Research

Riemann Conjecture Polytope

Formulation of Alpha Grid using Quasi Time curvature

Abstract

A fundamental problem of astrodynamics is that of getting from one

point in space to another in a predetermined time . Usually, we would

like to know what velocity is required at the first point in order to

coast along a conic orbit and arrive at the destination at the prescribed

time . If the object of the mission is to rendezvous with some other

satellite, then we may also be interested in the velocity we will have

upon arrival at the destination.

Applications of the Gauss problem are almost limitless and include

interplanetary transfers, Satellite intercept and rendezvous, ballistic

missile targeting, and ballistic missile interception.

Tubular Alpha Grid

Variations in the speed, position, and launch direction of the missile at thrust cutoff will produce errors at the impact point . These errors are of two types-errors in the intended plane which cause either a long or a short hit, and out-of-plane errors which cause the missile to hit to the right or left of the target. For brevity , we will refer to errors in the intended plane as "down-range " errors, and out-of-plane errors as "cross-range " errors. There are two possible sources of cross-range error and these will be treated first.

Phase Angle Shift

If the spacecraft is to encounter the target planet at the time it crosses the planet's orbit then obviously the Earth and the target planet must have the correct angular relationship at departure. The angle between the radius vectors to the departure and arrival planets is called 'Y1 , the phase angle at departure, and is illustrated in Figure 8 .3-2 for a Mars trajectory. The total sweep angle from departure to arrival is just the difference in true anomaly at the two points, v2 - VI ' which may be determined from the polar equation of a conic once p and e of the heliocentric transfer orbit have been selected.

Google Sites

Report abuse