Consider an astronaut Alice space station orbiting the earth at a radius R = 4R@ from the center, where Re orbit is circular. Consider a second astronaut Julie who's far away outside the earth's gravitational field and is at rest with respect to the earth. = 6.4 x 106 m is the earth's radius and Me = 0.44 cm. Assume the

Suppose an astronaut travels to a star 10 lightyears away at a significant fraction of the speed of light (for example, v=0.99c) and returns. Assume negligible amount of time is spent at the destination. Does this round-trip journey take less than, equal to, or more than 20 years as observed by an Earth-based observer? Does this round-trip journey take less than, equal to, or more than 20 years as observed by the astronaut?

Explain the fact the special  theory of relativity defines the limits for the validity of Newtonian mechanics.

Suppose a spaceship is approaching the Earth at 0.075c and a message capsule is sent toward it at 0.075c relative to the Earth. what is the ratio of the capsule's speed, as measured on the spaceship, to the speed of the light?

Imagine an alien spaceship traveling so fast that it crosses our galaxy (whose rest diameter is 100,000 ly) in only 100 y of spaceship time. Observers at rest in the galaxy would say that this was possible because the ship's speed B was so close to 1 that the proper time it measured between its entry into and departure from the galaxy was much shorter than the galaxy frame coordinate time (~ 100,000 y) between those events. But how does this look to the aliens? To them, their clocks are running normallu, but the galaxy, which moves backward relative to them at speed B~1, is Lorentz-contracted to a bit less than 100 ly across: this is what makes it possible for the whole galaxy to fly by them in only 100 y. Then find the diameter of the galaxy in the aliens' frame, and verify that it is possible for a galaxy moving at speed B with this diameter to passthe aliens' ship completely in 100y.   Answer: 0.9999995

A star is located 42.8 lightyears from Earth. A spaceship travels to the star with a speed of 0.9870c. If an astronaut aboard the spaceship is 21 years old when the spaceship leaves Earth, how old is she when she reaches the star: a) According to an observer on Earth? b) According to her?

Suppose there is an astronaut who is traveling at a significant fraction of the speed of light.  Part (a) How long, in years, does it take her to travel 4.05 ly at 0.95405c (as measured by the Earth-bound observer)?   Part (b)  How long does it take according to the astronaut in years?

Suppose Amelia traveled at a speed of 0.80c to a star that (according to Casper on Earth) is 8.0 light-years away. Casper ages 20 years during Amelia's round trip. How much younger than Casper is Amelia when she returns to Earth?

Question 8: A glow-worm of mass 5.0g emits red light (600nm) with a power of 0.10W entirely in the backward direction. To what speed will it have accelerated after ten years if released into free space and assumed to live?

Velma passes Mort at 30,000 km/s. What fraction of light speed is this? What is the duration of one of Velma's seconds (a time interval that Velma observes to be 1 second in duration) as observed by Mort?