Dermott's Law
Encyclopedia
Dermott's law is an empirical formula for the orbital period
of major satellites
orbiting planets in the solar system
. It was identified by the celestial mechanics
researcher Stanley Dermott in the 1960s and takes the form:
for
Where T(n) is the orbital period of the nth satellite, T(0) is of the order of days and C is a constant of the satellite system in question. Specific values are:
Such power-laws may be a consequence of collapsing-cloud models of planetary and satellite systems possessing various symmetries; see Titius-Bode law
. They may also reflect the effect of resonance
-driven commensurabilities
in the various systems.
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
of major satellites
Natural satellite
A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....
orbiting planets in the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
. It was identified by the celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
researcher Stanley Dermott in the 1960s and takes the form:
for
Where T(n) is the orbital period of the nth satellite, T(0) is of the order of days and C is a constant of the satellite system in question. Specific values are:
- Jovian system: T(0) = 0.444 dDayA day is a unit of time, commonly defined as an interval equal to 24 hours. It also can mean that portion of the full day during which a location is illuminated by the light of the sun...
, C = 2.03 - Saturnian system: T(0) = 0.462 d, C = 1.59
- Uranian system: T(0) = 0.488 d, C = 2.24
Such power-laws may be a consequence of collapsing-cloud models of planetary and satellite systems possessing various symmetries; see Titius-Bode law
Titius-Bode law
The Titius–Bode law is a hypothesis that the bodies in some orbital systems, including the Sun's, orbit at semi-major axes in a function of planetary sequence...
. They may also reflect the effect of resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
-driven commensurabilities
Commensurability (astronomy)
Commensurability is the property of two orbiting objects, such as planets, satellites, or asteroids, whose orbital periods are in a rational proportion....
in the various systems.