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Julian Date and Modiﬁed Julian Date

The characteristics of the Jovian planets contrast with those of the terrestrial planets, which are smaller, rocky, and close to the sun. The Jovian planets are sometimes also called the outer planets since they are located in the outer region of our solar system.

Julian calendar The calendar introduced by Julius Caesar in 46 B.C. which divided the year into 365 days with a leap year of 366 days every fourth year. Thus, a century has exactly 36,525 days.

Julian Date and Modiﬁed Julian Date

The number of days elapsed since noon Greenwich Mean Time on January 1, 4713 B.C. Thus January 1, 2000, 0h (midnight) GUT was JD 2,451,543.5. This dating system was introduced by Joseph Scaliger in 1582. Julian Dates provide a method of identifying any time since 4713 B.C. as a real number independent of time zone. The Julian Date (JD) is counted in whole days and fractions, measured in days from noon, 4713 B.C., on the Julian proleptic calendar. The Julian proleptic calendar is a backwards extension of the Julian calendar.

Sometimes the Julian Date is deﬁned by parsing the number just described into years, months, days, and a fractional day. In other cases, the Julian Day Number is taken to be the integer part of the Julian Date. For dates on or after Nov 17, 1858, the Modiﬁed Julian Date (MJD) is deﬁned as the Julian Date less 2,400,000.5; it is zero at midnight on the date just mentioned (Gregorian calendar). Note that the fraction 0.5 moves the start of an MJD to midnight, while the JD starts at noon.

Julian Date Systems Prior to 1972

For dates before January 1, 1972, Julian Dates generally refer to Greenwich Mean Solar Time (GMT) unless otherwise speciﬁed. For example, the Julian Date can instead be used to represent Ephemeris Time (ET), used for planetary and other ephemerides. Ephemeris Time, which came into usage in 1956, was replaced by Dynamical Time in 1984. Dynamical Time was later replaced by the two kinds of dynamical time mentioned in the next paragraph.

Julian Date Systems after December 31, 1971

Starting in 1972, GMT was split into Coordinated Universal Time (UTC), the basis of civil timekeeping, and UT1, which is a measure of Earth rotation. Furthermore, in 1977, Dynamical Time was split into two forms, Terrestrial Dynamical Time (TDT) and Barycentric Dynamical Time (TDB). Julian Dates can represent any of these time systems, as well as International Atomic Time (TAI). Nevertheless, the Astronomical Almanac speciﬁes UT1 as the system to be assumed in the absence of any other speciﬁcation. This convention must be followed in any application whose result is to be a measure of Earth rotation, for example in ﬁnding sidereal time. When high accuracy time determinations are needed, one of the other systems, such as TAI, TDT, or TDB should be used, according to the situation. The differences among all these systems, now reaching to over a minute difference between TDT and UTC, can inﬂuence the whole day number near a day boundary. When the whole Julian Date is used, the problem is present near UTC noon. When Modiﬁed Julian Date is used, the problem is at midnight. When the time stream being used is clearly speciﬁed, and the decimals carried are sufﬁcient to represent seconds, there is no real problem, but if the JD or MJD is truncated to whole days, the integer values can differ for different time streams when representing identical times.

Transformations among JD, MJD, and Gregorian calendar date

The Astronomical Almanac (published annually by the U.S. Naval Observatory) provides tables for the translation between Gregorian date and Julian Day number. Software for translating between Gregorian calendar date, Julian Date, and Modiﬁed Julian Date is available from the U.S. Naval Observatory, as follows: On a UNIX system, with e-mail, one can enter:

Mail -s cdecm adsmail@tycho.usno.navy.mil < /dev/null

A few explicit translations are given in the table.

See also Explanatory Supplement to the Astronomical Almanac, P.K. Seidelmann, Ed., (University Science Books, Mill Valley, CA, 1992), which provides algorithms for the translation.

Julian year

Gregorian Date (midnight)	Julian Date (UTC)	Modiﬁed Julian Date (UTC)
Jan 1, 1900	2415020.5	15020
Jan 1, 1980	2444239.5	44239
Jan 1, 2000	2451544.5	51544

For more information, see: http://www.capecod.net/pbaum/date/back.htm (and http://tycho.usno.navy.mil/systime.html)

Julian year

See year.

Juliet Moon of Uranus also designated UXI. Discovered by Voyager 2 in 1986, it is a small, irregular body, approximately 42 km in radius. Its orbit has an eccentricity of 0.0005, an inclination of 0◦, a precession of 223◦ y−1, and a semimajor axis of 6.44 × 104 km. Its surface is very dark, with a geometric albedo of less than 0.1. Its mass has not been measured. It orbits Uranus once every 0.493 Earth days.

Junge particle distribution A power-law distribution function [particles m−3 µm−1] often used to describe the particle concentration [particles m−3] per unit size interval [µm] vs. equivalent spherical diameter of particles; the number density for particles of equivalent diameter x is proportional to x−k. In natural waters k is typically 3 to 5.

Juno Third asteroid to be discovered, in 1804. Dimensions 230 by 288 km. Orbit: semimajor axis 2.6679 AU, eccentricity 0.25848, inclination to the ecliptic 12◦.96756, period 4.358 years.

Jupiter A gas giant, the ﬁfth planet from the sun with orbital semimajor axis 5.20AU (778,330,000 km), orbital eccentricity 0.0483; its orbital period is 11.8623 years. Jupiter is the largest planet, with equatorial radius 71,492 km, and mass 1.9 × 1027 kg; its mean density is 1.33 gm/cm3. It has a surface rotational period of 9.841 hours. Jupiter has an orbital inclination of 1.308◦ and an axial tilt of 3.12◦. Jupiter has an absolute magnitude of −2.7, making it usually the fourth brightest object in the sky, after the sun, moon, and Venus; occasionally Mars exceeds Jupiter in brightness.

