Astronomy Answers: AstronomyAnswerBook: Moons

Astronomy Answers
AstronomyAnswerBook: Moons


[Astronomy Answers] [Dictionary] [AnswerBook] [Universe Family Tree] [Science] [Starry Sky] [Planet Positions] [Calculate] [Colophon]

1. Moons and Satellites ... 2. Moons Around the Sun ... 3. Moons List ... 4. Large Moons ... 5. Great Moons of Jupiter ... 6. Bound Rotation

\(\def\|{&}\DeclareMathOperator{\D}{\bigtriangleup\!} \DeclareMathOperator{\d}{\text{d}\!}\)

This page answers questions about moons. The questions are:

You can also find information about moons in general on the Moons Page from the Universe Family Tree, and about the Moon of the Earth in particular on the Moon Page of the AnswerBook.

1. Moons and Satellites

There is no official definition of a moon, but if you look at celestial objects that are called moons, then you see that in practice a moon is a celestial object that orbits directly around a bigger celestial object that is not a star (such as the Sun).

In the same fashion, a satellite is more generally a thing that orbits around a bigger thing but is not a part of that bigger thing. That bigger thing can be a star, or even something like a galaxy.

[299]

Moons are made up of rocks and ice. Moons that are further away from the Sun tend to have more ice than moons that are closer to the Sun. Our Moon and the moons of Mars have no ice at all (except perhaps in deep craters near the poles), but the moon Europa of Jupiter has a layer of ice that is many kilometers thick.

[229]

2. Moons Around the Sun

It is not easy to say how many moons there are around the Sun, because that depends a lot on what you consider to be a moon around the Sun.

If you keep to the strict definition that I gave earlier, then the Sun has no moons at all, because then something that orbits directly around the Sun is by definition not a moon.

At the moment, at least 60 moons orbit around the planets with an official name. You could say that there are at least 60 named moons around the Sun.

You can also, less strictly, view the planets, comets, and asteroids as "moons" of the Sun. In that case, the number of officially named moons around the Sun is counted in the tens of thousands, of which most are asteroids.

The number of moons that has not yet been named or even discovered is most likely must greater still. There is no official least size for a moon, so with larger telescopes and better equipment you'll find ever smaller rocks and pebbles and clumps of ice that orbit around the Sun or the planets.

[298]

3. Moons List

Here is a list of moons of all planets. New small moons are still being discovered, so the list is probably not complete. I updated the list on 2006-05-22. The information came mostly from //ssd.jpl.nasa.gov/?sat_discovery and //ssd.jpl.nasa.gov/?sat_elem. The information provided for each moon is: the name of the planet; the name of the moon; the distance \(d\) to the planet, measured in thousands of kilometers (Mm; 1 km = 0.62 mi); the radius \(R\) of the moon, measured in kilometers; the strength \(g\) of the gravity at the surface, compared to that on Earth; the orbital period \(P\) in hours (h), days (d), and years (a); the year in which the moon was discovered; the alternative name; the provisional name. Newly discovered moons get a provisional name right away. When their orbit becomes sufficiently well known, then they receive an official name. See the page about names for more information about the origin of the names.

