P1.3 Imagine a freely falling reference frame near the sur- face of the earth. This reference frame has the form of a cube 44 m on a side. Imagine that floating balls are placed at point A in the frame's center, at point B 22 meters above A, and at point C 22 m below A. The frame's center of mass will fall at the same rate as the ball at A which is located at the frame's center. But due to tidal effects, the balls at B and C will fall a bit slower and faster respectively than the frame as a whole. What is the magnitude of the accelerations of the balls at B and C relative to A? Feel free to use Newtonian physics in this calculation: we will show later that general relativity leads to the same results near the surface of the earth to many decimal places. (Hint: You will need to use the binomial approxima- tion (1+x)" = 1 + nx. If you do not, you will find that your calculator does not keep enough digits to yield an accurate result.)
P1.3 Imagine a freely falling reference frame near the sur- face of the earth. This reference frame has the form of a cube 44 m on a side. Imagine that floating balls are placed at point A in the frame's center, at point B 22 meters above A, and at point C 22 m below A. The frame's center of mass will fall at the same rate as the ball at A which is located at the frame's center. But due to tidal effects, the balls at B and C will fall a bit slower and faster respectively than the frame as a whole. What is the magnitude of the accelerations of the balls at B and C relative to A? Feel free to use Newtonian physics in this calculation: we will show later that general relativity leads to the same results near the surface of the earth to many decimal places. (Hint: You will need to use the binomial approxima- tion (1+x)" = 1 + nx. If you do not, you will find that your calculator does not keep enough digits to yield an accurate result.)
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Transcribed Image Text:P1.3 Imagine a freely falling reference frame near the sur-
face of the earth. This reference frame has the form
of a cube 44 m on a side. Imagine that floating balls
are placed at point A in the frame's center, at point
B 22 meters above A, and at point C 22 m below A.
The frame's center of mass will fall at the same rate
as the ball at A which is located at the frame's center.
But due to tidal effects, the balls at B and C will fall
a bit slower and faster respectively than the frame as
a whole. What is the magnitude of the accelerations
of the balls at B and C relative to A? Feel free to use
Newtonian physics in this calculation: we will show
later that general relativity leads to the same results
near the surface of the earth to many decimal places.
(Hint: You will need to use the binomial approxima-
tion (1+x)" = 1 + nx. If you do not, you will find that
your calculator does not keep enough digits to yield an
accurate result. )
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