User:Physchim62/Planetmass

Planetary mass is a measure of the mass of a planet. Within the Solar System it is usually measured in the astronomical system of units, where the unit of mass is the solar mass, that is the mass of the Sun.

The mass of a planet within the Solar System is an adjusted parameter in the preparation of ephemerides. There are two basic procedures for measurement: In practice, both methods are used. The ephemeris is a model of the Solar System, and the planetary masses within that model are adjusted so as to give the best fit between the model and the observed positions of the planets.
 * If the planet has natural satellites, its mass can be calculated from Kepler's third law. The same procedure can be used for data from space probes such as the Voyager probes to the outer planets and the MESSENGER spacecraft to Mercury.
 * The mass of a planet can also be inferred from its effect on the orbits of other planets.

Choice of units
The choice of the solar mass as the basic unit for planetary mass comes directly from the calculations used to determine planetary mass. In the most precise case, that of the Earth itself, the mass is known in terms of solar masses to twelve significant figures: the same mass, in terms of kilograms or other Earth-based units, is only known to five significant figures, that is more than a million times less precise.

The difference comes from the way in which planetary masses are calculated. It is impossible to "weigh" a planet, and much less the Sun, against the sort of mass standards which are used in the laboratory. On the other hand, the orbits of the planets give a great range of observational data as to the relative positions of each body, and these positions can be compared to their relative masses using Newton's law of universal gravitation (with small corrections for Special Relativity where necessary). To convert these relative masses to Earth-based units such as the kilogram, it is necessary to know the value of the Newtonian gravitational constant, G. This constant is remarkably difficult to measure in practice, and its value is only known to a precision of one part in ten-thousand. .

The solar mass is quite a large unit on the scale of the solar system: 1.9884(2) kg. The largest planet, Jupiter, is 0.09% the mass of the Sun, while the Earth is about three millionths (0.0003%) of the mass of the Sun. Various different conventions are used in the literature to overcome this problem: for example, inverting the ratio so that one quotes the planetary mass in the 'number of planets' it would take to make up one Sun. Here, we have chosen to list all planetary masses in 'microSuns' – that is the mass of the Earth is just over three 'microSuns', or three millionths of the mass of the Sun – unless they are specifically quoted in kilograms.

When comparing the planets among themselves, it is often convenient to use the mass of the Earth (ME) as a standard, particularly for the terrestrial planets. For the mass of gas giants, and also for most extrasolar planets and brown dwarves, the mass of Jupiter (MJ) is a convenient comparison.

Planetary mass and planet formation
The mass of a planet has consequences for its structure, especially while it is in the process of formation. A body which is more than about one ten-thousandth of the mass of the Earth can overcome its compressive strength and achieve hydrostatic equilibrium: it will be roughly spherical, and since 2006 has been classified as a dwarf planet if it orbits around the Sun (that is, if it is not the satellite of another planet). Smaller bodies are classified as "small Solar System bodies".

A dwarf planet, by definition, is not large enough to have cleared its neighbouring region of planetesimals: it is not known quite how large a planet must be before it can effectively clear its neighbourhood, but one tenth of the Eath's mass is certainly sufficient.

If the protoplanet grows by accretion to more than about 5–10 times the mass of the Earth, its gravity become large enough to retain hydrogen in its atmosphere. It this case, it will grow into a gas giant, while the smaller planets remain as terrestrial planets (also called "telluric planets").

The theoretical minimum mass a star can have, and still undergo hydrogen fusion at the core, is estimated to be about 75 times the mass of Jupiter, though fusion of deuterium can occur at masses as low as 13 Jupiters.

Values from the DE405 ephemeris
The DE405/LE405 ephemeris from the Jet Propulsion Laboratory is a widely used ephemeris dating from 1998 and covering the whole Solar System. As such, the planetary masses form a self-consistent set, which is not always the case for more recent data (see below).

Earth mass and lunar mass
Where a planet has natural satellites, its mass is usually quoted for the whole system (planet + satellites), as it is the mass of the whole system which acts as a perturbation on the orbits of other planets. The distinction is very slight, as natural satellites are much smaller than their parent planets (as can be seen in the table above, where only the largest satellites are even listed).

The Earth and the Moon form a case in point, partly because the Moon is unusually large in relation to its parent planet (just over 1% of the mass of the Earth) compared with other natural satellites. There are also very precise data available for the Earth–Moon system, particularly from the Lunar Laser Ranging Experiment (LLR).

The geocentric gravitational constant – the product of the mass of the earth times the Newtonian gravitational constant – can be measured to high precision from the orbits of the Moon and of artificial satellites. The ratio of the two masses can be determined from the slight wobble in the Earth's orbit caused by the gravitational attraction of the moon.

More recent values
The construction of a full, high-precision Solar System ephemeris is an onerous task. It is possible (and somewhat simpler) to construct partial ephemerides which only concern the planets (or dwarf planets, satellites, asteroids) of interest by "fixing" the motion of the other planets in the model. The two methods are not strictly equivalent, especially when it comes to assigning uncertainties to the results: however, the "best" estimates – at least in terms of quoted uncertainties in the result – for the masses of dwarf planets and asteroids usually come from partial ephemerides. One example is the USNO/AE98 emphemeris of Ceres and fourteen asteroids, which is used for the Astronomical Almanac. This study gave new masses for Ceres, Vesta and Pallas that were notably different from the masses used in DE405.

Nevertheless, new complete ephemerides continue to be prepared, most notably the EPM2004 ephemeris from the Institute of Applied Astronomy of the Russian Academy of Sciences. EPM2004 is based on 317 014 separate observations between 1913 and 2003, more than seven times as many as DE405, and gave more precise masses for Ceres and five asteroids. The latest complete Jet Propulsion Laboratory ephemeris, DE421, has refined masses for ten asteroids based on a slightly different calculation procedure from EPM2004.

IAU current best estimates (2009)
A new set of "current best estimates" for various astronomical constants was approved the the XXVIIth General Assembly of the International Astronomical Union (IAU) in August 2009. It includes masses for all the planets except the Earth–Moon system, as well as Eris, Pluto, Ceres, Vesta and Pallas: values for the masses of Eris, Pluto, Ceres, Vesta and Pallas are as given in the table above. Except for those of Mercury and Uranus, all the planetary masses have been revised since the DE405 ephemeris (1998).

The ratio of the mass of the Moon to the mass of the Earth is given as 1.230 003  71(4), while the ratio of the mass of the Sun to the mass of the Earth can be calculated as the ratio of the heliocentric and geocentric gravitational constants: 332.946  0487(7), giving the mass of the Earth as 3.003  486  962(6)&thinsp;M⊙ or 5.9722(6) kg.