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a. What would be the fractional shift in wavelength in a lab on the earth's surface? (Hint You might find the binom ial approximation helpful: (1+x)D

a. What would be the fractional shift in wavelength in a lab on the earth's surface? (Hint You might find the binom ial approximation helpful: (1+x)D

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How do I solve part a of (P1.2)
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= 3.0 x 10 kg (15 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"] P12 Imagine that a flash of light is emitted by a laser on the roof of a laboratory, directed toward the floor a distance d= 25 m above (the laboratory is in a tower). This lab is equivalent (from the point of view of the gross effects of gravity) to an identical lab accelerat- ing upward in deep space with uniform acceleration of magnitude g. Imagine that we watch the process from an inertial lab alongside the accelerating lab. For the sake of simplicity, imagine that the two labs are at rest with respect to each other at the instant that pulse is emitted. In the time it takes the light to DEL
Transcribed Image Text: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= 3.0 x 10 kg (15 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"] P12 Imagine that a flash of light is emitted by a laser on the roof of a laboratory, directed toward the floor a distance d= 25 m above (the laboratory is in a tower). This lab is equivalent (from the point of view of the gross effects of gravity) to an identical lab accelerat- ing upward in deep space with uniform acceleration of magnitude g. Imagine that we watch the process from an inertial lab alongside the accelerating lab. For the sake of simplicity, imagine that the two labs are at rest with respect to each other at the instant that pulse is emitted. In the time it takes the light to DEL
reach the floor (as measured in the inertial lab), the accelerating lab attains a certain speed relative to the inertial lab. Thus (according to observers in the iner- tial lab) a detector at the floor of the accelerated lab will be moving toward the laser with this speed v at the time the pulse is absorbed. This means that the de- tector on the accelerating lab floor will measure the wavelength 2 of the light to be blue-shifted according to the relativistic Doppler shift formula to the value A = AoV (1 olc)/(1 ginal wavelength of the light emitted by the source and v is the detector's speed relative to the source. a. What would be the fractional shift in wavelength in a lab on the earth's surface? (Fint You might find the binom ial approxim ation helpful: (1+x)*%3D 1+ nx.) b. What would be the fractional shift in wavelength in a lab on the surface of the neutron star described in ale), where do is the ori- problem Pl.1? freely falling reference frame near the sur- has the form
Transcribed Image Text:reach the floor (as measured in the inertial lab), the accelerating lab attains a certain speed relative to the inertial lab. Thus (according to observers in the iner- tial lab) a detector at the floor of the accelerated lab will be moving toward the laser with this speed v at the time the pulse is absorbed. This means that the de- tector on the accelerating lab floor will measure the wavelength 2 of the light to be blue-shifted according to the relativistic Doppler shift formula to the value A = AoV (1 olc)/(1 ginal wavelength of the light emitted by the source and v is the detector's speed relative to the source. a. What would be the fractional shift in wavelength in a lab on the earth's surface? (Fint You might find the binom ial approxim ation helpful: (1+x)*%3D 1+ nx.) b. What would be the fractional shift in wavelength in a lab on the surface of the neutron star described in ale), where do is the ori- problem Pl.1? freely falling reference frame near the sur- has the form
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