Explore BrainMass

Explore BrainMass

    Newton's Law of Universal Gravitation

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Imagine a line drawn from the center of the earth to the center of the moon. At some point on this line the magnitude of the gravitational attraction of the moon on a space vehicle would be equal to the magnitude of the earth's gravitational attraction on the vehicle. If the distance from the earth to the moon is about 4.0 x 10^5 km and the mass of the moon is about 1/80 that of the earth, at what distance from the earth's center will the resultant force acting on the space vehicle be zero?

    © BrainMass Inc. brainmass.com December 24, 2021, 9:38 pm ad1c9bdddf
    https://brainmass.com/physics/solar-system/newtons-law-universal-gravitation-399128

    SOLUTION This solution is FREE courtesy of BrainMass!

    Hello and thank you for posting your question to Brainmass!

    The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

    Let be the distance from the earth's center, the distance from the moon's center and R is the distance between earth's and moon's center. is the mass of the earth, the mass of the moon and the mass of the spacecraft.

    Since the force exerted by the earth must be the same as the force exerted by the moon we have:
    (1.1)
    Or we can write:

    (1.2)
    We also know that:
    (1.3)
    Therefore:
    (1.4)

    Or:

    (1.5)
    All that is left is to plug in the numbers:

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:38 pm ad1c9bdddf>
    https://brainmass.com/physics/solar-system/newtons-law-universal-gravitation-399128

    Attachments

    ADVERTISEMENT