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A Note on the Generalized Hohmann Transfer Time

Kamel O. M.

Mechanics and Mechanical Engineering

2014

Vol. 18, nr 1

33--35

We calculate the transfer time from the inner to the outer elliptic planetary orbits of a space vehicle for the four feasible configurations and for the circular case. We find that the least time of transfer tT corresponds to the second configuration.

On the hyperbolic fly past problem as a velocity amplifier using the elliptic Hohmann transfer

Kamel O. M., Soliman A. S., Ammar M. K.

Mechanics and Mechanical Engineering

2011

Vol. 15, nr 1

25-38

We investigate the problem of fly past of a space vehicle traveling in a generalized elliptic Hohmann transfer system between the elliptic orbits of the Earth and Jupiter around the Sun. We consider the four feasible elliptic Hohmann configurations. We begin our treatment by a more precise expression for the hyperbolic excess velocity, because we deal with the elliptic not the circular Hohmann case. We assign the semi-major axes and the eccentricity of the hyperbolic trajectory that lies within the sphere of influence of the Jovian planet. Whence we have a more accurate determination of the elements of the hyperbolic trajectory before the vehicle's departure out of Jupiter's influence sphere to follow its trip to a further outer planet of the local solar system.

Optimum bi-impulsive non coplanar elliptic Hohmann type transfer

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2010

Vol. 14, nr 1

81-104

We optimize the Hohmann type bi-impulsive transfer between inclined elliptic orbits having a common center of attraction, for the four feasible configurations. Our criterion for optimization is the characteristic velocity ΔvT = Δv1 + Δv2 which is a measure of fuel consumption. We assigned the optimum value of our variable x (ratio between velocity after initial impulse and velocity before initial impulse) by a numerical solution of an algebraic eight degree equation. We have a single plane change angle α. We present terse new formulae constituting a new alternative approach for tackling the problem. The derivations of formulae of our treatment are simple, straightforward and exceptionally clear. This is advantageous. By this semi-analytic analysis we avoid many complexities and ambiguity that appear in previous work.

Optimal Generalized Coplanar Bi-Elliptic Transfer Orbit Part I

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2009

Vol. 13, nr 1

73-78

We have four feasible simple Bi-elliptic configurations for the transfer problem, for a central gravitational field. We restrict our selves to the first one in this part. We apply three impulses at the points A, C, B. x, z are our independent variables and are equal to the ratio between values of the velocities after and before the application of the impulses at points A, B respectively. Similarly y is defined as the corresponding parameter for the point C. We utilize the optimum condition of ordinary calculus for algebraic functions, to evaluate minimum values of x, z, y. We adopt the Earth - Mars bi-elliptic coplanar transfer system as an example, for the first configuration, to evaluate the numerical minimum values of x, z, y. In part II, we shall consider the other three configurations and expand to domain of application of the numerical results.