Planet Moon \({d}\) \({R}\) \({g}\) \({P}\)/h \({P}\)/d \({P}\)/a Discovered Name 2 Provisional Name
Earth Moon 384.4 1737.07 0.1658 658.7 27.4 0.1
Mars Phobos 9.38 11.14 0.0006 7.7 0.3 1877 MI
Mars Deimos 23.46 6.2 0.0003 30.3 1.3 1877 MII
Jupiter Metis 128 21.5 0.0018 7.1 0.3 1979 JXVI S/1979 J3
Jupiter Adrastea 129 10.13 0.0005 7.2 0.3 1979 JXV S/1979 J1
Jupiter Amalthea 181.4 86.21 0.0019 12.0 0.5 1892 JV
Jupiter Thebe 221.9 49.75 0.0041 16.2 0.7 1979 JXIV S/1979 J2
Jupiter Io 421.8 1821.6 0.1832 42.5 1.8 1610 JI
Jupiter Europa 671.1 1560.8 0.1341 85.2 3.6 1610 JII
Jupiter Ganymede 1070.4 2631.2 0.1457 171.7 7.2 1610 JIII
Jupiter Callisto 1882.7 2410.3 0.1261 400.4 16.7 1610 JIV
Jupiter Themisto 7284 4 0.0003 127.0 0.3 2000 JXVIII S/1975 J1 = S/2000 J1
Jupiter Leda 11165 10 0.0007 241.0 0.7 1974 JXIII
Jupiter Himalia 11461 85 0.0064 250.6 0.7 1904 JVI
Jupiter Lysithea 11717 18 0.0013 259.1 0.7 1938 JX
Jupiter Elara 11741 43 0.0032 259.8 0.7 1905 JVII
Jupiter S/2000 J11 12560 2 0.0000 287.5 0.8 2000 S/2000 J11
Jupiter S/2003 J12 15912 0.5 0.0000 410.0 1.1 2003 S/2003 J12
Jupiter Carpo 16989 1.5 0.0001 452.3 1.2 2003 JXLVI S/2003 J20
Jupiter Euporie 19304 1 0.0001 547.8 1.5 2001 JXXXIV S/2001 J10
Jupiter S/2003 J3 20221 1 0.0001 587.3 1.6 2003 S/2003 J3
Jupiter S/2003 J18 20514 1 0.0001 600.1 1.6 2003 S/2003 J18
Jupiter Orthosie 20720 1 0.0001 609.2 1.7 2001 JXXXV S/2001 J9
Jupiter Euanthe 20797 1.5 0.0001 612.6 1.7 2001 JXXXIII S/2001 J7
Jupiter Harpalyke 20858 2.2 0.0002 615.3 1.7 2000 JXXII S/2000 J5
Jupiter Praxidike 20907 3.4 0.0003 617.4 1.7 2000 JXXVII S/2000 J7
Jupiter Thyone 20939 2 0.0002 618.9 1.7 2001 JXXIX S/2001 J2
Jupiter S/2003 J16 20963 1 0.0001 619.9 1.7 2003 S/2003 J16
Jupiter Iocaste 21061 2.6 0.0002 624.3 1.7 2000 JXXIV S/2000 J3
Jupiter Mneme 21069 1 0.0001 624.6 1.7 2003 JXL S/2003 J21
Jupiter Hermippe 21131 2 0.0002 627.4 1.7 2001 JXXX S/2001 J3
Jupiter Thelxinoe 21162 1 0.0000 628.8 1.7 2004 JXLII S/2003 J22
Jupiter Helike 21263 2 0.0002 633.3 1.7 2003 JXLV S/2003 J6
Jupiter Ananke 21276 14 0.0010 633.9 1.7 1951 JXII
Jupiter S/2003 J15 22627 1 0.0001 695.2 1.9 2003 S/2003 J15
Jupiter Eurydome 22865 1.5 0.0001 706.2 1.9 2001 JXXXII S/2001 J4
Jupiter Arche 22931 1.5 0.0001 709.2 1.9 2002 JXLIII S/2002 J1
Jupiter S/2003 J17 23001 1 0.0001 712.5 2.0 2003 S/2003 J17
Jupiter Pasithee 23004 1 0.0001 712.6 2.0 2001 JXXXVIII S/2001 J6
Jupiter S/2003 J10 23042 1 0.0001 714.4 2.0 2003 S/2003 J10
Jupiter Chaldene 23100 1.9 0.0001 717.1 2.0 2000 JXXI S/2000 J10
Jupiter Isonoe 23155 1.9 0.0001 719.7 2.0 2000 JXXVI S/2000 J6
Jupiter Erinome 23196 1.6 0.0001 721.6 2.0 2000 JXXV S/2000 J4
Jupiter Kale 23217 1 0.0001 722.6 2.0 2001 JXXXVII S/2001 J8
Jupiter Aitne 23229 1.5 0.0001 723.1 2.0 2001 JXXXI S/2001 J11
Jupiter Taygete 23280 2.5 0.0002 725.5 2.0 2000 JXX S/2000 J9
Jupiter S/2003 J9 23384 0.5 0.0000 730.4 2.0 2003 S/2003 J9
Jupiter Carme 23404 23 0.0017 731.3 2.0 1938 JXI
Jupiter Sponde 23487 1 0.0001 735.2 2.0 2001 JXXXVI S/2001 J5
Jupiter Megaclite 23493 2.7 0.0002 735.5 2.0 2000 JXIX S/2000 J8
Jupiter S/2003 J5 23495 2 0.0002 735.6 2.0 2003 S/2003 J5
