According to the specs, the link laser will operate at a mean power of 60mW. Using F = P/c, we get a force of roughly 200fN (200 femto Newtons!). Just to give you some idea of the effect that would have, Artemis' mass at launch is 3100kg, so this means that if it was to emit a 60mW beam in the same direction for 10 years, its speed would change by approximately.01 mm per sec.
This is generally known as the Twin's Paradox, and is a popular question in elementary special relativity classes. At first, it would seem to be self-contradictory. After all, if 1 of a pair of twins goes off on the rocket and the other one stays at home then there must be a definite answer as to which one is younger when they meet back up again - it can't be dependent on whose perspective you take, since at this point their perspectives are identical.
The key is that Special Relativity is only valid in inertial (ie. non-accelerating) frames. We can consider the Earth to be in an approximately inertial frame, so special relativity is valid. However, whilst the rocket spends most of it's time in an inertial frame, there are 3 points at which it is most definitely not: when it's leaving the Earth (and accelerating up to high speed), when it's turning round, and when it's slowing down to a halt back on Earth. At these points special relativity no longer applies, and we must resort to general relativity.
Hence the symmetry between the 2 views is broken, and our solution becomes clear. The Earth is the only place where special relativity applies for the duration of the journey, and since from it's point of view time in the rocket must pass more slowly, then the rocket twin must be younger.
The calculations in general relativity are pretty horrible, if I remember correctly, but if you work through them it turns out (as it should) that the corrections on the 3 GR legs of the voyage are exactly what is required to ensure consistency between the two perspectives.
Finally, for any sceptics out there, all this has been experimentally proven with a pair of atomic clocks, one on the ground and one orbiting in a satellite.
As well as autocompletion, there's another way to shorten these paths. All long file names have 8.3 aliases, which are ~.. is allocated on a first come first served basis to ensure uniqueness. So for instance, 'C:\Program Files' is also
'C:\progra~1'
. This means you can most likely access the path
C:\Documents and Settings\Administrator\Start Menu\Programs\Microsoft Office Tools
using
C:\docume~1\admini~1\startm~1\programs\micros~1
(Although it's entirely possible that micros~1 will be micros~2, ~3). Some of the UNIX pathnames I have to put up with at work are far worse, often going 10 or 15 directories deep.
Without meaning to be pedantic, on Earth weight and mass are most definitely NOT the same. Whilst the terms are often used interchangeably in common parlance, they actually refer to completely different properties. It's a bit like me saying "At 60mph, 2 hrs and 120 miles are the same". All that can be said is that a mass of 100kg weighs 220lbs on Earth, just as one can say that 120 miles is travelled in 2hrs at 60mph.
This is fairly simple to work out for 3 hats, but the article states that a similar theory applies for n hats where n is one less than a power of two(eg. 3, 7, 15 etc). I'm guessing things get less obvious when you start dealing with more hats (hence the article)...
I'm afraid you're somewhat mistaken in your views on fusion. We know for a fact that fusion works, it powers the Sun, for one thing (and makes the big bang in H-bombs). However, fusing nuclei won't always give you more power than you put in (neither will fission, for that matter).
Without getting too deeply into the physics involved, the way it works is this: fusing any two nuclei less massive than iron will generally give you energy, just as fissioning any nuclei heavier than iron will. This is why we use Uranium in reactors. It's significantly heavier than iron, and so well in the region of positive net energy from fission. We choose U-235 in particular because it breaks apart nice and easily, all you have to do is chuck a neutron at it.
We obviously couldn't get more energy out of fusing two of the decay products of uranium back into uranium, via your free lunch argument. However, by fusing two hydrogen nuclei, for instance, we can in theory get more back out than we put in (since hydrogen is a nice light element). The problem we have at the moment in sustainable fusion is getting high enough pressures and temperatures in an efficient manner (ie. so we still get more out than we put in). I firmly believe that, with time, we will overcome the problems with fusion, but since the process is analogous to creating a mini-star in the lab, it's far from easy.
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According to the specs, the link laser will operate at a mean power of 60mW. Using F = P/c, we get a force of roughly 200fN (200 femto Newtons!). Just to give you some idea of the effect that would have, Artemis' mass at launch is 3100kg, so this means that if it was to emit a 60mW beam in the same direction for 10 years, its speed would change by approximately .01 mm per sec.
This is generally known as the Twin's Paradox, and is a popular question in elementary special relativity classes. At first, it would seem to be self-contradictory. After all, if 1 of a pair of twins goes off on the rocket and the other one stays at home then there must be a definite answer as to which one is younger when they meet back up again - it can't be dependent on whose perspective you take, since at this point their perspectives are identical.
The key is that Special Relativity is only valid in inertial (ie. non-accelerating) frames. We can consider the Earth to be in an approximately inertial frame, so special relativity is valid. However, whilst the rocket spends most of it's time in an inertial frame, there are 3 points at which it is most definitely not: when it's leaving the Earth (and accelerating up to high speed), when it's turning round, and when it's slowing down to a halt back on Earth. At these points special relativity no longer applies, and we must resort to general relativity.
Hence the symmetry between the 2 views is broken, and our solution becomes clear. The Earth is the only place where special relativity applies for the duration of the journey, and since from it's point of view time in the rocket must pass more slowly, then the rocket twin must be younger.
The calculations in general relativity are pretty horrible, if I remember correctly, but if you work through them it turns out (as it should) that the corrections on the 3 GR legs of the voyage are exactly what is required to ensure consistency between the two perspectives.
Finally, for any sceptics out there, all this has been experimentally proven with a pair of atomic clocks, one on the ground and one orbiting in a satellite.
using
African or European?
Without meaning to be pedantic, on Earth weight and mass are most definitely NOT the same. Whilst the terms are often used interchangeably in common parlance, they actually refer to completely different properties. It's a bit like me saying "At 60mph, 2 hrs and 120 miles are the same". All that can be said is that a mass of 100kg weighs 220lbs on Earth, just as one can say that 120 miles is travelled in 2hrs at 60mph.
This is fairly simple to work out for 3 hats, but the article states that a similar theory applies for n hats where n is one less than a power of two(eg. 3, 7, 15 etc). I'm guessing things get less obvious when you start dealing with more hats (hence the article)...
I'm afraid you're somewhat mistaken in your views on fusion. We know for a fact that fusion works, it powers the Sun, for one thing (and makes the big bang in H-bombs). However, fusing nuclei won't always give you more power than you put in (neither will fission, for that matter).
Without getting too deeply into the physics involved, the way it works is this: fusing any two nuclei less massive than iron will generally give you energy, just as fissioning any nuclei heavier than iron will. This is why we use Uranium in reactors. It's significantly heavier than iron, and so well in the region of positive net energy from fission. We choose U-235 in particular because it breaks apart nice and easily, all you have to do is chuck a neutron at it.
We obviously couldn't get more energy out of fusing two of the decay products of uranium back into uranium, via your free lunch argument. However, by fusing two hydrogen nuclei, for instance, we can in theory get more back out than we put in (since hydrogen is a nice light element). The problem we have at the moment in sustainable fusion is getting high enough pressures and temperatures in an efficient manner (ie. so we still get more out than we put in). I firmly believe that, with time, we will overcome the problems with fusion, but since the process is analogous to creating a mini-star in the lab, it's far from easy.