DATA Supernova! (a) Equation (16.30) can be written as f R = f S ( 1 − υ c ) 1 / 2 ( 1 + υ c ) − 1 / 2 where c is the speed of light in vacuum, 3.00 × 10 8 m/s. Most objects move much slower than this ( υ / c is very small), so calculations made with Eq. (16.30) must be done carefully to avoid rounding errors. Use the binomial theorem to show that if υ ≪ c , Eq. (16.30) approximately reduces to f R = f S [1 − ( υ / c )] . (b) The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. (The explosion was seen on the earth on July 4, 1054 C.E.) Its streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 × 10 14 Hz; the red light received from streamers in the Crab Nebula that are pointed toward the earth has frequency 4.586 × 10 14 Hz. Estimate the speed with which the outer edges of the Crab Nebula are expanding. Assume that the speed of the center of the nebula relative to the earth is negligible. (c) Assuming that the expansion speed of the Crab Nebula has been constant since the supernova that produced it, estimate the diameter of the Crab Nebula. Give your answer in meters and in light-years. (d) The angular diameter of the Crab Nebula as seen from the earth is about 5 arc-minutes ( 1 arc-minute = 1 60 degree ). Estimate the distance (in light-years) to the Crab Nebula, and estimate the year in which the supernova actually took place.
DATA Supernova! (a) Equation (16.30) can be written as f R = f S ( 1 − υ c ) 1 / 2 ( 1 + υ c ) − 1 / 2 where c is the speed of light in vacuum, 3.00 × 10 8 m/s. Most objects move much slower than this ( υ / c is very small), so calculations made with Eq. (16.30) must be done carefully to avoid rounding errors. Use the binomial theorem to show that if υ ≪ c , Eq. (16.30) approximately reduces to f R = f S [1 − ( υ / c )] . (b) The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. (The explosion was seen on the earth on July 4, 1054 C.E.) Its streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 × 10 14 Hz; the red light received from streamers in the Crab Nebula that are pointed toward the earth has frequency 4.586 × 10 14 Hz. Estimate the speed with which the outer edges of the Crab Nebula are expanding. Assume that the speed of the center of the nebula relative to the earth is negligible. (c) Assuming that the expansion speed of the Crab Nebula has been constant since the supernova that produced it, estimate the diameter of the Crab Nebula. Give your answer in meters and in light-years. (d) The angular diameter of the Crab Nebula as seen from the earth is about 5 arc-minutes ( 1 arc-minute = 1 60 degree ). Estimate the distance (in light-years) to the Crab Nebula, and estimate the year in which the supernova actually took place.
DATA Supernova! (a) Equation (16.30) can be written as
f
R
=
f
S
(
1
−
υ
c
)
1
/
2
(
1
+
υ
c
)
−
1
/
2
where c is the speed of light in vacuum, 3.00 × 108 m/s. Most objects move much slower than this (υ/c is very small), so calculations made with Eq. (16.30) must be done carefully to avoid rounding errors. Use the binomial theorem to show that if υ ≪ c, Eq. (16.30) approximately reduces to fR= fS [1 − (υ/c)]. (b) The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. (The explosion was seen on the earth on July 4, 1054 C.E.) Its streamers glow with the characteristic red color of heated hydrogen gas. In a laboratory on the earth, heated hydrogen produces red light with frequency 4.568 × 1014 Hz; the red light received from streamers in the Crab Nebula that are pointed toward the earth has frequency 4.586 × 1014 Hz. Estimate the speed with which the outer edges of the Crab Nebula are expanding. Assume that the speed of the center of the nebula relative to the earth is negligible. (c) Assuming that the expansion speed of the Crab Nebula has been constant since the supernova that produced it, estimate the diameter of the Crab Nebula. Give your answer in meters and in light-years. (d) The angular diameter of the Crab Nebula as seen from the earth is about 5 arc-minutes ( 1 arc-minute =
1
60
degree ). Estimate the distance (in light-years) to the Crab Nebula, and estimate the year in which the supernova actually took place.
A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.3 days. The average brightness of this star is 4.0 and its brightness changes by ±0.45. In view of these data,
the brightness of the star at time t, where t is measured in days, has been modeled by the function
B(t) = 4.0 +0.45 sin
(a) Find the rate of change of the brightness after t days.
dB
dt
(b) Find, correct to two decimal places, the rate of increase after five days.
dB
dt
Let À = 3.92i + 4.41j and B = -3.02i + -2.43j. What is the angle between À and B measured in degrees. Note that the angle may be greater than 90 degrees.
(I understand the basic steps of the question but I keep getting 115.432. My last step was Cos^-1(2.9/22.588)
A new satellite launched to the space. It is
orbiting the earth so that its displacement f
north of
the equator is given f =
A sin(wt + a). Sketch 2 cycles of f as a
function of t if A = 500 km, w = 3.6 rad/hour
and a = 0. Use proper scale to sketch graph.
Show detailed steps including how to find
the x-intercepts.
Chapter 16 Solutions
University Physics with Modern Physics (14th Edition)
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