Early and Late Launch to the One Day Construction Orbit

A fully powered, minimum launch loop can launch as many as 80 five tonne vehicles per hour. The most direct launch to a station in a construction orbit is synchronized to an arrival when the station reaches apogee. This is the "prime" launch time, occuring once per (86164.09 second) sidereal day. The destination cargo orbit is "synchronized" to the "celestial sphere", not the position of the Sun, so the Earth rotates a little extra each day relative to the sky, in relation to the "moving" Sun.

• A small additional complication is the oblateness of the Earth; the equatorial bulge modifies an elliptical construction orbit slightly, shifting apogee and perigee eastward by about 0.012 degrees ( 3 seconds of "extra" rotation ) per orbit. This turns the axis of the orbit one full turn around the sky approximately once per 80 years. Mission planners must consider this and other effects when designing the software to plan ultra-precise launch loop trajectories, along with tidal effects from the Moon, Sun, and Jupiter, as well as light pressure effects on vehicle surfaces. We will not worry about these small second order effects here, beyond noting that they exist, and must be compensated for with high precision measurement, launch and thrust control. The LAGEOS laser geodynamics satellites demonstrate that we can measure Earth orbits to micrometer precision over mega-meter distances; if we can avoid large turbulent rocket thrust, we can design space trajectories with 9 digit precision.

However, it is possible (with additional complication) to launch more vehicles in timeslots after the prime launch (and possibly before),

• greatly increasing deliveries and construction rates. If the construction station can capture 20 five tonne vehicles per day over 15 minutes, that is a net growth rate exceeding 300,000 tonnes per year. two years, an assembled station could be 500,000 tonnes with 100,000 tonnes of propellant and 10,000 inhabitants, which could be launched into an Aldrin Cycler orbit to Mars/Deimos. A fully powered minimum sized launch loop could support 100 of these constructions, and larger loops could supply the construction of vast habitats much more quickly.

Plane Change

Launch from the first minimum-sized loops is affected by extreme weather. The weather is benign (and boring to meteorologists) at 8°S latitude, 120°W longitude, due south of San Diego.

A loop at 8°S latitude will launch into a tilted orbital plane, with a perpendicular at 82°N latitude, which will rotate around the sky once per day. A launch before or after "prime time" will be into a slightly different orbital plane than the prime orbit and the construction station, necessitating a small plane-changing thrust into the construction station orbital plane before arrival.

How much thrust? Imagine a "velocity globe", with a diameter equal to the velocity of the vehicle near launch orbit apogee, approximately 900 meters per second. The prime launch velocity vector can be represented as a spot on the velocity globe at 82°N, "prime construction station meridian". Other launches throughout the day can be represented as spots around the circle.

For simplicity, pretend this is a 86,400 second circle, one solar day, rather than an 86141 second sidereal day. A 12 hour difference is a 180° (east or west) angular "longitude" difference on this circle; a one hour difference is 15° longitude difference. The plane change ΔV is simply the great circle distance (not the latitude line distance) between the spots, measured in velocity units.

However, for small plane changes, the "longitude line distance" is a quick (and slightly pessimistic) approximation. The radius of an 8° circle is V × sin( 8°), around 125 m/s for our example, and the circumference of the circle is 787 m/s. That circumference is divided by the sidereal day, so the ΔV per second of advance or delay is 9.1 millimeters per second per second, approximately 8 m/s of plane change ΔV with a 900 second launch advance or delay, or 0.4 m/s for a 45 second advance or delay. This thrust is small but necessary, without it, a 900 second early vehicle may arrive 4 kilometers south of the construction station.

So, presume we make the appropriate delta V where the orbit planes cross, which will be at a celestial longitude halfway between the early and prime orbit launch celestial longitudes, shifted by 180°, because apogee is 180° from launch at perigee. The plane change must be made near apogee, where the velocity (and thus the radius of the velocity globe) is much smaller than the radius of that globe near launch perigee.

• Note: a vehicle with wings, launched from a lower altitude, could make limited plane changes at perigee using aerodynamic lift. However, wings are expensive, and so is the drag of a lower altitude launch. Possible, but not recommended.

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