Figure trajectories by yourself.

[Brainkite]

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.

[UmbralRaptor]

These can get somewhat involved, and admittedly wikipedia doesn't always have things in the best format. The (ahem) textbook answer is Fundamentals of Astrodynamics. If you're looking purely for an online resource, @Ohiobob has done good work.

[Brainkite]

ok great thanks

[Spaceception]

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 This looks interesting, thanks for sharing, even though I'm not the one who asked this  

[UmbralRaptor]

3 hours ago, Spaceception said:

Hey, look what I'm getting on my Birthday 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. >_>

[Brainkite]

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

 

[Mad Rocket Scientist]

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

I think that since the r_ni isn't bold, it's a scalar, rather than a vector, which r_ni 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 r_ni/||r_ni||, where the double pipes mean norm, which produces the "normalized" vector with a magnitude of 1, thus only preserving direction. Then the ||r_ni|| 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

F_g = - ((GMm)/(r^2)) * (r/r)

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

[UmbralRaptor]

1 hour ago, Mad Rocket Scientist said:

I think that since the r_ni isn't bold, it's a scalar, rather than a vector, which r_ni 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 r_ni/||r_ni||, where the double pipes mean norm, which produces the "normalized" vector with a magnitude of 1, thus only preserving direction. Then the ||r_ni|| 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

F_g = - ((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 January 10, 2019 by UmbralRaptor