(a)
The radius of the orbit.
(a)
Answer to Problem 43P
The radius of the orbit is
Explanation of Solution
The gravitational force acting on the satellite is equal
Write the expression for the force acting on the satellite.
Here,
Equate the gravitational force, and centripetal force.
Here,
Substitute,
Here,
Conclusion
Substitute,
Therefore, the radius of the orbit is
(b)
The speed of the satellite.
(b)
Answer to Problem 43P
The speed of the satellite is
Explanation of Solution
Write the expression for speed in terms of period.
Conclusion:
Substitute,
Therefore, the speed of the satellite is
(c)
The fractional change in the frequency due to time dilation.
(c)
Answer to Problem 43P
The fractional change in the frequency due to time dilation is
Explanation of Solution
Write the expression for the frequency.
Here,
Take the derivative of equation (V) on both sides.
Substitute,
The fractional change in the frequency is equal to the fractional change in time period according to equation (VII).
Substitute,
Substitute,
Here,
Conclusion:
Substitute,
Therefore, the fractional change in the frequency due to time dilation is
(d)
The fractional change in frequency due to the change in position of the satellite.
(d)
Answer to Problem 43P
The fractional change in frequency due to the change in position of the satellite is
Explanation of Solution
Write the expression for the gravitational potential.
The fractional change in frequency due to the change in position of the satellite is.
Conclusion:
Substitute,
Substitute,
Therefore, the fractional change in frequency due to the change in position of the satellite is
(e)
The overall fractional change in the frequency.
(e)
Answer to Problem 43P
The overall fractional change in the frequency is
Explanation of Solution
The fractional change in frequency due to the change in position of the satellite is
Hence the overall change in the frequency is.
Conclusion:
Therefore, the overall fractional change in the frequency is
Want to see more full solutions like this?
Chapter 9 Solutions
Principles of Physics: A Calculus-Based Text
- (a) Find the value of for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an observer measures it to be 25.0 m. (b) What is the of the spaceship relative to Earth?arrow_forwardA communications satellite is in a circular orbit about the Earth at an altitude of 3.56 104 km. How many seconds does it take a signal from the satellite to reach a television receiving station? (Radio signals travel at the speed of light, 3.00 108 m/s.)arrow_forwardThe truck in Figure P39.1 is moving at a speed of 10.0 m/s relative to the ground. The person on the truck throws a baseball in the backward direction at a speed of 20.0 m/s relative to the truck. What is the velocity of the baseball as measured by the observer on the ground? Figure P39.1arrow_forward
- (i) Does the speed of an electron have an upper limit? (a) yes, the speed of light c (b) yes, with another value (c) no (ii) Does the magnitude of an electrons momentum have an upper limit? (a) yes, mec (b) yes, with another value (c) no (iii) Does the electrons kinetic energy have an upper limit? (a) yes, mec2 (b) yes, 12mec2 (c) yes, with another value (d) noarrow_forwardAn observer in a coasting spacecraft moves toward a mirror at speed v relative to the reference frame labeled by S in Figure P26.46. The mirror is stationary with respect to S. A light pulse emitted by the spacecraft travels toward the mirror and is reflected back to the spacecraft. The spacecraft is a distance d from the mirror (as measured by observers in S) at the moment the light pulse leaves the spacecraft. What is the total travel time of the pulse as measured by observers in (a) the S frame and (b) the spacecraft? Figure P26.46arrow_forwardSuppose an astronaut is moving relative to the Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of Earth-bound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between stars that lie on lines parallel to his motion? (e) Do he and an Earth-bound observer agree on his velocity relative to the Earth?arrow_forward
- Suppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?arrow_forward(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0x109ly away is receding from us at 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)arrow_forwardAs measured by observers in a reference frame S, a particle having charge q moves with velocity v in a magnetic field B and an electric field E. The resulting force on the particle is then measured to be F = q(E + v × B). Another observer moves along with the charged particle and measures its charge to be q also but measures the electric field to be E′. If both observers are to measure the same force, F, show that E′ = E + v × B.arrow_forward
- In the “redshift” of radiation from a distant galaxy, the light Hy, known to have a wavelength of 434 nm when observed in the laboratory, appears to have a wavelength of 462 nm. What is the speed of the galaxy in the line of sight relative to the Earth?arrow_forwardA distant galaxy emits light that has a wavelength of 617.7 nm. On earth, the wavelength of this light is measured to be 623.6 nm. (a) Decide whether this galaxy is approaching or receding from the earth. (b) Find the speed of the galaxy relative to the earth. (Give your answer to 4 significant digits. Use 2.998 × 108 m/s as the speed of light.) (a) The galaxy is (b) Number ◆ from the earth Units ✪arrow_forwardA distant galaxy emits light that has a wavelength of 655.7 nm. On earth, the wavelength of this light is measured to be 660.7 nm. (a)Decide whether this galaxy is approaching or receding from the earth. (b) Find the speed of the galaxy relative to the earth. (Give youranswer to 4 significant digits. Use 2.998 × 108 m/s as the speed of light.)arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning