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23 Nov 2019

A spaceship of mass m travels from the Earth to the Moon along aline that passes through the center of the Earth and the center ofthe Moon.

(a) At what distance from the center of the Earth is the force dueto the Earth equal to the magnitude of the force due to the Moon?(Astronomical data needed for this problem can be found on theinside back cover.)
------ m

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Tod Thiel
Tod ThielLv2
12 May 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

at a point between the earth and the moon, the magnitude of theforce exerted on an object by the earth's gravity equals themagnitude of the force exerted on the object by the moon's gravity.what is the distance from the center of the earth to thispoint?

distance from center of earth to center of moon = 383000 km
radius of earth= 6370 km
radius of moon=1738 km
acceleration due to gravity for the moon = 1.62 m/s^2

at a point between the earth and the moon, the magnitude of theforce exerted on an object by the earth's gravity equals themagnitude of the force exerted on the object by the moon's gravity.what is the distance from the center of the earth to thispoint?

distance from center of earth to center of moon = 383000 km
radius of earth= 6370 km
radius of moon=1738 km
acceleration due to gravity for the moon = 1.62 m/s^2

In the example 12.5 (Section 12.3) in the textbook we ignored thegravitational effects of the moon on a spacecraft en route from theearth to the moon. In fact, we must include the gravitationalpotential energy due to the moon as well. For this problem, you canignore the motion of the earth and moon.

Part A
If the moon of mass m_{\rm M} has radius R_{\rm M} and the distancebetween the centers of the earth and the moon is R_{\rm EM}, findthe total gravitational potential energy of the particle-earth andparticle-moon systems when a particle with mass m is between theearth and the moon, and a distance r from the center of the earth.Take the gravitational potential energy to be zero when the objectsare far from each other. Take the mass of earth as m_{\rm E}.

Part B
There is a point along a line between the earth and the moon wherethe net gravitational force is zero. Use the expression derived inpart (a) to find the distance of this point from the center of theearth.

Part C
With what speed must a spacecraft be launched from the surface ofthe earth just barely to reach this point?

Part D
If a spacecraft were launched from the earth's surface toward themoon with an initial speed of 11.2 {\rm km/s}, with what speedwould it impact the moon?

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