An alien spaceship, passing through our solar system, observes us by reflected sunlight from earth’s surface. We know the escape velocity from earth’s surface is vesc = √(2GME/RE). Suppose we can (magically) compress earth radius to a very small size RS so that the escape velocity equals the speed of light c. In that case, nothing, not even light, can escape earth’s gravity and the alien spaceship will observe us as a “dark black hole”! What would be the value of RS? (RS is called the Schwarzschild radius.

Q: (a) Calculate y for a proton that has a momentum of 1.47 kg. m/s. x (b) What is its speed (in m/s)?…

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A: Length Contraction is a phenomenon of shortening of measured length of moving object than its rest…

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A: given that,proper time, t0=32 nsv=0.8 c

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A: Proper length of airplane Lo=50 m and velocity of plane 600 m/s.  We need to find the length of the…

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Q: A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the…

A: The spacecraft has to be sent to infinity in space where the gravitational force on the spacecraft…

Q: What happens to the length of an object as its velocity approaches the speed of light? A. The object…

A: The object appears to shorten.

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A: We are authorized to answer one problem at a time, since you have not mentioned which one you are…

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A: Given data: The speed of proton is vp=99.9936%c. The speed of antiproton is vap=99.9936%c.

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Q: A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the…

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Q: Many expressions in special relativity contain the gamma (y) factor. 1 y = V1 – 04c2 In the…

A: We have γ=11-v2c2 where,v= velocity.            c=speed of ligth.

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A: Given data:-  The crew of an enemy spacecraft attempts to escape from your spacecraft by moving away…

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A: Concept used:

Q: A spacecraft with a proper length of 250 m passes by an observer on the Earth. According to this…

A: proper length (Lo) = 250 m Let the speed of spacecraft = v time taken to pass a point as observed by…

Q: (a) Calculate y for a proton that has a momentum of 1.47 kg m/s. x (b) What is its speed (in m/s)?…

A:

Q: The crew of an enemy spacecraft attempts to escape from your spacecraft by moving away from you at…

A:

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: Many expressions in special relativity contain the gamma (y) factor. 1 Y = √1-v²/c² In the equation,…

A: The gamma factor is expressed as follows. γ=11-v2c2

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A: Given: The distance of Proxima Centauri is 4.3 ly. The time duration is 4.9 years.

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A: speed of an observer, v = 0.900 c

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Q: A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the…

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Q: General relativity considers gravity as the a) warping of mass b) bending of light c) warping of…

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Q: You have been posted to a remote region of space to monitor traffic. Near the end of a quiet shift,…

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Q: A star is 5.00 ly from the Earth. At what speed must a spacecraft travel on its journey to the star…

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Q: Imagine that the entire Sun collapses to a sphere of radius R g such that the work required to…

A: Given the work done is equal to its rest mass energy.

Q: One of the primary goals of the Kepler space telescope is to search for Earth-like planets. Data…

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Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.