To circle Earth in low orbit, a satellite must have a speed of about 2.9 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 Units (b) Number Units

To circle Earth in low orbit, a satellite must have a speed of about 2.9 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 Units (b) Number Units

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter5: Relativity

Section: Chapter Questions

Problem 33P: (a) How far does the muon in Example 5.3 travel according to the earthbound observer? (b) How far...

See similar textbooks

Related questions

Q: Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length…

Q: The factor y (gamma) appears throughout the expressions of special relativity. It depends only on…

Q: Suppose a satellite has a mass of 2050 kg and is orbiting at 7.4 km/s. Use the approximation that γ…

Q: (a) State and explain the two traditional postulates from which special relativity originates. (b)…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to…

A: Given, Distance measured by an observer on the earth surface , l=3.43km=3430 m Speed measured by an…

Q: An electron moves with speed 0.95c. (a) what is the momentum of the electron according to Newton’s…

Q: An alien spaceship has a mass ofm= 3.2×109kg, and according to the crew, onboard the bow-to-stern…

A: mass of spaceship (m) = 3.2×109 kg Length measured onboard (Lo) = 680 m Length measured by…

Q: An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see…

Q: Find the speed of a GPS satellite (height is 20,200 km above the surface of Earth). Hence find the…

A: By using equation, v = ( G m2 / R + h )1/2 v= ( 6.67 x 10-11 x 5.98 x1024 / 20200 x 103 + 6.38 x 106…

Q: An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves…

A: The expression of time for the given case where the batteries on the space probe last as measured by…

Q: A proton in a particle accelerator has a total energy that is 360 times its rest energy. (a) What is…

A: (a) The total energy of proton is, E=rest energy+kinetic enerft =mc2+γ-1mc2…

Q: To circle Earth in low orbit, a satellite must have a speed of about 2.8 x 104 km/h. Suppose that…

A: Ans:- Image-1

Q: A spacecraft leaves Earth at a constant speed of 0.69c as measured by an observer on Earth. It heads…

A: Given: Constant speed of spacecraft, v=0.69c Distance of star system from the Earth=43.94 light…

Q: In special relativity, we introduced the momentum of a particle in a given Lorentz frame as pu = (E,…

A: Required to find the energy measured.

Q: An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: An important idea in relativity is to know when you can use classical mechanics and when you should…

A: When the classical formula for kinetic energy is valid within 2%, you can set up the following…

Q: To circle Earth in low orbit, a satellite must have a speed of about 2.7 x 104 km/h. Suppose that…

Q: An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves…

A: Note: As per guidelines we are allowed to solve 3 subset ques, please sent the other part speratly…

Q: You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c.…

A: Observer measure the length of the spacecraft, It is left measure by observer according to whom…

Q: A member of a colony on a moon of Jupiter is required to salute the UN flag at the same time as it…

Q: Protons in a University accelerator are accelerated to a kinetic energy of 16 times their rest…

Q: The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a…

A: a) The equation to determine the life time of the moving muon is,

Q: rocket is traveling through space and its Lorentz factor (y) is 3.9. Determine the rocket's speed…

Concept explainers

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

To circle Earth in low orbit, a satellite must have a speed of about 2.9 × 10ª 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
Units
(b) Number
Units

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Give a physical argument showing that it is impossible to accelerate an object of mass m to the speed of light, even with a continuous force acting on it.
Spacecraft I, containing students taking a physics exam, approaches the Earth with a speed of 0.600c (relative to the Earth), while spacecraft II, containing professors proctoring the exam, moves at 0.280c (relative to the Earth) directly toward the students. If the professors stop the exam after 50.0 min have passed on their clock, for what time interval does the exam last as measured by (a) the students and (b) an observer on the Earth?
Suppose our Sun is about to explode. In an effort to escape, we depart in a spaceship at v = 0.80c and head toward the star Tau Ceti, 12 lightyears away. When we reach the midpoint of our journey from the Earth, we see our Sun explode and, unfortunately, at the same instant we see Tau Ceti explode as well. (a) In the spaceship’s frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first? (b) In a frame of reference in which the Sun and Tau Ceti are at rest, did they explode simultaneously? If not, which exploded first?
As 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.
According to special relativity, a particle of rest mass m0 accelerated in one dimension by a force F obeys the equation of motion dp/dt = F. Here p = m0v/(1 –v2/c2)1/2 is the relativistic momentum, which reduces to m0v for v2/c2 << 1. (a) For the case of constant F and initial conditions x(0) = 0 = v(0), find x(t) and v(t). (b) Sketch your result for v(t). (c) Suppose that F/m0 = 10 m/s2 ( ≈ g on Earth). How much time is required for the particle to reach half the speed of light and of 99% the speed of light?
A spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of 50.0° above the horizontal, positive x-axis. Another spacecraft is moving past with a velocity of 0.700c in the negative x direction. Determine the magnitude and direction of the velocity of the first spacecraft as measured by the pilot of the second spacecraft.
As seen from Earth, two spaceships A and B are approaching along perpendicular directions. If A is observed by an Earth observer to have velocity uy = 0.90c and B to have a velocity ux = +0.90c, find the speed of ship A as measured by the pilot of B.
A spacecraft moves at a speed of 0.900c. If its length is L as measured by an observer on the spacecraft, what is the length measured by a ground observer?
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?
Joe and Moe are twins. In the laboratory frame at location S1 (2.00 km, 0.200 km, 0.150 km). Joe shoots a picture for aduration of t= 12.0 s. For the same duration as measured inthe laboratory frame, at location S2 (1.00 km, 0.200 km,0.300 km), Moe also shoots a picture. Both Joe and Moe begintaking their pictures at t = 0 in the laboratory frame. Determine the duration of each event as measured by an observer ina frame moving at a speed of 2.00 108 m/s along the x axisin the positive x direction. Assume that at t = t = 0, the origins of the two frames coincide.
Calculate the momentum of a proton moving with a speed of (a) 0.010c, (b) 0.50c, (c) 0.90c. (d) Convert the answers of (a)(c) to MeV/c.
Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34