Jupiter S/2003 J19 23533 1 0.0001 737.4 2.0 2003 S/2003 J19
Jupiter S/2003 J23 23563 1 0.0001 738.8 2.0 2003 S/2003 J23
Jupiter Kalyke 23566 2.6 0.0002 738.9 2.0 2000 JXXIII S/2000 J2
Jupiter S/2003 J14 23614 1 0.0001 741.2 2.0 2003 S/2003 J14
Jupiter Pasiphae 23624 30 0.0023 741.6 2.0 1908 JVIII
Jupiter Eukelade 23661 2 0.0002 743.4 2.0 2003 JXLVII S/2003 J1
Jupiter S/2003 J4 23930 1 0.0001 756.1 2.1 2003 S/2003 J4
Jupiter Sinope 23939 19 0.0014 756.5 2.1 1914 JIX
Jupiter Hegemone 23947 1.5 0.0001 756.9 2.1 2003 JXXXIX S/2003 J8
Jupiter Aoede 23981 2 0.0002 758.5 2.1 2003 JXLI S/2003 J7
Jupiter Kallichore 24043 1 0.0001 761.5 2.1 2003 JXLIV S/2003 J11
Jupiter Autonoe 24046 2 0.0002 761.6 2.1 2001 JXXVIII S/2001 J1
Jupiter Callirrhoe 24103 4.3 0.0003 764.3 2.1 1999 JXVII S/1999 J1
Jupiter Cyllene 24349 1 0.0001 776.0 2.1 2003 JXLVIII S/2003 J13
Jupiter S/2003 J2 29541 1 0.0001 1037.0 2.8 2003 S/2003 J2
Saturn Pan 133.6 12.8 0.0002 13.8 0.6 1990 SXVIII S/1981 S13
Saturn S/2005 S1 136.5 3 0.0000 14.3 0.6 2005 S/2005 S1
Saturn Atlas 137.7 16.26 0.0001 14.5 0.6 1980 SXV S/1980 S28
Saturn Prometheus 139.4 50.11 0.0005 14.8 0.6 1980 SXVI S/1980 S27
Saturn Pandora 141.7 42.18 0.0006 15.1 0.6 1980 SXVII S/1980 S26
Saturn Epimetheus 151.4 59.32 0.0010 16.7 0.7 1980 SXI S/1980 S3
Saturn Janus 151.5 89.19 0.0016 16.7 0.7 1966 SX S/1980 S1
Saturn Mimas 185.54 198.52 0.0065 22.7 0.9 1789 SI
Saturn Methone 194 3 0.0000 24.2 1.0 2004 SXXXII S/2004 S1
Saturn Pallene 211 4 0.0000 27.5 1.1 2004 SXXXIII S/2004 S2
Saturn Enceladus 238.04 249.29 0.0118 32.9 1.4 1789 SII
Saturn Tethys 294.67 529.98 0.0150 45.4 1.9 1684 SIII
Saturn Telesto 294.71 11.2 0.0004 45.4 1.9 1980 SXIII S/1980 S13
Saturn Calypso 294.71 9.86 0.0003 45.4 1.9 1980 SXIV S/1980 S25
Saturn Dione 377.42 562.5 0.0236 65.7 2.7 1684 SIV
Saturn Helene 377.42 16.29 0.0007 65.7 2.7 1980 SXII S/1980 S6
Saturn Polydeuces 377.42 4 0.0000 65.7 2.7 2004 SXXXIV S/2004 S5
Saturn Rhea 527.07 764.5 0.0269 108.5 4.5 1672 SV
Saturn Titan 1221.87 2575.5 0.1381 382.9 16.0 1655 SVI
Saturn Hyperion 1500.88 143.04 0.0018 521.3 21.7 0.1 1848 SVII
Saturn Iapetus 3560.84 734.5 0.0228 79.4 0.2 1671 SVIII
Saturn Kiviuq 11111 8 0.0004 437.5 1.2 2000 SXXIV S/2000 S5
Saturn Ijiraq 11124 6 0.0002 438.3 1.2 2000 SXXII S/2000 S6
Saturn Phoebe 12947.8 109.92 0.0047 550.4 1.5 1898 SIX
Saturn Paaliaq 15200 11 0.0005 700.1 1.9 2000 SXX S/2000 S2
Saturn Skathi 15541 4 0.0001 723.7 2.0 2000 SXXVII S/2000 S8
Saturn Albiorix 16182 16 0.0006 769.0 2.1 2000 SXXVI S/2000 S11
Saturn S/2004 S11 17119 3 0.0000 836.7 2.3 2005 S/2004 S11
Saturn Erriapo 17343 5 0.0002 853.2 2.3 2000 SXXVIII S/2000 S10
Saturn Siarnaq 17531 20 0.0007 867.1 2.4 2000 SXXIX S/2000 S3
Saturn Tarvos 17983 7.5 0.0003 900.9 2.5 2000 SXXI S/2000 S4
Saturn S/2004 S13 18403 3 0.0000 932.6 2.6 2005 S/2004 S13
Saturn Mundilfari 18685 3.5 0.0001 954.1 2.6 2000 SXXV S/2000 S9
Saturn Narvi 19007 3.5 0.0002 978.9 2.7 2003 SXXXI S/2003 S1
Saturn S/2004 S15 19338 3 0.0000 1004.6 2.8 2005 S/2004 S15
Saturn S/2004 S17 19447 2 0.0000 1013.1 2.8 2005 S/2004 S17
Saturn Suttungr 19459 3.5 0.0001 1014.0 2.8 2000 SXXIII S/2000 S12
