The proximity of Mercury's spin to Cassini state 1 from adiabatic invariance

Abstract The present ellipsoidal figure of the Moon requires a deformation that is significantly larger than the hydrostatic deformation in response to the present rotational and tidal potentials. This has long been explained as due to a fossil rotational and tidal deformation from a time when the Moon was closer to Earth. Previous studies constraining the orbital parameters at the time the fossil deformation was established find that high orbit eccentricities (e ≳ 0.2) are required at this ancient time, which is difficult to reconcile with the freezing of a fossil figure owing to the expected large tidal heating. We extend previous fossil deformation studies in several ways. First, we consider the effect of removing South Pole−Aitken (SPA) contributions from the present observed deformation using a nonaxially symmetric SPA model. Second, we use the assumption of an equilibrium Cassini state as an additional constraint, which allows us to consider the fossil deformation due to nonzero obliquity self-consistently. A fossil deformation established during Cassini state 1, 2, or 4 is consistent with the SPA-corrected present deformation. However, a fossil deformation established during Cassini state 2 or 4 requires large obliquity and orbit eccentricity (ϵ ∼ 68° and e ∼ 0.65), which are difficult to reconcile with the corresponding strong tidal heating. The most likely explanation is a fossil deformation established during Cassini state 1, with a small obliquity (ϵ ∼ −0.2°) and an orbit eccentricity range that includes zero eccentricity (0 ≤ e ≲ 0.3).

Download Full-text

The Model Penal Code and the War on Crime

10.1093/oso/9780198744290.003.0008 ◽

2018 ◽

Author(s):

Markus D. Dubber

Keyword(s):

Penal Code ◽

Modern State ◽

Model Penal Code ◽

State Punishment ◽

Liberal Democratic ◽

Democratic State ◽

Penal State ◽

War On Crime ◽

Integrate State ◽

State 1

Part III of Dual Penal State uses dual penal state analysis to generate a comparative-historical account of American penality. With comparative glimpses at Germany and, to a lesser extent, England, it distinguishes between two responses to the shared challenge of legitimating state penal power in a modern liberal democratic state: (1) the failure to appreciate the legitimatory challenge of modern state penal power in particular (United States) and of modern state power in general (England); and (2) the failure to address the legitimatory challenge of modern state penal power as an ongoing existential threat to the legitimacy of the state (Germany). Chapter 7 brings the narrative of modern American penality up-to-date, following on the heels of the discussion of Jefferson’s Virginia criminal law bill of 1779 in Chapter 6. Chapter 7 focuses on the Model Penal Code of 1962, which was far superior to Jefferson’s draft in every respect but one: it, too, failed to integrate state punishment into the American legal-political project, leaving the penal paradox unaddressed and unresolved to this day.

Download Full-text

Thomas Jefferson’s Virginia Criminal Law Bill

10.1093/oso/9780198744290.003.0007 ◽

2018 ◽

Author(s):

Markus D. Dubber

Keyword(s):

Criminal Law ◽

Critical Analysis ◽

Criminal Code ◽

The State ◽

Modern State ◽

Historical Account ◽

Liberal Democratic ◽

Democratic State ◽

Penal State ◽

State 1

Part III of Dual Penal State uses dual penal state analysis to generate a comparative-historical account of American penality. With comparative glimpses at Germany and, to a lesser extent, England, it distinguishes between two responses to the shared challenge of legitimating state penal power in a modern liberal democratic state: (1) the failure to appreciate the legitimatory challenge of modern state penal power in particular (United States) and of modern state power in general (England); and (2) the failure to address the legitimatory challenge of modern state penal power as an ongoing existential threat to the legitimacy of the state (Germany). Chapter 6 undertakes a critical analysis of Jefferson’s 1779 draft of a criminal law bill for the State of Virginia, concluding that it fell well short of a criminal code that reflected the ideals of the American legal-political project as spelled out, for instance, in Jefferson’s Declaration of Independence of 1776.

Download Full-text

Introduction

10.1093/oso/9780198803409.003.0001 ◽

2018 ◽

Author(s):

Laurens van Apeldoorn ◽

Robin Douglass

Keyword(s):

The State ◽

Modern State ◽

Religious Thought ◽

State 1

This volume investigates the complex and rich intersections between Thomas Hobbes’s political and religious thought. Hobbes is often credited with being one of the first great theorists of the modern state,1 but the state he theorized, as the title of his most famous work announces, was a commonwealth ecclesiastical and civil. One of the main goals of ...

Download Full-text

Autonomous Geometrical Mechanics

10.1093/oso/9780198822370.003.0022 ◽

2018 ◽

Author(s):

Peter Mann

Keyword(s):

Phase Space ◽

Contact Structure ◽

Invariant Tori ◽

Time Dependent ◽

Contact Structures ◽

Natural Setting ◽

Adiabatic Invariance ◽

Jet Bundle ◽

Integrability Theorem ◽

Extended Phase

This chapter examines the structure of the phase space of an integrable system as being constructed from invariant tori using the Arnold–Liouville integrability theorem, and periodic flow and ergodic flow are investigated using action-angle theory. Time-dependent mechanics is formulated by extending the symplectic structure to a contact structure in an extended phase space before it is shown that mechanics has a natural setting on a jet bundle. The chapter then describes phase space of integrable systems and how tori behave when time-dependent dynamics occurs. Adiabatic invariance is discussed, as well as slow and fast Hamiltonian systems, the Hannay angle and counter adiabatic terms. In addition, the chapter discusses foliation, resonant tori, non-resonant tori, contact structures, Pfaffian forms, jet manifolds and Stokes’s theorem.

Download Full-text