Earth/Moon trip with slow light

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In summary: The distance to the moon would also change as the Earth rotated, so the astronauts would have to take account of this when calculating the time it would take to make the trip. The journey would take about four days for the surface of the Earth and four days for the moon, but the astronauts would have to wait for the orbiting spacecraft to complete one orbit before they could return.
  • #1
PatrickPowers
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I am working on an imaginary world -- call it science fiction if you like -- in which the speed of light is much slower but nothing else is changed. Yes, I know that this is impossible. The speed of light I have chosen is that the distance to the moon is one light year, which means c=12.7 m/sec.

The specific question that interests me is the Apollo moon mission. Since momentum is unchanged, then the astronauts will still be able to go to the moon in four days and return in four days more, as far as their own clock is concerned. The question is, what is the Earth clock doing?

I'm assuming the angular momentum of objects on the surface of the Earth is unchanged from that in our world. So the Earth is rotating at .99962 c and a day is still 24 of our hours. Yes, I know that this is impossible. What interests me is that since the rotation is so fast the clocks on the Earth will be dilated by a factor of 36.45. The velocity of the astronauts relative to the Earth is not constant, so it seems that it would be necessary to integrate the the time dilation of the astronauts relative to the center of the Earth over the entire trip, which is doable but not all that easy. Is there a shortcut for the calculation of the relative time dilations of the two paths: surface of the Earth, and trip to the moon?

The surface of the Moon would be rotating at a mere 0.3c, so once on the moon then the astronauts would lose almost all of their time dilation and have a wait of two or three weeks for the orbiting spacecraft to complete one orbit. As far as the orbiting astronaut is concerned the moon orbit takes two hours.

Anyway, I hope that this crazy problem interests someone who understands these things better than I and can point me in the right direction.
 
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With c = 12.7 m/s and unchanged gravity, the Earth would turn into a black hole, making the trip impossible. Since the speed of sound can't be greater than the speed of light, having rigid objects will also be impossible, unless you change some more constants of nature.
 
  • #3
Time Observed = Time / √(1-v2/c2)

So if on Earth v = .99962c
And moon v = 0.3c

Tearth = Time / √(1-(.99962c)2/c2)
Tmoon = Time / √(1-(.3c)2/c2)

Doing algebra...

Time = Tearth * √(1-(.99962c)2/c2)

Tmoon = (Tearth * √(1-(.99962c)2/c2)) / √(1-(.3c)2/c2)

Tmoon = Tearth * √((1-(.99962c)2/c2) / (1-(.3c)2/c2))

Tmoon = Tearth * √((1-(.99962c)2) / (1-(.3c)2))
 
  • #4
willem2 said:
With c = 12.7 m/s and unchanged gravity, the Earth would turn into a black hole, making the trip impossible. Since the speed of sound can't be greater than the speed of light, having rigid objects will also be impossible, unless you change some more constants of nature.

Thanks for the feedback. I calculated the Schwarzschild radius of the Earth with such slow light and it turns out to be 8.9 * 10^13 meters, so the entire solar system is well inside this. The moon would also be a black hole, but the solar system would also be inside it's smaller radius. Interstellar travel would require accelerating the Earth and Moon, which seems rather drastic.

The Earth would be rotating very quickly and would be a Kerr black hole. This gives a lot more grist for the mill.
 
  • #5
With the Earth rotating so rapidly the distance to the moon would change by a factor of a thousand or so when measured from different locations on the surface.
 

1. How long would it take for a trip to the Moon using slow light?

The amount of time it would take to travel to the Moon using slow light would depend on the specific speed of the slow light being used. Generally, it would take longer than traditional methods of travel, such as spacecraft, which can reach the Moon in approximately 3 days.

2. What is slow light and how does it work?

Slow light refers to the ability to manipulate the speed of light by controlling the properties of the medium it is traveling through. This can be done using materials like metamaterials or Bose-Einstein condensates, which have unique properties that can slow down light. This is achieved by changing the refractive index of the medium, which affects the speed of light passing through it.

3. How would a trip to the Moon using slow light impact the environment?

Using slow light for a trip to the Moon would have minimal impact on the environment as it does not involve the use of traditional fuels or emissions. However, the production and use of materials for manipulating light, such as metamaterials, may have some environmental implications that would need to be carefully considered.

4. Are there any potential risks associated with traveling to the Moon using slow light?

Like any form of space travel, there are inherent risks involved in traveling to the Moon using slow light. These could include malfunctions in the technology used, exposure to radiation, or other unforeseen challenges. However, with proper precautions and safety measures, these risks can be minimized.

5. How could slow light technology be used for future space exploration?

The use of slow light technology could have many applications for future space exploration, including faster travel to distant planets or even exploration beyond our solar system. It could also potentially be used for communication with spacecraft and satellites, as well as for improving the accuracy of telescopes and other space observation equipment.

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