Saturn S/2004 S14 19856 3 0.0000 1045.2 2.9 2005 S/2004 S14
Saturn S/2004 S12 19878 2.5 0.0000 1046.9 2.9 2005 S/2004 S12
Saturn S/2004 S18 20129 3.5 0.0000 1066.8 2.9 2005 S/2004 S18
Saturn S/2004 S9 20390 2.5 0.0000 1087.7 3.0 2005 S/2004 S9
Saturn Thrymr 20474 3.5 0.0001 1094.4 3.0 2000 SXXX S/2000 S7
Saturn S/2004 S10 20735 3 0.0000 1115.4 3.1 2005 S/2004 S10
Saturn S/2004 S7 20999 3 0.0000 1136.7 3.1 2005 S/2004 S7
Saturn S/2004 S16 22453 2 0.0000 1256.8 3.4 2005 S/2004 S16
Saturn Ymir 23040 9 0.0004 1306.4 3.6 2000 SXIX S/2000 S1
Saturn S/2004 S8 25108 3 0.0000 1486.2 4.1 2005 S/2004 S8
Uranus Cordelia 49.8 20.1 0.0008 8.1 0.3 1986 UVI S/1986 U7
Uranus Ophelia 58.8 21.4 0.0008 10.3 0.4 1986 UVII S/1986 U8
Uranus Bianca 59.2 25.7 0.0010 10.4 0.4 1986 UVIII S/1986 U9
Uranus Cressida 61.8 39.8 0.0015 11.1 0.5 1986 UIX S/1986 U3
Uranus Desdemona 62.7 32 0.0012 11.4 0.5 1986 UX S/1986 U6
Uranus Juliet 64.4 46.8 0.0017 11.9 0.5 1986 UXI S/1986 U2
Uranus Portia 66.1 67.6 0.0025 12.3 0.5 1986 UXII S/1986 U1
Uranus Rosalind 69.9 36 0.0013 13.4 0.6 1986 UXIII S/1986 U4
Uranus Cupid 74.8 12 0.0000 14.8 0.6 2003 UXXVII S/2003 U2
Uranus Belinda 75.3 40.3 0.0015 15.0 0.6 1986 UXIV S/1986 U5
Uranus Perdita 76.42 13 0.0000 15.3 0.6 1999 UXXV S/1986 U10
Uranus Puck 86 81 0.0030 18.3 0.8 1985 UXV S/1985 U1
Uranus Mab 97.7 16 0.0000 22.1 0.9 2003 UXXVI S/2003 U1
Uranus Miranda 129.9 235.68 0.0081 33.9 1.4 1948 UV
Uranus Ariel 190.9 578.9 0.0275 60.5 2.5 1851 UI
Uranus Umbriel 266 584.7 0.0233 99.5 4.1 1851 UII
Uranus Titania 436.3 788.9 0.0386 209.0 8.7 1787 UIII
Uranus Oberon 583.5 761.4 0.0354 323.2 13.5 1787 UIV
Uranus Francisco 4276 6 0.0003 267.2 0.7 2001 UXXII S/2001 U3
Uranus Caliban 7231 49 0.0021 587.5 1.6 1997 UXVI S/1997 U1
Uranus Stephano 8004 10 0.0004 684.2 1.9 1999 UXX S/1999 U2
Uranus Trinculo 8504 5 0.0002 749.3 2.1 2001 UXXI S/2001 U1
Uranus Sycorax 12179 95 0.0041 1284.2 3.5 1997 UXVII S/1997 U2
Uranus Margaret 14345 5.5 0.0002 1641.5 4.5 2003 UXXIII S/2003 U3
Uranus Prospero 16256 15 0.0006 1980.3 5.4 1999 UXVIII S/1999 U3
Uranus Setebos 17418 15 0.0006 2196.3 6.0 1999 UXIX S/1999 U1
Uranus Ferdinand 20901 6 0.0003 2887.0 7.9 2001 UXXIV S/2001 U2
Neptune Naiad 48.23 33.45 0.0012 7.1 0.3 1989 NIII S/1989 N6
Neptune Thalassa 50.08 41.25 0.0015 7.5 0.3 1989 NIV S/1989 N5
Neptune Despina 52.53 75.26 0.0025 8.0 0.3 1989 NV S/1989 N3
Neptune Galatea 61.95 87.75 0.0033 10.3 0.4 1989 NVI S/1989 N4
Neptune Larissa 73.55 97.45 0.0035 13.3 0.6 1989 NVII S/1989 N2
Neptune Proteus 117.65 209.87 0.0078 26.9 1.1 1989 NVIII S/1989 N1
Neptune Triton 354.8 1353.4 0.0795 141.1 5.9 1846 NI
Neptune Nereid 5513.4 170 0.0073 360.1 1.0 1949 NII
Neptune S/2002 N1 15728 24 0.0011 1734.8 4.7 2002 S/2002 N1
Neptune S/2002 N2 22422 24 0.0011 2952.9 8.1 2002 S/2002 N2
Neptune S/2002 N3 23571 24 0.0011 3182.8 8.7 2002 S/2002 N3
Neptune S/2003 N1 46695 14 0.0005 8874.5 24.3 2003 S/2003 N1
Neptune S/2002 N4 48387 30 0.0012 9361.2 25.6 2002 S/2002 N4
Pluto Charon 19.6 593 0.0313 164.5 6.9 1978 PI S/1978 P1
Pluto Nix 48.7 25 0.0007 635.2 24.9 0.1 2005 S/2005 P2
Pluto Hydra 64.8 25 0.0011 975.2 38.2 0.1 2005 S/2005 P1

[302]

4. Large Moons

Our Moon is large, but the moons Ganymede (of Jupiter), Titan (of Saturn), Callisto (of Jupiter), and Io (of Jupiter) are larger than our Moon is. The first two are larger than even the planet Mercury. Compared to its planet, the moon Charon (of Pluto) is larger than our Moon. See the Moons Page in the UniverseFamilyTree.

Moons and planets are formed from numerous large and small fragments that collide with each other and sometimes partially stick together. It seems that our Moon was formed when the Earth was hit by another object that was about the size of Mars. Because of the impact, lots of material was thrown into orbit around the Earth, and some of that material clumped together to form the Moon. If the Earth hadn't been struck by such a large object in just that way, then the Earth might not have had such a relatively large Moon. See also question 189.

[400] [405]

5. Great Moons of Jupiter

Jupiter has four great moons and a large number of small moons. The four great moons of Jupiter (Io, Europa, Ganymede, Callisto) were discovered by Galileo Galilei and are therefore sometimes called the Galilean moons. There is an orbital resonance between the four moons that prevents all four moons to ever be on the same side of Jupiter at the same time.

De large satellites of Jupiter orbit in a plane that is perpendicular to the rotation axis of Jupiter, i.e., in the equatorial plane of the planet. Most large satellites of all planets orbit in or near the equatorial plane of their planet, just like most planets orbit near the equatorial plane of the Sun. This suggests that the satellites were formed together with the planets, and the planets together with the Sun.

