So, I was reading this memorandum to make some c# classes helping with keplerian/newtonian orbital simulations. Then, I found this weird piece for solving for $n$...

$n = (0, 0, 1)^T × h = (−h_y, h_x, 0)^T$

The paradox is, it doesn't mention any variable T beforehand. An answer that just solves the problem this part of the paper addresses (part c) works too.

In that case, we have the following given values:

The relative positional vector $r$
The velocity vector $r˙$
The standard gravitational parameter $µ$
The orbital momentum vector $h$
The eccentricity vector $ɛ$

and we want to find...

The vector $n$ pointing towards the ascending node
The true anomaly $v$

I saw this post, but it didn't explain everything for me.

Any help appreciated. Sorry for my slightly bizzare wording.


1 Answer 1


That T is not a variable. It indicates that you should take the matrix transpose of those row vectors, making them into column vectors.

  • 1
    $\begingroup$ Ah, weird formatting. $\endgroup$
    – LydiasPost
    Commented Dec 28, 2021 at 5:10

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