A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 11 years have elapsed on earth, and 7.0 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth? Earth time Spaceship departs earth Number Ship time Units Earth time s Ship time t 7 f² Spaceship arrives at distant planet

A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 11 years have elapsed on earth, and 7.0 years have elapsed on board the ship. How far away (in meters) is the planet, according to observers on earth? Earth time Spaceship departs earth Number Ship time Units Earth time s Ship time t 7 f² Spaceship arrives at distant planet

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter26: Relativity

Section: Chapter Questions

Problem 2P: A spaceship moves past Earth with a speed of 0.900c. As it is passing, a person on Earth measures...

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If you use an Earth based telescope to project a laser beam onto the moon, you can move the spot across the moon's surface at a velocity greater than the speed of light Does this violate modern relativity? (Note that light is being sent from the Earth to the moon, not across the surface of the moon.)
You have an assistantship with a math professor in a future world where space travel is common and spacecraft regularly achieve near-light speeds. A spacecraft has taken of recently to carry individuals to colonize an Earth-like planet around a nearby star. Your professor, who remains on Earth, is teaching the students on the spacecraft via the future version of distance learning. It is time for the students on the spacecraft to take a math exam. The professor wishes the students to have a time interval tp = 2.00 h to complete the exam, so just as the spacecraft passes Earth on its last trip around the Sun at its constant cruising speed of 0.960c, she sends a signal to the proctor to have the students begin the exam. Knowing of your experience in physics courses, the professor asks you to determine the time interval through which she should wait before sending a radio signal to the departing spacecraft to tell the proctor to have the students stop working on the exam.
An astronaut has a heartbeat rate of 66 beats per minute as measured during his physical exam on Earth. The heartbeat rate of the astronaut is measured when he is in a spaceship traveling at 0.5c with respect to Earth by an observer (A) in the ship and by an observer (B) on Earth. (a) Describe an experimental method by which observer B on Earth will able to determine the heartbeat rate of the astronaut when the astronaut is in the spaceship. (b) What will be the heartbeat rate(s) of the astronaut reported by observers A and B?
A spaceship moves past Earth with a speed of 0.900c. As it is passing, a person on Earth measures the spaceship's length to be 75.0 m. (a) Determine the spaceships proper length. (b) Determine the time required for the spaceship to pass a point on Earth as measured by a person on Earth and (c) by an astronaut onboard the spaceship.
A spaceship moves past Earth with a speed of 0.900c. As it is passing, a person on Earth measures the spaceship's length to be 75.0 m. (a) Determine the spaceships proper length. (b) Determine the time required for the spaceship to pass a point on Earth as measured by a person on Earth and (c) by an astronaut onboard the spaceship.
A physics professor on Earth gives an exam to her students who are on a spaceship traveling at speed v relative to Earth. The moment the ship passes the professor, she signals the start of the exam. If she wishes her students to have time T0 (spaceship time) to complete the exam, show that she should wait a time (Earth time) of before sending a light signal telling them to stop. (Hint: Remember that it takes some time for the second light signal to travel from the professor to the students.)
The identical twins Speedo and Goslo join a migration from Earth to Planet X, which is 20.0 light-years away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same time on different spacecraft. Speedos craft travels steadily at 0.950c, Goslos at 0.750c. Calculate the age difference between the twins after Goslos spacecraft lands on Planet X. Which twin is the older?
An astronaut is traveling in a space vehicle moving at 0.500c relative to the Earth. The astronaut measures her pulse rate at 75.0 beats per minute. Signals generated by the astronauts pulse are radioed to the Earth when the vehicle is moving in a direction perpendicular to the line that connects the vehicle with an observer on the Earth. (a) What pulse rate does the Earth-based observer measure? (b) What If? What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?
The identical twins Speedo and Goslo join a migration from the Earth to Planet X, 20.0 ly away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same moment on different spacecraft. Speedos spacecraft travels steadily at 0.950c and Goslos at 0.750c. (a) Calculate the age difference between the twins after Goslos spacecraft lands on Planet X. (b) Which twin is older?
You have been hired as an expert witness in the future by an attorney representing the driver of a spacecraft. The driver is accused of exceeding the galactic speed limit of 0.700c relative to the Earth while being chased by a galactic police spacecraft. The driver claims he is innocent, that his speed was well below that limit. You have been provided with the following data: the police spacecraft was traveling at 0.600c while chasing the driver and a technician on the police spacecraft measured the suspected spacecraft as traveling at 0.300c relative to the police spacecraft. What advice should you give the attorney?
Two astronomical events are observed from Earth to occur at a time of 1 s apart and a distance separation of 1.5109m from each other. (a) Determine whether separation of the two events is space like or time like. (b) State what this implies about whether it is consistent with special relativity for one event to have caused the other?
Review. A global positioning system (GPS) satellite moves in a circular orbit with period 11 h 58 min. (a) Determine the radius of its orbit. (b) Determine its speed. (c) The nonmilitary GPS signal is broadcast at a frequency of 1 575.42 MHz in the reference frame of the satellite. When it is received on the Earths surface by a GPS receiver (Fig. P38.41), what is the fractional change in this frequency due to time dilation as described by special relativity? (d) The gravitational blueshift of the frequency according to general relativity is a separate effect. It is called a blueshift to indicate a change to a higher frequency. The magnitude of that fractional change is given by ff=Ugmc2 where Ug is the change in gravitational potential energy of an objectEarth system when the object of mass m is moved between the two points where the signal is observed. Calculate this fractional change in frequency due to the change in position of the satellite from the Earths surface to its orbital position. (e) What is the overall fractional change in frequency due to both time dilation and gravitational blueshift? Figure P38.41