[462]

A moon of Jupiter returns to about the same position relative to Jupiter after on average one synodical period. The answer to question 461 explains how you can calculate the synodical period from sidereal periods. You might think that you can predict when the moons of Jupiter will have occultations and transits, from the synodical periods.

However, predictions based on synodical periods won't be very accurate, because Jupiter does not move at constant speed along a circular orbit around the Earth, but at a constantly varying speed along an elliptical orbit around the Sun. Jupiter travels slower than average in one part of its orbit, and faster than average in another part, which makes phenomena involving its moons appear to be later or earlier than average, depending on where Jupiter is in its orbit.

In addition, we do not observe Jupiter from the Sun but from Earth, which itself orbits around the Sun, but that motion is not taken into account in the calculation of the synodical period, so that, too, causes a delay or advance of the phenomena (up to about 1/30th part of the period of the moon).

Moreover, the distance between Jupiter and the Earth is not constant. Because light has a finite speed, images of a far-away occultation take longer to reach Earth than images of a nearby occultation, so a far-away occultation seems to occur later than average, and a nearby occultation earlier than average (up to about 11 minutes).

Also, the moons of Jupiter do not orbit around Jupiter in the exact same plane as the one in which Jupiter orbits around the Sun, and the orbit of Jupiter around the Sun is not in the same plane as the orbit of the Earth around the Sun, and these facts have an effect on the calculation of phenomena where the exact position is very important (such as for the beginning of an occultation of a moon), but these effects are not taken into account in the calculation of the synodical period, either. The further a moon is from Jupiter, the harder it is to get an occultation. It is possible that such a moon only gets occulted by Jupiter if Jupiter is in a particular small part of its orbit around the Sun.

All in all, synodical periods are not enough to be able to accurately predict occultations and other phenomena. They can be used to show when such a phenomenon will definitely not happen, but not every prediction of such a phenomenon using synodical periods will come true. This is similar to how it goes with solar eclipses and lunar eclipses involving the Earth's Moon. One can tell, using synodical periods, when there is a chance for such an eclipse (namely, a chance for a solar eclipse at every New Moon, and a chance for a lunar eclipse at every Full Moon -- no eclipse will occur at any other phase of the Moon), but one can't tell exactly whether those eclipses will occur, because not every Full Moon has a lunar eclipse, and not every New Moon has a solar eclipse, and the details of such eclipses are not very easy to calculate.

If you do want to be able to make accurate predictions for the occultations and transits of the moons of Jupiter, then you'll have to calculate the positions of the moons and Jupiter to great accuracy, which is a lot more difficult than just using the synodical periods. The book [Meeus] devotes 12 pages to this problem and refers to some other chapters for some of the calculations, so those should be added in as well.

[592]

6. Bound Rotation

Regular moons are moons with roughly circular orbits (i.e., with small eccentricity) roughly above the planet's equator (i.e., with a small inclination), that traverse their orbit in the same direction as the rotation of the planet around its axies. Such moons were likely formed together with their planet.

Of all regular moons in our Solar System, only moon Hyperion of planet Saturn does not always show the same face to its planet. All other regular planets do always show the same face to their planet. This is called bound rotation, and means that the rotational period of those moons (around their axis of rotation) is equal to their orbital period (around their planet). The rotation of Hyperion around its axis is chaotic, and predictable for only a short time. There appears to be a combination of causes for this: Hyperion has a very irregular shape (clearly not spherical), has a moderately varying distance to its planet (an eccentricity of 0.12, quite high for a regular moon), and its orbit is near to that of a far larger Moon (Titan).

Irregular moons (with a strongly inclined orbit and/or a strongly eccentric orbit and/or orbiting counter to the direction in which the planet orbits around its axis) are often very far from their planet, where tidal forces are much weaker and haven't had enough time to lock the rotation of the Moon around its axies to its motion around the planet.

Our Moon is a relatively large Moon near a not-so-large planet, so it is relatively more difficult for the tidal forces of the Earth upon the Moon to change the rotation of the Moon around its axis than it is for a moon that is smaller or near a larger planet ― which means most moons. Yet even the rotational period of the Moon is already equal to its orbital period. I don't consider it remarkable that nearly all regular Moons always show the same face to their planets.



[AA]

[vorige][volgende]


languages: [en] [nl]

//aa.quae.nl/en/antwoorden/manen.html;
Last updated: 2021-07-19