A rocket is traveling at a constant speed of 5 x 10^7 m/s and is leaving the inn

Question

                     A rocket is traveling at a constant speed of 5 x 10^7 m/s and is leaving the inner solar system, a distance of 300 million km away from the earth. At this instant, a message is sent to Earth via electromagnetic radiation. The message includes the location of the rocket relative to the Earth at the instant the message transmission was initiated.
                    

                     At the very instant the message reaches the Earth, a reply message is initiated and sent back to the rocket, which is still moving away from Earth at the same speed. The reply message includes the expected time interval for the reply to reach the rocket.
                    

                     b) How long will it take for the reply message to get back to the ship, according to the Earth-based observers?                 

                                      c) Major Tom on the rocket calculates the time his friends on Earth assume pased between two events listed above. How does the elapsed time on the rocket compare to this calculation? P

Explanation / Answer

The main reason is that astronomical objects are usually formed by smaller pieces coming together. Initially, very small stuff (dust size) sticks together by colliding and since this is a random process, is just as likely to stick a little piece on any part of a larger piece with which it collides; therefore the initial "seeds" tend to be roughly spherical. Then, when a piece gets big enough to have significant gravity, it starts "sucking up" neighboring smaller pieces to grow but, because the gravitational force is spherically symmetric (i.e. it is equally strong in any direction the same distance from the object), it tends to maintain a basically spherical shape as it grows. If it were hot dog shaped, gravity would pull harder on the ends than the sides and it would tend back toward spherical shape. I read a good analogy somewhere: Suppose you want to build a building 1000 stories high, essentially a nonspherical bump on our essentially spherical earth. You would likely fail because gravity would cause it to collapse under its own weight. The earth is actually slightly oblate, that is fatter at the equator than the poles, because it is rotating and the centrifugal force pulls it out at the equator.

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