The gravitational constant may also be calculated by analyzing the motion of a r

Question

The gravitational constant may also be calculated by analyzing the motion of a rocket. Suppose a rocket is sent from the surface of the earth at an initial velocity of vi. It is equipped with an altimeter to determine its peak. Find an expression of the gravitational constant from the initial velocity, mass of the earth ME, and the initial and final heights (given that 1/rinitial - 1/rfinal = x ). Start with accelerationa = dv/dt, and use the chain rule to write a = (dv/dr)(dr/dt), but dr/dt = v, thus a = v(dv/dr). Use this definition of acceleration along with the acceleration from the Law of Universal Gravitation.

Explanation / Answer

We start with a description of forces from the free body diagram of the shuttle, and assume that the positive direction is away from Earth. There will only be one force, that of gravity. From Newton

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.