the spacecraft's speed before it hits the Earth
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Very far from earth (at R= infinity), a spacecraft has run out of fuel and its kinetic energy is zero. If only the gravitational force of the earth were to act on it (i.e., neglect the forces from the sun and other solar system objects), the spacecraft would eventually crash into the earth. The mass of the earth is M_e and its radius is R_e. Neglect air resistance throughout this problem, since the spacecraft is primarily moving through the near vacuum of space.
a). Now find the spacecraft's speed when its distance from the center of the earth is R= alpha * R_e, where alpha is greater than or equal to 1.
Express the speed in terms of s_e and alpha.
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Solution Summary
It shows how to find the spacecraft's speed before it hits the Earth after it runs out of fuel.
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