance, in light-year, does Han Solo measure for the trip as he pilots the ship? light-year Which person measures the proper distance of the trip? Which person would measure the proper length of the Millennium Falcon? ✪arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityStars and Galaxies (MindTap Course List)PhysicsISBN:9781337399944Author:Michael A. SeedsPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning