Planetary mass
Planetary mass is a measure of the mass of a planet-like object. Within the Solar System, planets are usually measured in the astronomical system of units, where the unit of mass is the solar mass (M☉), the mass of the Sun. In the study of extrasolar planets, the unit of measure is typically the mass of Jupiter (MJ) for large gas giant planets, and the mass of Earth (M⊕) for smaller rocky terrestrial planets.
The mass of a planet within the Solar System is an adjusted parameter in the preparation of ephemerides. There are three variations of how planetary mass can be calculated:
- If the planet has natural satellites, its mass can be calculated using Newton's law of universal gravitation to derive a generalization of Kepler's third law that includes the mass of the planet and its moon. This permitted an early measurement of Jupiter's mass, as measured in units of the solar mass.
- The mass of a planet can be inferred from its effect on the orbits of other planets. In 1931-1948 flawed applications of this method led to incorrect calculations of the mass of Pluto.
- Data from influence collected from the orbits of space probes can be used. Examples include Voyager probes to the outer planets and the MESSENGER spacecraft to Mercury.
- Also, numerous other methods can give reasonable approximations. For instance, potential dwarf planet, known as Varuna, rotates very quickly upon its axis, as does the dwarf planet Haumea. Haumea, for example, has to be very dense in order to not rip apart due to its rotation. Through some calculations, one could place a limit on the object's density. Thus, if the object's size is known, a limit on the mass can be determined. See the links in the aforementioned articles for more details on this.
Choice of units
The choice of solar mass, M☉, 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, which is less than a millionth as precise.[1]
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 General 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.[2]
The solar mass is quite a large unit on the scale of the Solar System: 1.9884(2)×1030 kg.[1] 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.[1] 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 or M⊕) as a standard, particularly for the terrestrial planets. For the mass of gas giants, and also for most extrasolar planets and brown dwarfs, the mass of Jupiter (MJ) is a convenient comparison.
| Planet | Mercury | Venus | Earth | Mars | Jupiter | Saturn | Uranus | Neptune |
|---|---|---|---|---|---|---|---|---|
| Earth mass M⊕ | 0.06 | 0.82 | 1 | 0.11 | 317.8 | 95.2 | 14.6 | 17.2 |
| Jupiter mass MJ | 0.000 17 | 0.002 56 | 0.003 15 | 0.000 34 | 1 | 0.299 | 0.046 | 0.054 |
Planetary mass and planet formation
The mass of a planet has consequences for its structure by having a large mass, especially while it is in the hand of 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 like asteroids are classified as "small Solar System bodies".
A dwarf planet, by definition, is not massive enough to have gravitationally 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 Earth's mass is certainly sufficient.
The smaller planets retain only silicates, and are terrestrial planets like Earth or Mars, though multiple-ME super-Earths have been discovered. The interior structure of rocky planets is mass-dependent: for example, plate tectonics may require a minimum mass to generate sufficient temperatures and pressures for it to occur.[3]
If the protoplanet grows by accretion to more than about 5–10 M⊕, its gravity become large enough to retain hydrogen in its atmosphere. In this case, it will grow into a gas giant. If the planet then begins migration, it may move well within its system's frost line, and become a hot Jupiter orbiting very close to its star, then gradually losing small amounts of mass as the star's radiation strips its atmosphere.
The theoretical minimum mass a star can have, and still undergo hydrogen fusion at the core, is estimated to be about 75 MJ, though fusion of deuterium can occur at masses as low as 13 Jupiters.[4][5][6]
Values from the DE405 ephemeris
The DE405/LE405 ephemeris from the Jet Propulsion Laboratory[1][7] 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).
| Planetary mass × 10−6 (relative to the Sun) |
Satellite mass (relative to the parent planet) |
Absolute mass |
Mean density | ||
|---|---|---|---|---|---|
| Planets and natural satellites | |||||
| Mercury | 0.16601 | 3.301×1023 kg | 5.43 g/cm3 | ||
| Venus | 2.4478383 | 4.867×1024 kg | 5.24 g/cm3 | ||
| Earth/Moon system | 3.04043263333 | 6.046×1024 kg | 4.4309 | ||
| Earth | 3.00348959632 | 5.972×1024 kg | |||
| Moon | 1.23000383×10−2 | 7.346×1022 kg | |||
| Mars | 0.3227151 | 6.417×1023 kg | 3.91 g/cm3 | ||
| Jupiter | 954.79194 | 1.899×1027 kg | 1.24 g/cm3 | ||
| Io | 4.70×10−5 | 8.93×1022 kg | |||
| Europa | 2.53×10−5 | 4.80×1022 kg | |||
| Ganymede | 7.80×10−5 | 1.48×1023 kg | |||
| Callisto | 5.67×10−5 | 1.08×1023 kg | |||
| Saturn | 285.8860 | 5.685×1026 kg | 0.62 g/cm3 | ||
| Titan | 2.37×10−4 | 1.35×1023 kg | |||
| Uranus | 43.66244 | 8.682×1025 kg | 1.24 g/cm3 | ||
| Titania | 4.06×10−5 | 3.52×1021 kg | |||
| Oberon | 3.47×10−5 | 3.01×1021 kg | |||
| Neptune | 51.51389 | 1.024×1026 kg | 1.61 g/cm3 | ||
| Triton | 2.09×10−4 | 2.14×1022 kg | |||
| Dwarf planets and asteroids | |||||
| Pluto/Charon system | 0.007396 | 1.471×1022 kg | 2.06 g/cm3 | ||
| Ceres | 0.00047 | 9.3×1020 kg | |||
| Vesta | 0.00013 | 2.6×1020 kg | |||
| Pallas | 0.00010 | 2.0×1020 kg | |||
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 (just over 1% of the mass of the Earth) in relation to its parent planet 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.[8] 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 minor planets and asteroids usually come from partial ephemerides.
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 317014 separate observations between 1913 and 2003, more than seven times as many as DE405, and gave more precise masses for Ceres and five asteroids.[8]
| EPM2004[8] | Vitagliano & Stoss (2006)[9] |
Brown & Schaller (2007)[10] |
Tholen et al. (2008)[11] |
Pitjeva & Standish (2009)[12] |
Ragozzine & Brown (2009)[13] | |
|---|---|---|---|---|---|---|
| 136199 Eris | 84.0(1.0)×10−4 | |||||
| 134340 Pluto | 73.224(15)×10−4 [note 1] | |||||
| 136108 Haumea | 20.1(2)×10−4 | |||||
| 1 Ceres | 4.753(7)×10−4 | 4.72(3)×10−4 | ||||
| 4 Vesta | 1.344(1)×10−4 | 1.35(3)×10−4 | ||||
| 2 Pallas | 1.027(3)×10−4 | 1.03(3)×10−4 | ||||
| 15 Eunomia | 0.164(6)×10−4 | |||||
| 3 Juno | 0.151(3)×10−4 | |||||
| 7 Iris | 0.063(1)×10−4 | |||||
| 324 Bamberga | 0.055(1)×10−4 |
IAU current best estimates (2009)
A new set of "current best estimates" for various astronomical constants[14] was approved the 27th General Assembly of the International Astronomical Union (IAU) in August 2009.[15] 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).
| Planet | Ratio of the solar mass to the planetary mass |
Planetary mass × 10−6 (relative to the Sun) |
Mass (kg) | Ref |
|---|---|---|---|---|
| Mercury | 6023.6(3)×103 | 0.166014(8) | 3.3010(3)×1023 | [16] |
| Venus | 408.523719(8)×103 | 2.08106272(3) | 4.1380(4)×1024 | [17] |
| Mars | 3098.70359(2)×103 | 0.3232371722(21) | 6.4273(6)×1023 | [18] |
| Jupiter [note 2] | 1.0473486(17)×103 | 954.7919(15) | 1.89852(19)×1027 | [19] |
| Saturn | 3.4979018(1)×103 | 285.885670(8) | 5.6846(6)×1026 | [20] |
| Uranus | 22.90298(3)×103 | 43.66244(6) | 8.6819(9)×1025 | [21] |
| Neptune | 19.41226(3)×103 | 51.51384(8) | 1.02431(10)×1026 | [22] |
The ratio of the mass of the Moon to the mass of the Earth is given as 1.23000371(4)×10−2,[12] 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: 332.9460487(7)×103, giving the mass of the Earth as 3.003486962(6)×10−6 M☉ or 5.9722(6)×1024 kg.[23]
See also
Notes
- ↑ For ease of comparison with other values, the mass given in the table is for the entire Pluto system: this is also the value which appears in the IAU "current best estimates". Tholen et al. also give estimates for the masses of the four bodies which comprise the Pluto system: Pluto 6.558(28)×10−9 M☉, 1.304(5)×1022 kg; Charon 7.64(21)×10−10 M☉, 1.52(4)×1021 kg; Nix 2.9×10−13 M☉, 5.8×1017 kg; Hydra 1.6×10−13 M☉, 3.2×1017 kg.
- ↑ The value quoted by the IAU Working Group on Numerical Standards for Fundamental Astronomy (1.047348644×103) is inconsistent with the quoted uncertainty (1.7×10−3): the value has been rounded here.
References
- 1 2 3 4 "2009 Selected Astronomical Constants" in The Astronomical Almanac Online, USNO–UKHO.
- ↑ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Reviews of Modern Physics. 80 (2): 633–730. Bibcode:2008RvMP...80..633M. arXiv:0801.0028
. doi:10.1103/RevModPhys.80.633. Direct link to value.. - ↑ CfA Press Release Release No.: 2008-02 January 09, 2008 Earth: A Borderline Planet for Life?
