PL.1 Another consequence of the Equivalence Principle is that light will be bent in a gravitational field. This has never been measured on the surface of the earth, but was verified qualitatively by observing starlight pass- ing near the sun's edge during a total eclipse in 1919. Let's explore how much bending we would prediet in a laboratory at rest on the surface of the earth. What one would observe in such a laboratory should be the same as what one would observe in a laboratory ac- celerating in deep space with a uniform acceleration of a =-, where g is the local acceleration of gravity on the earth's surface. Imagine that a laser at one end of the laboratory emits a beam of light that originally travels parallel to the laboratory floor. This light shines on the opposite wall of the laboratory a distance d= 3.0 m away from the laser. a. Find the magnitude of this deflection in a laboratory on the surface of the earth. b. Find the magnitude of this deflection if the labora- tory is on the surface of a neutron star of mass M= 3.0x 10" kg( 15 the mass of the sun) and a radius R=12 km. [Hint: First estimate the magnitude of g, using Newton's law of universal gravitation. G= 6.67 x 10 "N- m'/kg. h of light is emitted by a laser on he floor a
PL.1 Another consequence of the Equivalence Principle is that light will be bent in a gravitational field. This has never been measured on the surface of the earth, but was verified qualitatively by observing starlight pass- ing near the sun's edge during a total eclipse in 1919. Let's explore how much bending we would prediet in a laboratory at rest on the surface of the earth. What one would observe in such a laboratory should be the same as what one would observe in a laboratory ac- celerating in deep space with a uniform acceleration of a =-, where g is the local acceleration of gravity on the earth's surface. Imagine that a laser at one end of the laboratory emits a beam of light that originally travels parallel to the laboratory floor. This light shines on the opposite wall of the laboratory a distance d= 3.0 m away from the laser. a. Find the magnitude of this deflection in a laboratory on the surface of the earth. b. Find the magnitude of this deflection if the labora- tory is on the surface of a neutron star of mass M= 3.0x 10" kg( 15 the mass of the sun) and a radius R=12 km. [Hint: First estimate the magnitude of g, using Newton's law of universal gravitation. G= 6.67 x 10 "N- m'/kg. h of light is emitted by a laser on he floor a
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Transcribed Image Text:PL.1 Another consequence of the Equivalence Principle is
that light will be bent in a gravitational field. This has
never been measured on the surface of the earth, but
was verified qualitatively by observing starlight pass-
ing near the sun's edge during a total eclipse in 1919.
Let's explore how much bending we would predict in
a laboratory at rest on the surface of the carth. What
one would observe in such a laboratory should be the
same as what one would observe in a laboratory ac-
reach the floor (a
accelerating lab a
incrtial lab. Thus
tial lab) a detecto
will be moving E
the time the pulse
tector on the ace
wavelength A of t
to the relativistic
celerating in deep space with a uniform acceleration of
ginal wavelength
v is the detector's
a. What would b
in a lab on the
where
g is the local acceleration of gravity
on the earth's surface. Imagine that a laser at one end
of the laboratory emits a beam of light that originally
travels parallel to the laboratory floor. This light shines
on the opposite wall of the laboratory a distance d=
3.0 m away from the laser.
a. Find the magnitude of this deflection in a laboratory
on the surface of the earth.
b. Find the magnitude of this deflection if the labora-
find the binom
1+ r.)
b. What would be
a lab on the sun
problem Pl 1?
PL3 Imagine a freely
face of the earth.
of a cube 44 ma
tory is on the surface of a neutron star of mass MD
3.0x 10" kg (=1.5 the mass of the sun) and a radius
R=12 km. [Hint: First estimate the magnitude of
8. using Newton's law of universal gravitation. G=
6.67 x 10 N m'/kg.1
are placed at poi
B 22 meters abov
The frame's cente
as the ball at A w
But due to tidal e
Imagine that a flash of light is emitted by a laser on
u directed toward the floor a
in a tower).
a
bit slower and
a whole. What is.
Ciha balls at B
Expert Solution
Step 1
a.
consider the following figure which represents the motion of the laser in the laboratory frame.
Let the horizontal distance traveled by the laser in a laboratory on the surface of the Earth be d, the initial speed (horizontal) of laser be v, the time taken by the laser to cover this horizontal distance d be t, and vertical deflection suffered by the laser due to the acceleration due to gravity be h.
The time taken by the laser to cover this horizontal distance is given by the following Newton’s equation of motion.
Let the vertical component of the initial velocity of the laser be uy and the vertical component of the acceleration of the laser beam be ay.
In this case,
uy = 0
According to Newton’s equation of motion, the vertical deflection of laser is given by the following equation.
Here, the negative sign indicates that the laser has been deflected towards the floor (or along the negative y-axis).
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