Reply: The Solar System Model for the Reconstructive Ladder

ABSTRACT A successful Solar system model must reproduce the four terrestrial planets. Here, we focus on (1) the likelihood of forming Mercury and the four terrestrial planets in the same system (a 4-P system); (2) the orbital properties and masses of each terrestrial planet; and (3) the timing of Earth’s last giant impact and the mass accreted by our planet thereafter. Addressing these constraints, we performed 450 N-body simulations of terrestrial planet formation based on narrow protoplanetary discs with mass confined to 0.7–1.0 au. We identified 164 analogue systems, but only 24 systems contained Mercury analogues, and eight systems were 4-P ones. We found that narrow discs containing a small number of embryos with individual masses comparable to that of Mars and the giant planets on their current orbits yielded the best prospects for satisfying those constraints. However, serious shortcomings remain. The formation of Mercury analogues and 4-P systems was too inefficient (5 per cent and 2 per cent, respectively), and most Venus-to-Earth analogue mass ratios were incorrect. Mercury and Venus analogues also formed too close to each other (∼0.15–0.21 au) compared to reality (0.34 au). Similarly, the mutual distances between the Venus and Earth analogues were greater than those observed (0.34 versus 0.28 au). Furthermore, the Venus–Earth pair was not reproduced in orbital-mass space statistically. Overall, our results suggest serious problems with using narrow discs to explain the inner Solar system. In particular, the formation of Mercury remains an outstanding problem for terrestrial planet formation models.

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Constructing ballistic capture orbits in the real Solar System model

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/s10569-014-9580-5 ◽

2014 ◽

Vol 120 (4) ◽

pp. 433-450 ◽

Cited By ~ 14

Author(s):

Z.-F. Luo ◽

F. Topputo ◽

F. Bernelli-Zazzera ◽

G.-J. Tang

Keyword(s):

Solar System ◽

System Model ◽

Ballistic Capture ◽

The Real

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Trajectory refinement of three-body orbits in the real solar system model

Advances in Space Research ◽

10.1016/j.asr.2017.01.039 ◽

2017 ◽

Vol 59 (8) ◽

pp. 2117-2132 ◽

Cited By ~ 18

Author(s):

Diogene A. Dei Tos ◽

Francesco Topputo

Keyword(s):

Solar System ◽

System Model ◽

The Real ◽

Three Body

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The Pan-STARRS Synthetic Solar System Model: A Tool for Testing and Efficiency Determination of the Moving Object Processing System

Publications of the Astronomical Society of the Pacific ◽

10.1086/659833 ◽

2011 ◽

Vol 123 (902) ◽

pp. 423-447 ◽

Cited By ~ 39

Author(s):

Tommy Grav ◽

Robert Jedicke ◽

Larry Denneau ◽

Steve Chesley ◽

Matthew J. Holman ◽

...

Keyword(s):

Solar System ◽

Processing System ◽

Moving Object ◽

System Model ◽

Object Processing ◽

Efficiency Determination

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Erratum to: Constructing ballistic capture orbits in the real Solar System model

Celestial Mechanics and Dynamical Astronomy ◽

10.1007/s10569-014-9595-y ◽

2014 ◽

Vol 120 (4) ◽

pp. 451-452

Author(s):

Z.-F. Luo ◽

F. Topputo ◽

F. Bernelli-Zazzera ◽

G.-J. Tang

Keyword(s):

Solar System ◽

System Model ◽

Ballistic Capture ◽

The Real

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The Nuclear Atom

10.1093/oso/9780198808275.003.0006 ◽

2017 ◽

Author(s):

Frank S. Levin

Keyword(s):

Angular Momentum ◽

Solar System ◽

Atomic Structure ◽

Ad Hoc ◽

Niels Bohr ◽

System Model ◽

Quantization Procedure ◽

Nuclear Atom ◽

Charged Nucleus ◽

Positively Charged

Chapter 5 describes how the concept of quantization (discretization) was first applied to atoms. This was done in 1913 by Niels Bohr, using Ernest Rutherford’s paradigm-changing, solar-system model of atomic structure, wherein the positively charged nucleus occupies a tiny central space, much smaller than the known sizes of atoms. Bohr, postulating a quantized version of this model for hydrogen, was able to explain previously inexplicable experimental features of that atom. He did so via an ad hoc quantization procedure that discretized the single electron’s energy, its angular momentum, and the radii of the orbits it could be in around the nucleus, formulas forwhich are presented, along with a diagram displaying the quantized energies. Despite this success, Bohr’s model failed not only for helium, with its two electrons, but for all other neutral atoms. It left some physicists hopeful, ready for whatever the next step might be.

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