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

100%

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

Mechanics and Mechanical Engineering

2012

tom Vol. 16, nr 1

41--49

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.

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

100%

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

Mechanics and Mechanical Engineering

2004

tom Vol. 7, nr 2

107-119

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.

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

100%

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

Mechanics and Mechanical Engineering

2013

tom Vol. 17, nr 3

251--259

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.