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

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2013

Vol. 17, nr 3

261--268

We express the geometrical and algebraic aspects of the problem of galactic rotation on the motion of the stars represented by fig. (2). We verify the equations involving third order terms of the orbits of the stars. That means taking into account higher order terms in our analysis, namely up to O(r/R0)3. These terms allow a generalization and high precision for the results. We acquired a higher order Taylor’s expansion for V as denoted in fig. (2). U‘, V‘ are the linear components of the velocity of the group of stars S. After some lengthy expansions and reductions, we obtained the formulae for U‘, V‘. Consequently [...], η, ζ the linear components of S corresponding to the two proper motion equalities in galactic longitude and latitude and radial velocity Δρ. Expansions are performed up to the third order in (r/R0).

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

2013

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.

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

2012

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.

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

Kamel O. M., Soliman A. S.

Mechanics and Mechanical Engineering

2012

Vol. 16, nr 2

81--89

We express the geometrical and algebraic aspects of the problem of galactic rotation on the motion of the stars represented by fig. (2). We verify the equations involving third order terms of the orbits of the stars. That means taking into account higher order terms in our analysis, namely up to O(r=R0)3. These terms allow a generalization and high precision for the results. We acquired a higher order Taylor’s expansion for V as denoted in fig. (2). U′, V ′ are the linear components of the velocity of the group of stars S. After some lengthy expansions and reductions, we obtained the formulae for U′, V ′. Consequently ξ, ƞ, Ϛ the linear components of S corresponding to the two proper motion equalities in galactic longitude and latitude and radial velocity Δρ. Expansions are performed up to the third order in (r=R0).