Brainkite

Figure trajectories by yourself.

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Hey guys,

the map view and the trajectories are very convenient but i would like to know a little bit more about the maths behind those trajectories. What are the mathematic formulas and functions to draw those trajectories and how much deltaV modify them.

Thanks for the help.

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On 1/6/2019 at 8:19 PM, UmbralRaptor said:

The (ahem) textbook answer is Fundamentals of Astrodynamics.

 

Hey, look what I'm getting on my Birthday :D This looks interesting, thanks for sharing, even though I'm not the one who asked this :) 

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3 hours ago, Spaceception said:

Hey, look what I'm getting on my Birthday :D This looks interesting, thanks for sharing, even though I'm not the one who asked this :) 

It covers a reasonable amount of topics. Perhaps more importantly it's the only textbook I've seen where the US edition is reasonably priced. >_>

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6 hours ago, Brainkite said:

Ok I'm starting to digg in, and I have a question about the form of gravity equation that is used.

Why do they keep a distance vector in the multiplyer and don't reduce the equation like this?:

https://tof.cx/image/fkoD7

think that since the rni isn't bold, it's a scalar, rather than a vector, which rni is. Vector division isn't really defined, so I think that this is dividing by the norm (or magnitude) of the vector, then multiplying by rni/||rni||, where the double pipes mean norm, which produces the "normalized" vector with a magnitude of 1, thus only preserving direction. Then the ||rni|| is moved over to the fraction on the left.

It seems like they also do this in 1.1.3 on pg 4, where they define Newton's law of universal gravitation as

Fg = - ((GMm)/(r^2)) * (r/r)

I'm not really sure why they would use unbolded variables as the magnitude though.

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1 hour ago, Mad Rocket Scientist said:

think that since the rni isn't bold, it's a scalar, rather than a vector, which rni is. Vector division isn't really defined, so I think that this is dividing by the norm (or magnitude) of the vector, then multiplying by rni/||rni||, where the double pipes mean norm, which produces the "normalized" vector with a magnitude of 1, thus only preserving direction. Then the ||rni|| is moved over to the fraction on the left.

It seems like they also do this in 1.1.3 on pg 4, where they define Newton's law of universal gravitation as

Fg = - ((GMm)/(r^2)) * (r/r)

I'm not really sure why they would use unbolded variables as the magnitude though.

This is a moderately common convention in various physics texts. I think it ends up being easier to typeset than getting the arrows and hats over the vectors right?

Edited by UmbralRaptor

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