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**Physics, Astronomy & Cosmology / The Ultimate Special Relativity Question to Help Amateurs Understand**

« **on:**19/07/2019 16:34:20 »

Understanding Special Relativity for Amateurs

This scenario has been written to assist in the understanding a multitude of aspects of special relatively for the amateurs of us interested in cool physics (including me). I would be grateful for a physicist with a University degree to answer in detail (sorry no half baked musings on this on please).

Scenario:

C <-- 100 million light years --> A <-- 100 million light years --> B

1 --> (a = 20 m/s/s until 0.99999c)

2 --> (a = 20 m/s/s until 0.5c)

<-- 3 (a = 20 m/s/s until 0.99999c)

<-- 4 (a = 20 m/s/s until 0.5c)

Primary Details:

- Spaceships 1 and 2 set out from observer A towards observer B who is 100 million light years away. Each accelerate at 20 m/s/s (i.e. ~2g) until cruising velocity is made. 1 accelerates to 0.99999c while 2 only accelerates to 0.5c

-Similarly spaceships 3 and 4 set out from observer A to C.

- Each spaceship also decelerates at 20m/s/s as it approaches the target observer such that they stop when they reach the target.

- 1, 2, 3, 4, A, B, C are all fitted with 6 lasers each, directed to each of the different observers and spaceships. The lasers flash once per 100 seconds for 1 second duration. i.e. on the 99th second the lasers turns on for 1 second. The light is green (wavelength of say 532 nm).

Secondary Details for Auxiliary questions :

- Each laser makes 1 GW of effective light emitted during the 1 second bursts.

- Each spaceship weighs 10 Tonnes excluding fuel. Let's assume each ship has some sort of particle accelerate to use as thrust that can accelerate the particles used as thrust to ~0.9c. Also it is powered by let's say some theoretical antimatter/matter source and the whole system can convert all matter into thrust at 99.9% energy efficiency.

Assumptions:

- Each observer is stationary relative to the others (i.e. in the same velocity frame) and also in a straight line such that observers C and B are 200 million light years away from each other.

- Please ignore the expansion of the universe.

- 200 million years ago (according to A), observer A sent a message to observers B and C that this experiment would commence at the specific time. So 100 million years prior to launch A, B, C started their lasers flashing. Everyone is prepared for their observations (when the light from each item finally reaches each observer) and have started their local timers at the same time.

Q1.

a) According to spaceship 1, how long did it take to reach B?

b) According to spaceship 1, when does spaceship 2 arrive at B?

c) describe, inducing a rough timeline, what spaceship 1 observes from the laser lights (i.e. the wavelength, how long between flashes and duration of flashes, the energy intensity) , originating from A, B, 2, 3, 4 as it accelerates to 0.99999c, cruises at 0.99999c, and finally approaches B.

Q2.

a) According to spaceship 2, how long did it take to reach B?

b) According to spaceship 2, when does 1 arrive at B?

c) describe, including a rough timeline, what spaceship 2 observes from the laser light originating from A, B, 1, 3, 4 as it accelerates to 0.5c, cruises at 0.5c, and finally approaches B.

Q3.

a) According to observer B, when does 1 reach it?

b) According to observer B, when does 2 reach it?

c) Describe, including a rough timeline, what observer B observes from the laser light originating from 1, 2, 3, 4.

Q4.

a) According to observer A, when does 1 reach B?

b) According to observer A, when does 2 reach B?

c) Describe, including a rough timeline, what observer A observes from the laser light originating from 1, 2, 3, 4.

d) According to observer A, how fast are 1 and 3 moving away from each other?

Auxiliary Questions.

a) how much fuel do spaceship 1 and 2 need.

b) If each laser had a narrow enough focus and the observers had a large enough receiver to capture all of the light emitted to them from each spaceship, what would the energy levels (GW) look like from each spaceship.

This scenario has been written to assist in the understanding a multitude of aspects of special relatively for the amateurs of us interested in cool physics (including me). I would be grateful for a physicist with a University degree to answer in detail (sorry no half baked musings on this on please).

Scenario:

C <-- 100 million light years --> A <-- 100 million light years --> B

1 --> (a = 20 m/s/s until 0.99999c)

2 --> (a = 20 m/s/s until 0.5c)

<-- 3 (a = 20 m/s/s until 0.99999c)

<-- 4 (a = 20 m/s/s until 0.5c)

Primary Details:

- Spaceships 1 and 2 set out from observer A towards observer B who is 100 million light years away. Each accelerate at 20 m/s/s (i.e. ~2g) until cruising velocity is made. 1 accelerates to 0.99999c while 2 only accelerates to 0.5c

-Similarly spaceships 3 and 4 set out from observer A to C.

- Each spaceship also decelerates at 20m/s/s as it approaches the target observer such that they stop when they reach the target.

- 1, 2, 3, 4, A, B, C are all fitted with 6 lasers each, directed to each of the different observers and spaceships. The lasers flash once per 100 seconds for 1 second duration. i.e. on the 99th second the lasers turns on for 1 second. The light is green (wavelength of say 532 nm).

Secondary Details for Auxiliary questions :

- Each laser makes 1 GW of effective light emitted during the 1 second bursts.

- Each spaceship weighs 10 Tonnes excluding fuel. Let's assume each ship has some sort of particle accelerate to use as thrust that can accelerate the particles used as thrust to ~0.9c. Also it is powered by let's say some theoretical antimatter/matter source and the whole system can convert all matter into thrust at 99.9% energy efficiency.

Assumptions:

- Each observer is stationary relative to the others (i.e. in the same velocity frame) and also in a straight line such that observers C and B are 200 million light years away from each other.

- Please ignore the expansion of the universe.

- 200 million years ago (according to A), observer A sent a message to observers B and C that this experiment would commence at the specific time. So 100 million years prior to launch A, B, C started their lasers flashing. Everyone is prepared for their observations (when the light from each item finally reaches each observer) and have started their local timers at the same time.

Q1.

a) According to spaceship 1, how long did it take to reach B?

b) According to spaceship 1, when does spaceship 2 arrive at B?

c) describe, inducing a rough timeline, what spaceship 1 observes from the laser lights (i.e. the wavelength, how long between flashes and duration of flashes, the energy intensity) , originating from A, B, 2, 3, 4 as it accelerates to 0.99999c, cruises at 0.99999c, and finally approaches B.

Q2.

a) According to spaceship 2, how long did it take to reach B?

b) According to spaceship 2, when does 1 arrive at B?

c) describe, including a rough timeline, what spaceship 2 observes from the laser light originating from A, B, 1, 3, 4 as it accelerates to 0.5c, cruises at 0.5c, and finally approaches B.

Q3.

a) According to observer B, when does 1 reach it?

b) According to observer B, when does 2 reach it?

c) Describe, including a rough timeline, what observer B observes from the laser light originating from 1, 2, 3, 4.

Q4.

a) According to observer A, when does 1 reach B?

b) According to observer A, when does 2 reach B?

c) Describe, including a rough timeline, what observer A observes from the laser light originating from 1, 2, 3, 4.

d) According to observer A, how fast are 1 and 3 moving away from each other?

Auxiliary Questions.

a) how much fuel do spaceship 1 and 2 need.

b) If each laser had a narrow enough focus and the observers had a large enough receiver to capture all of the light emitted to them from each spaceship, what would the energy levels (GW) look like from each spaceship.