Differences between revisions 3 and 4

Construction2

The older rendezvous page, Construction1, started from a launch time and an exact associated longitude; calculations were complicated and the radial velocity at capture was large.

A better approach is to start with the capture angle at the construction orbit, which defines an exact radius and radial velocity. From there, find a launch orbit with an apogee, launch angle, and launch time that arrives at the construction orbit with the same radius and arrival velocity. The tangential velocity will be different, on the order of 100 m/s, but we can accommodate that with a "passive net capture system".

So, given the construction orbit, choose an angle from apogee

\theta

. Construction orbits have low perigees and very high apogees, far beyond GEO, so the apogee velocity is small and the angular velocity very small near apogee. Given a desired arrival time

t_{ac}

referenced from

t_{ac} = 0

at apogee, we can estimate

\theta

given the apogee radius

r_{ac}

and apogee velocity

v_{ac}

The construction orbit perigee should be well above LEO; assume an altitude of 2000 km above the equatorial radius 6378 km, thus

r_{pc}

= 8378 km. The construction orbit semimajor axis is defined from the orbit period, which should be a multiple

of an 86164.0905 second sidereal day. From that, we can compute the apogee radius, velocity, and angular velocity

\omega_{ac}

, then iterate from the desired arrival time to the exact capture angle.

	period	semimajor	apogee	apogee V	ang.freq.	1 hr angle
N	P_c	a_c	r_{ac}	v_{ac}	\omega_{ac}	radians
sdays	seconds	km	km	km/s	radians/sec	est.	exact
1	86164.1
2	86164.1
3	86164.1
4	86164.1
5	86164.1
6	86164.1
7	86164.1

-  ⇤ ← Revision 3 as of 2019-03-16 18:50:47 → 
  Size: 1997
  Editor: KeithLofstrom
  Comment:
+   ← Revision 4 as of 2019-03-16 18:51:11 → ⇥
  Size: 2013
  Editor: KeithLofstrom
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
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+#format jsmath

Diff for "Construction2"

Construction2