The spaceship Lilac, based on the Purple Planet, is 711 m long when measured at rest. When the Lilac passes Earth, observers there measure its length to be 655 m. At what speed ? is the Lilac moving with respect to Earth? Express your answer as a multiple of the speed of light ?.

In our inertial reference frame, we see a particle accelerating with a velocity   dx/dt = ( 1 - e-gt )1/2 in units where c = 1 (speed of light)  When we watch the particle's trajectory from t=0 to t=T, how much time passes in the particle's non inertial frame? Now express the answer such that T and the time have units of seconds instead of meters What's the 4-velocity in units c=1?

Astronomers discover a planet orbiting around a star similar to our sun that is 20 lightyears away. How fast must a rocket ship go if the round trip is to take no longer than 40 years in time for the astronauts aboard? How much time will the trip take as measured on Earth?

The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as  L' = L    1 −  v2 c2  where L is the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 52 percent of the speed of light? L − L' L =

A spaceship has proper length L_p and passes by a person standing on Earth. The personstanding on Earth measures that it takes time delta_t for the spaceship to pass a fixed point on theEarth. What is the speed (v) of the spaceship, according the person standing on Earth? Giveyour answer for v in terms of L_p, delta_t, and c (the speed of light).

A spaceship moves by Earth at 2.8×108 m/s. A satellite moves by Earth in the opposite direction at 1.3×108 m/s. Use the Galilean transformation to calculate the speed vsatellite,x of the satellite relative to the spaceship. vsatellite,x = ? m/s

A cosmic ray particle is released from an exploding star that is 2600 Light Years from Earth. If the particle traveled at 98% the speed of light, how far did it travel in its own frame of reference before hitting Earth?

V 1 c²r The time dilation a distance from Earth's center is 3 = 2GM. The speed of a satellite in a stable circular orbit is v= GM due to the speed of a satellite + dilation due to gravity exactly equal the dilation experienced by a person at Earth's surface where 3 = two clocks run at the same rate? At what height above Earth's surface will the dilation 2GM? In other words, at what height will the V C² RE

The 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 Units

The Minkowski interval between Alice’s birth and Alice’s death is −144yrs . How long did Alice live? Will other observers agree or disagree with that judgement?