Gravitational attraction force between two objects with masses m, and m2, separated by distance x, is F = G ™1m2 x2 = 6.67 × 10-11 is constant. where G Suppose a 1.5 x 1013 [kg] comet is passing the orbit of Mars (x = 2.28 × 1011[m]) heading straight for the Sun (m = 2 x 1030 [kg]) at a speed v = 3.5 × 104 [m/s]. What will its speed be when it crosses the orbit of Mercury (x = 5.79 × 10° [m] ) ? [Hint: How much work is done by gravity when the separation changes from x, to x2 ?]

Gravitational attraction force between two objects with masses m, and m2, separated by distance x, is F = G ™1m2 x2 = 6.67 × 10-11 is constant. where G Suppose a 1.5 x 1013 [kg] comet is passing the orbit of Mars (x = 2.28 × 1011[m]) heading straight for the Sun (m = 2 x 1030 [kg]) at a speed v = 3.5 × 104 [m/s]. What will its speed be when it crosses the orbit of Mercury (x = 5.79 × 10° [m] ) ? [Hint: How much work is done by gravity when the separation changes from x, to x2 ?]

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.49P

See similar textbooks

Similar questions

Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2
If a spacecraft is headed for the outer solar system, it may require several gravitational slingshots with planets in the inner solar system. If a spacecraft undergoes a head-on slingshot with Venus as in Example 11.6, find the spacecrafts change in speed vS. Hint: Venuss orbital period is 1.94 107 s, and its average distance from the Sun is 1.08 1011 m.
A planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is (a) four times as large (b) twice as large (c) the same (d) half as large (e) one-fourth as large as the gravitational force exerted by the planet on Moon 1.
A single-stage rocket of mass 308 metric tons (not including fuel) carries a payload of 3150 kg to low-Earth orbit. The exhaust speed of the rockets cryogenic propellant is 3.20 103 m/s. a. If the speed of the rocket as it enters orbit is 8.00 km/s, what is the mass of propellant used during the rockets burn? b. The rocket is redesigned to boost its exhaust speed by a factor of two. What is the mass of propellant used in the redesigned rocket to carry the same payload to low-Earth orbit? c. Because the exhaust speed of the redesigned rocket is increased by a factor of two, why is the fuel consumption of the redesigned rocket not exactly half that of the original rocket?
It was stated that a satellite with negative total energy is in a bound orbit, whereas one with zero or positive total energy is in an unbounded orbit. Why zero or positive total energy is in an unbounded orbit. Why is this true? What choice for gravitational potential energy was made such that this is true?
A planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is (a) four times as large (b) twice as large (c) the same (d) half as large (e) one-fourth as large as the gravitational force exerted by the planet on Moon 1.
Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)
For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?
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?
Calculate 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?
A meteoroid is moving towards a planet. It has mass m = 0.18×109 kg and speed v1 = 3.8×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.26×107 m. The mass of the planet is M = 10×1025 kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.
A spacecraft is on a journey between 2 planets. The masses of the Planet A and Planet B are 6.96x1024 kg and 2.08x1022 kg. The distance between the centers of the planets is 6.49x108 m. At what point, as measured from the center of Planet A, does the gravitational force exerted on the craft by Planet A equal 6 times the magnitude of Planet B on the craft? Use g=9.8