Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?
Let T denote the period of revolution of the satellite. Kepler’s third law says that the square of T is proportional to the cube of the major semiaxis a of its elliptical orbit. In particular, if GM D 1, then?
The point specified by the polar coordinates (7.00, 35.0º) is which of the following when converted to Cartesian coordinates?
Group of answer choices
(5.73, 4.02)
(9.17, 6.26)
(7.35, 7.35)
(3.00, 4.00)
(5.83, 3.71)
(4.02, 5.73)
the potential energy function U(r) of a projectile, plotted outward from the surface of a planet of radius Rs. If the projectile is launched radially outward from the surface with a mechanical energy of2.0 * 10^9 J, what are (a) its kinetic energy at radius r = 1.25Rs and (b) its turning point (see Module 8-3) in terms of Rs?
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- Consider a satellite in elliptical orbit around a planet of mass M, and suppose that physical units are so chosen that GM D 1 (where G is the gravitational constant). If the planet is located at the origin in the xy-plane, then Explain the equations of motion of the satellite?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_forwardLet 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.)arrow_forward
- In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?arrow_forwardIn the shown figure, the length of the side of the square is 2a , if q1=Q is placed at point “1”, the E at the center of the square is given by Select one: a. b. c. d. e.arrow_forwardOne model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M= 4.1 * 1024 kg and R = 6.0 *106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet?arrow_forward
- The point specified by the Cartesian coordinates (3, 5) is which of the follow when converted to polar coordinates? Group of answer choices (8.00, 31.0º) (8.00, 53.1º) (5.83, 59.0º) (5.83, 31.0º) (6.72, 53.1º) (6.72, 31.0º)arrow_forwardFind the angle between the vectors a = <1,2,-3> and b = <-2,1,1> in degreesarrow_forwardThe Cartesian coordinates of point P are (- 6.50 m, 8.75 m). Question 4 The length of P is ...... Question 5 The polar angle of P is ...arrow_forward
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