Integral criteria of injection accuracy

Аuthors

Panchukov A. A.

Abstract

The injection accuracy is one of the main characteristics defining the perfection and competitiveness of the space-mission vehicle (SMV). The data of the modern SMV injection accuracy is published in the International User Manual, which is devoted to launch vehicles [1], for 24 versions of thebase target orbits, in which amount the circular or close-to-circular orbit is included. The list of controlled parameters is specified by each developer of SMV in the useful for him form and, as a rule, with a reference to an orbit inclination, which complicates a comparison and tradeoff analysis of the injection accuracy values acceptable for customers and assured by developers.

The paper describes and analyzes universal criteria of the injection accuracy for close-to-circular orbits. The requirements for spacecraft injection accuracy in the orbit plane are set by one or another combination of inequalities given below:

Here, are deviations of radii of the perigee r_π , the apogee r_α; , radius r_в at the insertion point, of T period; index * marks their maximum allowable absolute values. During the requirements development for the near-circular orbits injection accuracy of the Energia launch vehicle a universal and capacious criterion was proposed:

(1)

for any argument of latitude u ∈ (0-360°), i.e. the altitude of the real orbit has to deviate fr om the design one at any point of a circuit by a value not exceeding Δr^*.

If these deviations at any point of a circuit are so that their values belong to the indicated three-dimensional region, the radial deviation throughout the motion process will not exceed the set value ∆r^*.

For near-circular orbits condition (1) is equivalent to the unique set of conditions set by it, namely

and it can be recommended as a universal criterion of the injection accuracy.

The angular position of the injection orbit plane inspace is usually set by orbital inclination i and longitude of the ascending node Ω . Allowable errors of the orbit plane position are set by limiting deviations of ∆i and ∆Ω of the mentioned parameters, respectively, fr om the design ones. It is known that the same errors of the injection orbit plane shaping (specifically a targeting error) lead to the different deviations ∆i, ∆Ω depending on the inclination and latitude of the start point. Therefore, to assess the injection accuracy in lateral direction, it is also advisable to use the integral criterion 

|z(u)| ≤ z*   (2)

for any argument of latitude u ∈ (0-360°), wh ere z is a deviation along the normal to the orbit plane.

The terms of (1) and (2) lim it the tube of disturbed trajectories by a torus. In this case, the areas of allowable deviations of kinematic parameters are convex set, which makes possible the geometrical visual comparison of these parameters with characteristics of scattering correlation matrices (ellipsoids of equal probabilities).

Integral criteria |∆r(u)| ≤ ∆r^* , |z(u)|≤ z^* are connected with deviations of kinematic parameters at any point of a circuit and can be useful during the comparative characteristics analysis of the insertion accuracies for different SMV.

Keywords:

launch vehicle, injection accuracy, near-circular orbits, maximum deviations of orbital elements

References

1. Isakowitz S.I., Hopkins J.B., Hopkins J.P. International Reference Guide to Space Launch Systems, AIAA, 2004, 550 p.
2. Elyasberg P.E. Vvedenie v teoriyu poleta iskusstvennykh sputnikov Zemli (Introduction to the Earths satellites flight theory), Moscow, Nauka, 1965, 540 p.
3. Ilin V.A., Kuzmak G.E. Optimalnye perelety Moscow, Nauka, 1976, 744 p.