To circle Earth in low orbit, a satellite must have a speed of about 2.7 x 104 km/h. Suppose that two such satellites orbit Earth in opposite directions. (a) What is their relative speed as they pass, according to the classical Galilean velocity transformation equation? (b) What fractional error do you make in (a) by not using the (correct) relativistic transformation equation? (a) Number i Units (b) Number Units
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![To circle Earth in low orbit, a satellite must have a speed of about 2.7 x 104 km/h. Suppose that two such satellites orbit Earth in
opposite directions. (a) What is their relative speed as they pass, according to the classical Galilean velocity transformation equation?
(b) What fractional error do you make in (a) by not using the (correct) relativistic transformation equation?
(a) Number
i
Units
(b) Number
Units](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e16c7ee-fda7-4451-9f13-239fca167486%2Fb9e9f797-7dab-4e75-bb58-50dccaa44d3d%2Fe16oym_processed.png&w=3840&q=75)
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- Chapter 37, Problem 025 = 780 m. As detected by observer S', the two flashes Observer S detects two flashes of light. A big flash occurs at x1 = 1390 m and, 5.13 µs later, a small flash occurs at x2 occur at a single coordinate x'. (a) What is the speed parameter of S', and (b) is S' moving in the positive or negative direction of the x axis? To S', (c) which flash occurs first and (d) what is the time interval between the flashes? (a) Number Units (ь) (c) (d) Number UnitsThe center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23000 ly (measured in the Galaxy frame) in exactly 25 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip? (a) Number (b) Number I Units UnitsAn interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 74.0% of the speed of light. Its nuclear-powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 19.4 years as measured in a rest frame. Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the time the battery fails. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) yr (b) How far is the probe from Earth when its batteries fail as measured by mission control? (Ignore the delay between the time the battery fails and the time mission control stops receiving the signal.) ly (c) How far is the probe from Earth as measured by its built-in trip odometer when its batteries fail? ly (d) For what total time…
- 1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?a) Find the value of y for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an earthbound observer measures it to be 25 m. b) What is the speed of the spaceship relative to Earth?The cosmic rays of highest energy are protons that have kinetic energy on the order of 1013 MeV. (a) From the point of view of the proton, how many kilometers across is the galaxy? (b) How long would it take a proton of this energy to travel across the Milky Way galaxy, having a diameter ~ 105 light-years, as measured in the proton’s frame?
- Protons in a University accelerator are accelerated to a kinetic energy of 16 times their rest energy. (a) What is the relativistic factor gamma for these protons? (b) What is the speed of these protons? (express in terms of c, the speed of light) (c) What is their kinetic energy in MeV? (d) What is the rest energy of the protons? (e) What is their momentum in MeV/c?Observers in reference frame S see an explosion located at x1=620 m. A second explosion occurs 6.0 micro-s later at x2=1500 m.In reference frame S', which is moving along the +x-axis at speed V, the explosions occur at the same point in space. What is the separation in time delta t' between the two explosions as measured in frame S'? Express your answer in microseconds (micro-s). delta t' = ? micro-sA futuristic rocket ship of mass m,hip = 6.0 × 10° kg is sent into space carrying one person with the goal of traveling to nearby stars. The ship uses a newly discovered matter-antimatter drive that converts matter into energy at 100% efficiency. We will take Earth as the rest frame. For parts (a) through (d) you are interested in the portion of the spaceship's travel where it is using its drive to convert matter into the kinetic energy of the ship. (a) What is the speed of the ship when the work done by the ship's drive is equal to 150,000 TWh (the total energy used by humanity in 2014)? (b) How much work must the drive do for the rocket to reach a final speed of 0.95c? (c) How much matter would the drive need to annihilate in order for the ship to reach the final speed of 0.95c? Assume that the matter used in the antimatter drive is collected from the interstellar medium and that the mass of the ship remains constant. (d) When at the final speed of 0.95c, by what factor is the ship's…
- Chapter 37, Problem 015 The center of our Milky Way galaxy is about 24000 ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly 24000 ly (measured in the Galaxy frame) in exactly 27 y (measured in your frame)? (b) Measured in your frame and in lightyears, what length of the Galaxy would pass by you during the trip? (a) Number Units (b) Number UnitsConsider a proton that has a momentum of 1.00 kg·m/s. Part (a) Calculate the relativistic parameter γ for the proton. You will have to use a 2.998 × 108 for the speed of light to get this answer correct. Part (b) What is its speed, in meters per second? Such protons form a rare component of cosmic radiation with uncertain origins.The distance to a particular star, as measured in the earth's frame of reference, is 7.11 light- years (1 light-year is the distance that light travels in 1 y). A spaceship leaves the earth and takes 3.35 y to arrive at the star, as measured by passengers on the ship. (a) How long does the trip take, according to observers on earth? (b) What distance for the trip do passengers on the spacecraft measure?