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Marchal, C.

Publications and source records attributed to Marchal, C..

10 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Effects of inclination and eccentricity on optimal trajectories between earth and Venus

The true optimal transfers, including the effects of the inclination and eccentricity of the planets' orbits, between earth and Venus are presented as functions of the corresponding idealized Hohmann transfers. The method of determining the optimal transfers using the calculus of variations is presented. For every possible Hohmann window, specified as a continuous function of the longitude of perihelion of the Hohmann trajectory, the corresponding numerically exact optimal two-impulse transfers are given in graphical form. The cases for which the optimal two-impulse transfer is the absolute optimal, and those for which a three-impulse transfer provides the absolute optimal transfer are indicated. This information furnishes everything necessary for quick and accurate orbit calculations for preliminary Venus mission analysis. This makes it possible to use the actual optimal transfers for advanced planning in place of the standard Hohmann transfers.

Gravier, J.-P.↗
NASA NTRS1972

Optimal trajectories between Earth and Mars in their true planetary orbits.

The optimal transfers from Earth to Mars and from Mars to Earth, considering the actual planetary orbits, are presented as functions of the corresponding idealized Hohmann transfers. The numerically exact two-impulse optimal trajectories are given in graphical form for all possible Hohmann windows. The two-impulse transfers which are absolute optimals and those for which a third impulse provides the absolute optimal are delineated. These data are designed to provide all the information necessary for quick orbit calculations for preliminary Martian mission analysis. In this form, they are as easy to use as the standard Hohmann transfer approximations and provide much greater accuracy.

Gravier, J. P.↗
NASA NTRS1972

Analytical solutions of a class of optimum orbit modifications.

A space vehicle in an orbit around a spherical planet is considered. It is proposed to bring the vehicle, by a series of orbital maneuvers, into a final orbit. It is sought to minimize the total characteristic velocity for the maneuver. Since for a high-thrust propulsion system the characteristic velocity provides a direct measure of the fuel consumption, the optimal trajectory considered yields the minimum fuel expenditure. It is assumed that the planet is surrounded by a spherical atmosphere.

Vinh, N. X.↗
NASA NTRS1971

Optimum transfer between hyperbolic asymptotes with turn angle less than the maximum natural turn angle.

The impulsive transfer of minimum characteristic velocity between two given hyperbolic asymptotes associated with a real planet is considered. The constraint of remaining above the surface of the planet introduces a maximum natural turn angle. This divides the problem naively into two categories. The first is the case when the turn angle required by the given asymptotes is less than or equal to the maximum natural turn angle. This is the more reasonable situation for a swingby maneuver, and is the case considered in this paper. The resulting optimal transfers are of five basic types. In boundary conditions space, by far the largest area of transfers are either single impulse transfers or transfers through the parabolic level requiring two finite impulses. In no case has an optimal transfer been found which uses more than two finite impulses and three infinitesimal impulses. Complete results are presented for the case in which the given turn angle is less than or equal to the maximum natural turn angle.

Walton, J. M.↗
NASA NTRS1971

Study of the determination of the coefficients beta and gamma of the generalized metric of Robertson and of the dynamical oblateness of the sun

Motion of a space probe about a spherical center of attraction is considered, applying the general theory of relativity. Motion of a probe under the influence of the sun's oblateness is also discussed. Estimates of beta, gamma, and J20 using solar probe motion are presented. It is concluded that such measurements are possible if the unknown long-period perturbing acceleration is of the order of 10 to the -11th or -12th power m/sec. sq.

Marchal, C.↗