Differences between revisions 4 and 6 (spanning 2 versions)

Changing Orbits to M288

How do we get from any arbitrary orbit to M288? The following techniques may not be optimal for minimal \Delta V , but they set an upper bound. We will assume Kepler orbits and a circular M288 destination orbit, and heavy objects unaffected by light pressure. Actual thinsat orbits are elliptical and precess over a year with J2 and light pressure.

The origin elliptical Kepler orbit has four parameters we need to compute two \Delta V burns for our transfer orbit:

* Apogee r_a

* Perigee r_p

* Inclination i

* argument of perigee \omega

We can compute the semimajor axis a and the eccentricity e from the apogee and perigee

The angle of the ascending and descending nodes do not affect the \Delta V burns, though they do affect when we make our burns so we insert into the desired destination region of the M288 orbit.

Maneuvers use the least \Delta V farther out, so we will use different strategies depending on whether the apogee of the origin orbit is higher or lower than the M288 orbit r_288 .

Describing an arbitrary Kepler Orbit

Assume an x,y,z coordinate space and an orbit in the horizontal X,Y plane:
Add 45 degree argument of perigee (rotate around vertical Z axis):
Add 30 degree inclination (rotate around horizontal X axis):

-  ⇤ ← Revision 4 as of 2013-01-21 21:56:32 → 
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+   ← Revision 6 as of 2013-01-21 23:24:22 → ⇥
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 How do we get from any arbitrary orbit to M288?   The following techniques may not be optimal for minimal $ \Delta V $, but they set an upper bound.  We will assume Kepler orbits and a circular M288 destination orbit, and heavy objects unaffected by light pressure.  Actual thinsat orbits are elliptical and precess over a year with J2 and light pressure.
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-Manuevers use the least $ \Delta V $ farther out, so we will use different strategies depending on whether the apogee of the origin orbit is higher or lower than the M288 orbit $ r_288 $.
+Maneuvers use the least $ \Delta V $ farther out, so we will use different strategies depending on whether the apogee of the origin orbit is higher or lower than the M288 orbit $ r_288 $.
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-Assume an x,y,z coordinate space and an orbit in the x,z plane:

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+|| Assume an x,y,z coordinate space and an orbit in the horizontal X,Y plane: || {{ attachment:orb01.png | |width=256 }} ||
|| Add 45 degree argument of perigee (rotate around vertical Z axis):         || {{ attachment:orb02.png | |width=256 }} ||
|| Add 30 degree inclination         (rotate around horizontal X axis):       || {{ attachment:orb04.png | |width=256 }} ||

Diff for "OrbitChange"

Changing Orbits to M288

Describing an arbitrary Kepler Orbit