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January 24, 2009

On the forums Vincent does some maths

Vincent writes:

Since Bungie were obliging enough to give us some numbers (albeit vague ones), I thought I'd try and work out a rough idea of it's deceleration. Fair warning: several assumptions from this point on.

We are given that the dreadnough takes 9 days (777600 seconds) to get to Earth.

It "arrives in the sol system" - I'll assume for now it starts at the edge of the system, which I'll put at just past the kuiper belt, or about 50AU (50 x 149.60 x 109 metres) away.

It then proceeds to Earth at "near relativistic speeds" - call it .99c (0.99 x 3.00 x 108 metres/second) for now, but could be much lower - I'll assume it starts at that speed and decelerates uniformly the whole distance.

----Warning: maths to follow!----

We can work out acceleration with the formula s=ut+½at², where s=distance, u=initial speed, t=time, and a=acceleration. So:

50 x 149.60 x 10^9 = (0.99 x 3.00 x 108 x 777600) + (0.5a x 777600²)
7480000000000 = 230947200000000 + 302330880000a
-223467200000000 = 302330880000a
a = -739ms-2

----End maths----

What this tells us is that, assuming all assumptions are correct, the dreadnought would have had to decelerate at 739ms-2, or 75 times the force of gravity.

You can of course change this number by changing the speed we assume it to start at, the distance it travels, etc. - this is merely an idea of the kind of numbers we're talking about.

Though I do wonder why Truth took almost twice as long getting to Earth as he did travelling from High Charity...

I am assured that you, loyal reader, will be more content to double check that maths. Perhaps you'll have an answer for Vincent's final question. I, on the other hand, will continue the search of the graveyard that is your speculation.

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