scholarly journals Pairwise tidal equilibrium states and the architecture of extrasolar planetary systems

2019 ◽  
Vol 488 (1) ◽  
pp. 1446-1461 ◽  
Author(s):  
Fred C Adams

ABSTRACT Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order mp ∼ 10 M⊕. Motivated by the observational sample, this paper determines the tidal equilibrium states for this class of extrasolar planetary systems. We start by considering two-planet systems with fixed orbital spacing and variable mass ratios. The basic conjecture explored in this paper is that the planet formation process will act to distribute planetary masses in order to achieve a minimum energy state. The resulting minimum energy configuration – subject to the constraint of constant angular momentum – corresponds to circular orbits confined to a plane, with nearly equal planetary masses (as observed). We then generalize the treatment to include multiple planet systems, where each adjacent pair of planets attains its (local) tidal equilibrium state. The properties of observed planetary systems are close to those expected from this pairwise equilibrium configuration. In contrast, observed systems do not reside in a global minimum energy state. Both the equilibrium states of this paper and observed multiplanet systems, with planets of nearly equal mass on regularly spaced orbits, have an effective surface density of the form σ ∝ r−2, much steeper than most disc models.

2004 ◽  
Vol 202 ◽  
pp. 175-177
Author(s):  
Tapan K. Chatterjee ◽  
V. B. Magalinsky

It is significant that the orbits of the planets in the solar system are very nearly circular, except for Mercury and Pluto where, conceivably, due to their comparatively small sizes, the tidal forces have played a less active role. Most of the suspected planets orbiting pulsars have nearly circular orbits. These systems tend to have minimum energy and are subjected to tidal forces. We find that a planet circularizes its orbit, in an effort to attain orbital stability and the ground state. Details can be found in Magalinsky & Chatterjee, 1997, and Magalinsky and Chatterjee, 2000.


2001 ◽  
Vol 12 (02) ◽  
pp. 293-305 ◽  
Author(s):  
HÜSEYIN OYMAK ◽  
ŞAKIR ERKOÇ

We have investigated the minimum-energy distribution of N, 3 ≤ N ≤ 97, equal point charges confined to the surface of a sphere. Charges interact with each other via the Coulomb potential of the form 1/r. Minimum-energy distributions have been determined by minimizing the tangential forces on each charge. Further numerical evidence shows that in the minimum-energy state of N charges on the sphere, it is not possible to place a charge at the geometrical center. Besides, it has been found that the most and reliable information about the relative stability properties of the distributions can be obtained with the help of second difference energy consideration.


1993 ◽  
Vol 62 (6) ◽  
pp. 1829-1832 ◽  
Author(s):  
Mitsuaki Suzuki ◽  
Makoto Saito ◽  
Eiki Hotta

1986 ◽  
Vol 56 (8) ◽  
pp. 842-845 ◽  
Author(s):  
S. O. Knox ◽  
Cris W. Barnes ◽  
G. J. Marklin ◽  
T. R. Jarboe ◽  
I. Henins ◽  
...  

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