- ↑ Boss, Alan (2001-04-03), Are They Planets or What?, Carnegie Institution of Washington, archived from the original on 2006-09-28, retrieved 2006-06-08
- ↑ Shiga, David (2006-08-17), Mass cut-off between stars and brown dwarfs revealed, New Scientist, retrieved 2006-08-23
- ↑ Basri, Gibor (2000), "Observations of Brown Dwarfs", Annual Review of Astronomy and Astrophysics, 38: 485, Bibcode:2000ARA&A..38..485B, doi:10.1146/annurev.astro.38.1.485
- ↑ Standish, E. M. (1998), JPL Planetary and Lunar Ephemerides, DE405/LE405 (PDF), JPL IOM 312.F-98-048.
- 1 2 3 Pitjeva, E. V. (2005), "High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants" (PDF), Solar System Research, 39 (3): 176–86, Bibcode:2005SoSyR..39..176P, doi:10.1007/s11208-005-0033-2.
- ↑ Vitagliano, A.; Stoss, R. M. (2006), "New mass determination of (15) Eunomia based on a very close encounter with (50278) 2000CZ12", Astron. Astrophys., 455 (3): L29–31, Bibcode:2006A&A...455L..29V, doi:10.1051/0004-6361:20065760.
- ↑ Brown, Michael E.; Schaller, Emily L. (15 June 2007). "The Mass of Dwarf Planet Eris". Science. 316 (5831): 1585. Bibcode:2007Sci...316.1585B. PMID 17569855. doi:10.1126/science.1139415.
- ↑ Tholen, David J.; Buie, Marc W.; Grundy, William M.; Elliott, Garrett T. (2008), "Masses of Nix and Hydra", Astron. J., 135 (3): 777–84, Bibcode:2008AJ....135..777T, arXiv:0712.1261 , doi:10.1088/0004-6256/135/3/777.
- 1 2 Pitjeva, E. V.; Standish, E. M. (2009), "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit", Celest. Mech. Dyn. Astron., 103 (4): 365–72, Bibcode:2009CeMDA.103..365P, doi:10.1007/s10569-009-9203-8.
- ↑ Ragozzine, Darin; Brown, Michael E. (2009), "Orbits and Masses of the Satellites of the Dwarf Planet Haumea = 2003 EL61", Astron. J., 137 (6): 4766–76, Bibcode:2009AJ....137.4766R, arXiv:0903.4213 , doi:10.1088/0004-6256/137/6/4766.
- ↑ "The Final Session of the General Assembly" (PDF), Estrella d'Alva, p. 1, 2009-08-14.
- ↑ Anderson, John D.; Colombo, Giuseppe; Esposito, Pasquale B.; Lau, Eunice L.; et al. (1987), "The Mass Gravity Field and Ephemeris of Mercury", Icarus, 71 (3): 337–49, Bibcode:1987Icar...71..337A, doi:10.1016/0019-1035(87)90033-9.
- ↑ Konopliv, A. S.; Banerdt, W. B.; Sjogren, W. L. (1999), "Venus Gravity: 180th Degree and Order Model", Icarus, 139 (1): 3–18, Bibcode:1999Icar..139....3K, doi:10.1006/icar.1999.6086.
- ↑ Konopliv, Alex S.; Yoder, Charles F.; Standish, E. Myles; Yuan, Dah-Ning; et al. (2006), "A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris", Icarus, 182 (1): 23–50, Bibcode:2006Icar..182...23K, doi:10.1016/j.icarus.2005.12.025.
- ↑ Jacobson, R. A.; Haw, R. J.; McElrath, T. P.; Antreasian, P. G. (2000), "A Comprehensive Orbit Reconstruction for the Galileo Prime Mission in the J2000 System", J. Astronaut. Sci., 48 (4): 495–516.
- ↑ Jacobson, R. A.; Antreasian, P. G.; Bordi, J. J.; Criddle, K. E.; et al. (2006), "The gravity field of the Saturnian system from satellite observations and spacecraft tracking data", Astron. J., 132 (6): 2520–26, Bibcode:2006AJ....132.2520J, doi:10.1086/508812.
- ↑ Jacobson, R. A.; Campbell, J. K.; Taylor, A. H.; Synott, S. P. (1992), "The Masses of Uranus and its Major Satellites from Voyager Tracking Data and Earth-based Uranian Satellite Data", Astron. J., 103 (6): 2068–78, Bibcode:1992AJ....103.2068J, doi:10.1086/116211.
- ↑ Jacobson, R. A. (3 April 2009). "The Orbits of the Neptunian Satellites and the Orientation of the Pole of Neptune". The Astronomical Journal. 137 (5): 4322–4329. Bibcode:2009AJ....137.4322J. doi:10.1088/0004-6256/137/5/4322.
- ↑ Ries, J. C.; Eanes, R. J.; Shum, C. K.; Watkins, M. M. (1992), "Progress in the Determination of the Gravitational Coefficient of the Earth", Geophys. Res. Lett., 19 (6): 529–31, Bibcode:1992GeoRL..19..529R, doi:10.1029/92GL00259.