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Effect of Galactic Rotation on Radial Velocities and Proper Motion. Part I

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

Mechanics and Mechanical Engineering

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2013

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Vol. 17, nr 3

251--259

EN

We expand Δfi the radial velocity of a group of stars moving around the center of galaxy, firstly in circular orbits. The expansion of Δfi is performed up to the third order of O(r/R0)3. A new result is encountered. The Oort constant is splitted into 3 parts A1, A2, A3 instead of one constant A. Moreover we verify the problem when the motion of the stars is elliptic. For proper motion components, there is no split of the second Oort‘s constant B. In all involved expansions orders of magnitude higher than the third in ΔR or r/R0 are neglected.

2

Effect of Galactic Rotation on Radial Velocities and Proper Motion. Part I

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

Mechanics and Mechanical Engineering

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2012

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Vol. 16, nr 1

41--49

EN

We expand Δρ the radial velocity of a group of stars moving around the center of galaxy, firstly in circular orbits. The expansion of Δρ is performed up to the third order of O(r=R0)3. A new result is encountered. The Oort constant is splitted into 3 parts A1, A2, A3 instead of one constant A. Moreover we verify the problem when the motion of the stars is elliptic. For proper motion components, there is no split of the second Oort‘s constant B. In all involved expansions orders of magnitude higher than the third in ΔR or r=R0 are neglected.

3

Solution of the Gaussian transfer orbit equations of motion

Kamel O. M., Ammar M. K.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 1

39-46

EN

This article deals with an orbit transfer problem by the application of only one motor thrust engine impulse at any point (r , v) on the elliptic initial orbit. The terminal orbits are elliptic. We consider the coplanar non-limited duration case. We succeeded to attain an analytical solution for the transfer Lagrange-Gauss modulated equations of motion. We selected the eccentric anomaly to be the independent parameter. We evaluated the integrals that appear in the R.H.S. of the equations of motion for da/dE, de/dE and edw/dE. Accordingly the three elements defining the final orbit are determined from (a - ao), (e - eo), e(w - wo).

4

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

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2011

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Vol. 15, nr 1

25-38

EN

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.

5

The change in the hyperbolic orbital elements due to application of a small impulse

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

Mechanics and Mechanical Engineering

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2004

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Vol. 7, nr 2

107-119

EN

The differential variations in the hyperbolic orbital classical element s due to a small impulse in the direction of the velocity vector are computed. We applied the method of Gauss for secular perturbations using the Lagrangian form of planetary equations.