Speed of light answers

[makc]

Ok, this is not an official faq thread or anything, this is basically for myself to gather these old (and not so old) posts in one place not having to dig them via google all the time. Dont take my word for it, and use your best judgement on their accuracy.

how fast do we need to go
Question:

...i do remember the fact being stated that at just 1/10 light speed no one has any idea on how to protect ones ship considering that at that speed even a particle of dust hitting this ship would in effect have the destructive power of a atomic bomb hitting it. My question, is this true about a particle of dust having that effect at just 1/10th light speed

My answer:

All I know is that a bird can kill an airplane. But it's not that hard to do the math.

1st, we need the energy of the bomb. According to this page, the most powerful bomb generated 240,000 TJ (2.4e+17 Joules). 2nd, according to this page, shockwave and heat (two most destructive factors) account for 85% of that energy (0.85 * 2.4e+17 ~ 2e+17 Joules). 3rd, this energy goes outwards in all directions, so if your ship has crossection area S, amount of energy it recieves at the distance R is 2e+17*S/(4*pi*R^2) ~ 1.6e+16*S/R^2 Joules. Shuttle have wing a bit smaller than triangular, so I think it is safe to assume area S to be somewhere near 0.3*37*24 ~ 270 m^2. Which means that if you were to put shuttle at 1km distance from the most powerful explosion ever, it would receive approximately 1.6e+16*270/1e+6 ~ 4.3e+12 Joules.

Now, back to our question... I have no idea how much of moving dust particle energy could be consumed by a spacecraft as it passes through it but, assuming it is at least 10%, we now have for 10 gram particle, this equation: 4.3e+12 J = 0.1 * 0.01 kg * (299,792,458 m/s)^2 * (1/sqrt(1 - v^2/(299,792,458 m/s)^2) - 1), or v^2/(299,792,458)^2 ~ 0.0892, or v^2 ~ 8.02e+15, or finally v ~ 8.96e+7 m/s, which is ~ 0.3 of speed of light.

Question:

I was just wondering at what speed we would need to be able to reach the nearest galaxy in two weeks time?

My answer:

that is easy. 1st you go to wiki and read about "the Large and the Small Magellanic Clouds, whose perigalacticon is at ~180,000 light-years", then you go to google, and calculate that 180,000 ly is 1.7e21 meters (A). if someone were to go there at speed V m/s, it would took him A/V seconds, according to Earth observer. However, due to SRT, in his own opinion, our traveller would make it in just about A * sqrt(1 - (V/c)^2) / V seconds. Two weeks = 2 * 7 * 24 * 60 * 60 ~ 1.2e6 seconds (B). This gives the equation, A * sqrt(1 - (V/c)^2) / V = B, or 1 - (V/c)^2 = (VB/A)^2. Let's substitude (V/c)^2 with Z, then we have 1 - Z = Z*(cB/A)^2, or Z = 1 / (1 + (cB/A)^2). This finally gives us V = c * 0.99999999999997761 if I did the math correctly.

Speed of light
Question:

why the speed of light is 300,000 kps, and not some other faster or slower speed? Why 300,000 kps and not 200,000 or 400,000?

My answer:

quoting SI brochure section 2.1.1.1:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
It follows that the speed of light in vacuum is exactly 299 792 458 metres per second

This is by definition. If you were to use light seconds as units of length, you'd have c = 1.

[makc]

Turned one of these to interactive calculator: http://wonderfl.net/c/dfqa/fullscreen

[Beyond]

o-o-o-o-ok. Now what

[makc]

Now I made the simulator where you can drag worldline anchors around and see how that ffffchanges spacetime curvature

[Beyond]

Anchors is right Once i moved the 6-blue dots a little, everythings anchored They don't move anymore. But then... i don't have the faintest idea of what I'm doing, with what you did.

[makc]

you should see there a grid where horizontal lines represent same time and vertical lines - same distance from blue traveller point of view. when you move dots around, his worldline and the grid changes accordingly. the scale of the grid is such that light travels at 45 degrees, so you cant move dots too far from other dots without blue traveller going FTL - that's why they stop, I guess. you should move other dots before the stopped one could go any further.

[Beyond]

I don't really seem to get anything out of moving dots around and distorting black & white squares, which remind me of a company that used to make dog food about 35-40 years ago.

[makc]

Even though you're probably right that it needs more explanation, I am not going to give one It's like TL;DW but maybe reading through this page http://en.wikipedia.org/wiki/Minkowski_diagram could give my previous post more meaning.

[Beyond]

I don't know what TL;DW is, but i gather that you're showing how perception changes as the relationship between space and time vary, due to different influences that we don't usually get to see here on earth? IF so... perhaps instead of black & white squares, a picture full of flowers would work better?? A 3-d picture bending out of shape just could be a wowser!!

[makc]

Seems that 40 years ago "dog food" was the acid nickname)