A particle of mass m is moving in the Earth's gravitational field under the force whose magnitude is F=GmM/r^2, where r is distance from particle to the center of the Earth. At the Earth's surface, r=R, R is radius of the Earth.

Suppose that a particle will move along the straight line that goes through the center of the Earth and initial position of a particle on the Earth's surface. Write differential equation of motion and determine velocity of a particle in function of it's distance from the center of the Earth if at initial moment its velocity was V.

Question

A particle of mass m is moving in the Earth's gravitational field under the force whose magnitude is F=GmM/r^2, where r is distance from particle to the center of the Earth. At the Earth's surface, r=R, R is radius of the Earth.

Suppose that a particle will move along the straight line that goes through the center of the Earth and initial position of a particle on the Earth's surface. Write differential equation of motion and determine velocity of a particle in function of it's distance from the center of the Earth if at initial moment its velocity was V.

gorica · Answer

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