The effects of rotation of the central body on its planetary orbits, after the Whitehead theory of gravitation

1955 ◽  
Vol 232 (1188) ◽  
pp. 135-148 ◽  
Keyword(s):  
Angular Velocity ◽  
Central Body ◽  
Order Of Approximation ◽  
Exterior Field ◽  
Homogeneous Sphere ◽  
Rotating Sphere ◽  
Planetary Orbits ◽  
Theory Of Gravitation ◽  
Effects Of Rotation ◽  
Central Sphere

The Whitehead gravitation tensor for the exterior field due to a finite, uniform rotating sphere is evaluated in closed form. The advance of perihelion of an equatorial orbit is then calculated, making no assumption as to the smallness of the angular velocity of the central sphere. Finally, the perturbing forces on the Newtonian elliptical orbit due to rotation of the central sphere are determined with neglect of the square of this angular velocity. It is remarkable that the results of the present paper based on Whitehead’s theory agree very closely with those obtained by Lense & Thirring (1918) using Einstein’s linearized law of gravitation. In fact, for a homogeneous sphere, it is impossible to distinguish between the results in the two theories, to the order of approximation considered.

An interpretation of the Kerr metric in general relativity

1965 ◽  
Vol 61 (2) ◽  
pp. 531-534 ◽  
Author(s):  
R. H. Boyer ◽  
T. G. Price
Keyword(s):  
Vacuum Solution ◽  
Preceding Paper ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Rotating Fluid ◽  
Exterior Field ◽  
Rotating Sphere ◽  
Rotating Body ◽  
Planetary Orbits ◽  
Kerr Field

The preceding paper ((1)) dealt with some general properties of the gravitational field of a rotating fluid mass. An interesting example of a vacuum solution that might be the exterior field of some rotating body was recently found by Kerr ((4)). It was natural to apply the preceding theory to the Kerr solution. This paper deals with other aspects of that solution, particularly the behaviour of its bounded geodesics (planetary orbits). It would seem desirable to know what sort of rotating body could be a source of the Kerr field. It will appear that one of the parameters in Kerr's solution can plausibly be related to the angular momentum per unit mass of a uniformly rotating sphere, the other parameter being a measure of the mass of the sphere.

Experimental Measurement of the Magnus Force on a Rotating Sphere at Low Reynolds Numbers

1985 ◽  
Vol 107 (4) ◽  
pp. 484-488 ◽  
Author(s):  
Yutaka Tsuji ◽  
Yoshinobu Morikawa ◽  
Osamu Mizuno
Keyword(s):  
Angular Velocity ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Equation Of Motion ◽  
Inclined Plate ◽  
Magnus Force ◽  
Empirical Expression ◽  
Low Reynolds Numbers ◽  
Rotating Sphere ◽  
Low Reynolds

The Magnus force on a rotating sphere at low Reynolds numbers was obtained from trajectories of the sphere which impinged on an inclined plate and bounced. An empirical expression for the lift coefficient which is proportional to the angular velocity was deduced by comparing measurements of the range of flight with the solutions of the equation of motion.

Hydromagnetic Stokes flow past a rotating sphere

1978 ◽  
Vol 88 (4) ◽  
pp. 757-768 ◽  
Author(s):  
V. U. K. Sastry ◽  
K. V. Rama Rao
Keyword(s):  
Magnetic Field ◽  
Numerical Methods ◽  
Stokes Flow ◽  
Flow Reversal ◽  
Magnetic Pole ◽  
Rotating Sphere ◽  
Flow Past ◽  
Effects Of Rotation ◽  
The Magnetic Field

In the present investigation we consider hydromagnetic Stokes flow past a rotating sphere. The magnetic field is produced by a magnetic pole placed at the centre of the sphere. The problem is analysed by a combination of perturbation and numerical methods. It is seen that the flow reversal (due to rotation) at the rear portion of the sphere is enhanced as the strength of the magnetic field increases. In addition, we obtain the simultaneous effects of rotation and a magnetic field on the streamlines.

Equilibrium of liquid drops under the effects of rotation and acoustic flattening: results from USML-2 experiments in Space

1998 ◽  
Vol 354 ◽  
pp. 43-67 ◽  
Author(s):  
C. P. LEE ◽  
A. V. ANILKUMAR ◽  
A. B. HMELO ◽  
T. G. WANG
Keyword(s):  
Experimental Study ◽  
Angular Velocity ◽  
Liquid Drop ◽  
Sound Field ◽  
Theoretical Models ◽  
Liquid Drops ◽  
Complementary Effect ◽  
Rotating Liquid ◽  
Neutral Equilibrium ◽  
Effects Of Rotation

Previous Space-based experiments (Wang et al. 1994a) showed that a rotating liquid drop bifurcates into a two-lobed shape at a lower critical angular velocity, if it is flattened acoustically by the leviating sound field. In this work, we undertake a systematic experimental study of the effect of acoustic flattening on the rotational bifurcation of a liquid drop. We also look into the complementary effect of rotation on the equilibrium of an acoustically drastically flattened drop. Theoretical models are developed for each of the two effects and then woven into a unified picture. The first effect concerns neutral equilibrium, while the second concerns loss of equilibrium, neither of them involving instability. The theories agree well with the experiments.

Planetary orbits for a moving Sun

1969 ◽  
Vol 47 (20) ◽  
pp. 2161-2164 ◽  
Author(s):  
Peter Rastall
Keyword(s):  
The Sun ◽  
Coordinate Systems ◽  
Scalar Theory ◽  
Planetary Orbits ◽  
Theory Of Gravitation

The scalar theory of gravitation is known to be in agreement with observed planetary motions if the Sun is assumed to be stationary with respect to the preferred coordinate systems of the theory. We now assume that the Sun is moving, and we find that, unless its speed is improbably small, there are observable effects on the planetary orbits. The difficulty can be overcome if one assumes that the Newtonian charts are determined by the distribution of matter.

Kelvin–Helmholtz problem in a rotating Hall plasma

1980 ◽  
Vol 24 (2) ◽  
pp. 213-219 ◽  
Author(s):  
A. T. Granik
Keyword(s):  
Angular Velocity ◽  
Wave Vector ◽  
Shear Plane ◽  
Helmholtz Problem ◽  
Effects Of Rotation ◽  
Hall Plasma ◽  
The Stability ◽  
Special Case ◽  
Small Angular Velocity

The Kelvin–Helmholtz problem in a Hall plasma, including the effects of rotation, is studied. In contrast to previous results, it is shown that if the angular velocity is normal to the wave vector that describes perturbations of the interface, the rotation does not affect the stability of a shear plane. The special case of very small angular velocity is studied and it is shown that the rotation has either a stabilizing or a destabilizing effect, according as the gravitational speed is greater or less than the Alfvén speed.

The angular velocity of a freely rotating sphere in a weakly viscoelastic matrix fluid

2011 ◽  
Vol 23 (5) ◽  
pp. 051702 ◽  
Author(s):  
Kostas D. Housiadas ◽  
Roger I. Tanner
Keyword(s):  
Angular Velocity ◽  
Rotating Sphere ◽  
Viscoelastic Matrix
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