7. A satellite of mass m orbits the Earth, whose mass is M, at twice the Earth's radius R.What is the total energy of the satellite-Earth system?1 GmM1 GmMGmM2GMMA)B)-c) –4GMMD)E)4 R2 RRRR

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Answered: 7. A satellite of mass m orbits the…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 13PQ: A massive black hole is believed to exist at the center of our galaxy (and most other spiral...

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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?
Which 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.
Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way.
(a) What is the approximate force of gravity on a 70-kg person due to the Andromeda Galaxy, assuming its total mass is 1013 that of our Sun and acts like a single mass 0.613 Mpc away? (b) What is the ratio of this force to the person’s weight? Note that Andromeda is the closest large galaxy.
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.)
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.1011 solar masses. A star orbiting on the galaxy's periphery is about 6.0104 light years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
An astronaut, of total mass 85.0 kg including her suit, stands on a spherical satellite of mass 375 kg, both at rest relative a nearby space station. She jumps at a speed of 2.56 m/s directly away from the satellite, as measured by an observer in the station. At what speed does that observer measure the satellite traveling in the opposite direction? (See Section 6.2.)
Show that the velocity of a star orbiting its galaxy in a circular oibit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.
An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planet
An asteroid has speed 15.5km/s when it is located 2.00 AU from the sun. At its closest approach, it is 0.400 AU from the Sun. What is its speed at that point?
Two black holes (the remains of exploded stars), separated by a distance of 10.0 AU (1 AU = 1.50 1011 m), attract one another with a gravitational force of 8.90 1025 N. The combined mass of the two black holes is 4.00 1030 kg. What is the mass of each black hole?
. How many years would you have to wait to observe a 1° angular shift in the perihelion of Mercury due to general relativistic effects?

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7. A satellite of mass m orbits the Earth, whose mass is M, at twice the Earth's radius R. What is the total energy of the satellite-Earth system? 1 GmM 1 GmM GmM 2GMM A) B) - c) – 4GMM D) E) 4 R 2 R R R R