# environment relativistic perception of a moving object

## Beginner's thought experinment

Let's assume that a spacecraft moving at some speed, for demonstration let's say almost the speed of light, passes by a planet heading towards an other one 300.000 km away (rounded up). the planets are stationary just for our example.

An external observer would feel the trip lasting for about 1 second, but the astronaut inside the ship would feel it much less.

## Q1

So would it be like, from the astronaut's point of view, he perceived these stationary objects (planets) pass by at a speed:

1. equal and opposite from his, such as in classical mechanics (not likely. compering to the velocity of a light beam moving opposite to spacecraft)
2. higher than light's, considering that objects 300.000 km apart pass by at less than a sec at his own perceived time (not likely. i suppose that his perception of space would be different).
3. less than light's (straight deduction from eliminating (1) and (2) ???)

## Q2

If the astronaut turned on a light bulb in the interior and the light spread radially in his reference frame, what would be the velocity of its light in the direction of spacecraft's velocity and opposite to that? Also relative to him and to an external observer

• In the spacecraft frame the distance is a lot less than 300000 km Commented Oct 12, 2016 at 15:30
• Some reference would be helpful Commented Oct 12, 2016 at 19:33

# Q1

If I understood you correctly, the answer is 1: the planet passes the astronaut with a speed which is equal by absolute value to the speed of astronaut in the reference frame of the planet, but in the opposite direction. Why do you think that it is not likely?

# Q2

Both are equal to the speed of light in the vacuum, according to Einstein's 2nd postulate.

• If the principles of classical mechanics about relative velocities apply here too, then i end up in a contradiction. I explain: Commented Oct 12, 2016 at 19:04
• If we turn on the light bulb when passing by the 1st planet, then the photons in the backward direction would be stationary relative to an external observer (c-c=0). If so, when we pass by the 2nd planet the light beam in the backward direction would have spread in a distance of 300.000 km . Meanwhile, the beam in the forward direction would have spread in much less range because of the dictated top speed of light (improbable in my opinion). ...to be continued Commented Oct 12, 2016 at 19:20
• It would be like, if the spacecraft spanned 300k km in either direction of the light bulb (crazy i know), by the time we reachd 2nd planet the light would have reached the rear side of the ship but not the front, which contradicts with the assumption of uniform spread of light in the spacecraft reference frame. I have one missing peace of the puzzle which i hope to find in the answers of Q1, Q2 Commented Oct 12, 2016 at 19:25
• @x.alex have you heard of the relativity of simultaneity? The light reaches the two sides of the spacecraft simultaneously in one reference system, but these events are not simultaneous in another. Commented Oct 12, 2016 at 23:34
• I had not. Great!! This answers everything!! Thank you Commented Oct 13, 2016 at 8:02