A spaceship is on a straight-line path between Earth and the Moon. At what distance from Earth is the net gravitational force on the spaceship zero?
Net gravitational force on the spaceship is zero at a distance of from the earth.
The distance between the Earth and the Moon is .
Let the distance from Earth to the spaceship be r.
where m is the mass of the spaceship.
Solving for r, we obtain
The net gravitational force on the spaceship is zero at a distance of from the earth.
Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth’s center. Satellite A is to orbit at an altitude of . Satellite B is to orbit at an altitude of . The radius of Earth is .
(a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit?
(b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit?
(c) Which satellite has the greater total energy if each has a mass of ?
(d) By how much?
Mooneffect Some people believe that the Moon controls their activities. If the Moon moves from being directly on the opposite side of Earth from you to being directly overhead, by what percent does (a) the Moon’s gravitational pull on you increase and (b) your weight (as measured on a scale) decrease? Assume that the Earth–Moon (center-to-center) distance is and Earth’s radius is .
In Fig. 13-24, two particles of masses, m and 2m, are fixed in place on an axis. (a) Where on the axis can a third particle of mass 3m be placed (other than at infinity) so that the net gravitational force on it from the first two particles is zero: to the left of the first two particles, to their right, between them but closer to the more massive particle, or between them but closer to the less massive particle? (b) Does the answer change if the third particle has, instead, a mass of 16m ? (c) Is there a point off the axis (other than infinity) at which the net force on the third particle would be zero?
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