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The model structure of Jupiter envisions a rocky core of order 10 to 15 M , at a temperature ≈ 2×105 K, maintained by the gravitational compression of the planet. Because of this heating, Jupiter radiates considerably more energy than it receives from the sun. Above this core is a layer of liquid metallic hydrogen (at pressure depths exceeding 4 million atmospheres). Liquid metallic hydrogen is an electrical conductor and large scale currents in this material produce Jupiter’s magnetic ﬁeld, via the dynamo effect. Jupiter’s ﬁeld is 14 times stronger at Jupiter’s “surface” equator (4.3 Gauss), than is Earth’s at its equator (0.3 Gauss). Jupiter’s magnetic ﬁeld is roughly dipolar, with its axis offset by 10,000 km from the center of the planet and tipped 11◦ degrees from Jupiter’s rotation axis. Jupiter’s magnetosphere extends more than 650 million kilometers outward, but only a few million kilometers sunward.

Above the metallic hydrogen is a region composed primarily of ordinary molecular hydrogen (90%) and helium (10%) which is liquid in the interior and gaseous further out.

Three distinct cloud layers exist in the atmosphere, consisting of ammonia ice, ammonium hydrosulﬁde, and a mixture of ice and water. Jupiter’s atmosphere has high velocity winds (exceeding 600 km/h), conﬁned in latitudinal bands, with opposite directions in adjacent bands. Slight chemical and temperature differences between these bands are responsible for the colored bands that dominate the planet’s appearance. The reddish colors seem to be associated with the highest clouds, the bluish colors with the deepest. Intermediate clouds have brown-cream-white colors.

Jupiter posseses a very long-lived atmospheric phenomenon, the Great Red Spot, which has been observed for over 300 years. This is a reddish colored elliptical shaped storm, about 12,000 by 25,000 km.

Jupiter has three faint and small, low (about 0.05) albedo rings (called Halo, Main, and Gos-

Jupiter

samer) extending from 100,000 km to as much as 850,000 km from the center of the planet. They are comparable to Saturn’s, but much less prominent.

Jupiter has 16 known satellites, the four large Galilean moons Io, Europa, Ganymede, and Callisto, all discovered by Galileo in 1610, and 12 small ones.

Kelvin temperature scale

Kaiser–Stebbins effect (1984) Anisotropies in the cosmic microwave background generated by cosmic strings present after the time of the decoupling of the cosmic radiation. For a string moving transversely to the line of sight, light rays passing on opposite sides of the string will suffer different Doppler shifts. The result is then the existence of step-like blackbody effective temperature T discontinuities, with relative magnitude change on different sides of the string given by

δT /T = 8πGUγs nˆ · vs × sˆ

where γs is the relativistic Lorentz factor, vs is the string velocity with respect to the observer, sˆ is the string segment orientation and nˆ points in the direction of the line of sight. G is Newton’s constant, units are chosen so that h¯ = c = 1 and U is the (effective) mass per unit length of the (wiggly) cosmic string. See cosmic string, cosmic topological defect, deﬁcit angle (cosmic string).

katabatic wind A wind that is created by air ﬂowing downhill; wind ﬂowing down slope at night as the valley ﬂoor cools. Examples of drainage winds are the Mistral in France and the Santa Ana in California. Another example is winds from the Greenland plateau where a pool of cold dense air forms and if forced off the plateau seaward accelerates downslope.

K corona The K (or kontinuerlich) corona is generated by the scattering of photospheric radiation from coronal electrons. The high speeds of the scattering electrons smear out the Fraunhofer lines except the H- and K-lines. The K corona dominates below 2R where its intensity ranges from 10−6 to 10−8 of the diskcenter intensity. The K corona is polarized by the electron scattering with the electric vector parallel to the limb.

k-correction A necessary correction in observing redshifted objects. Since the visual or blue magnitudes in such sources correspond to absolute luminosities at higher frequencies than is the case for nearer sources, the k-correction for this effect depends on modeling the spectrum of the source.

Kelvin–Helmholtz instability Also called “shear instability”. An instability of an unbounded parallel shear ﬂow to the growth of waves with phase speed in the ﬂow direction approximately equal to the speed of the inﬂection point of the shear. The instability occurs due to a resonant coupling between wave-like disturbances on either ﬂank of the shear ﬂow where the gradient of the shear is non-zero.

Kelvin material Also called a Kelvin solid. A viscoelastic material that, in response to a suddenly imposed constant loading, deforms as an incompressible, linearly viscous ﬂuid over a short time but as a linearly elastic solid over a long time. The stress for the Kelvin material is the combination of the elastic stress according to Hooke’s law and the viscous stress according to the Newtonian ﬂow law. The relation between the volumetric strain θ = εii and pressure p = σii /3 is elastic: p = Kθ, where K is the bulk modulus. The constitutive relation for the deviatoric strain ε ij = εij − θδij /3 and deviatoric stress σ ij = σij − pδij is

∂ε σij = 2Gεij + 2µ ∂tij

where G is shear modulus, and µ is viscosity. Quantity τK = µ/G is called the Kelvin relaxation time, a time roughly deﬁning the transition from predominantly viscous to predominantly elastic behavior after a suddenly imposed constant loading.

Kelvin temperature scale Absolute temperature scale. At 0 K all thermal motion of matter would be at a standstill; thus, in the Kelvin scale no negative temperatures can exist. 0 K correpsonds to −273.15◦C; therefore, absolute temperatures T in the Kelvin scale are related to temperatures θ in centigrades by T = θ + 273.15 K.

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