# How "locked" are Pluto and Charon? How much does each librate as seen from the other?

Discussion below Are all or some geostationary satellites tidally locked to the Earth? got me thinking about Pluto and Charon. According to Wikipedia:

Charon and Pluto orbit each other every 6.387 days. The two objects are gravitationally locked to one another, so each keeps the same face towards the other. This is a case of mutual tidal locking, as compared to that of the Earth and the Moon, where the Moon always shows the same face to Earth, but not vice versa. The average distance between Charon and Pluto is 19,570 kilometres (12,160 mi). The discovery of Charon allowed astronomers to calculate accurately the mass of the Plutonian system, and mutual occultations revealed their sizes. However, neither indicated the two bodies' individual masses, which could only be estimated, until the discovery of Pluto's outer moons in late 2005. Details in the orbits of the outer moons revealed that Charon has approximately 12% of the mass of Pluto.

Question: How "locked" are Pluto and Charon? How much does each librate as seen from the other? Charon's orbit has an eccentricity of only about 0.0002 but I think the total apparent libration motion depends upon orbital inclination and the alignment of each body's rotational axis.

Related to lunar libration motion quantification:

To give some idea of what libration looks like here are two GIFs of our Moon's libration from Who does these mesmerizing simulations of the phases of the Moon? And how?

Sources: above and below

• – uhoh
Jul 15, 2020 at 2:39

Here's the result obtained with NAIF's SPICE library:

The graph shows the azimuth and the elevation of Charon as seen from an observer on the surface of Pluto with position: latitude = 45° and longitude = 0 (az and el are corrected for one-way light time and stellar aberration).

This is probably a better view:

You would not see any change in azimuth or elevation.

EDIT: the data files used by SPICE are: "pck00010.tpc" and "plu055.bsp".

pck00010.tpc:
Prime meridian constant (W0) terms for Pluto and Charon are from: Archinal, B.A., A'Hearn, M.F., Conrad, A., Consolmagno, G.J., Courtin, R., Fukushima, T., Hestroffer, D., Hilton, J.L., Krasinsky, G.A., Neumann, G., Oberst, J., Seidelmann, P.K., Stooke, P., Tholen, D.J., Thomas, P.C., and Williams, I.P. "Erratum to: Reports of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2006 & 2009."

The orientation of Pluto north pole is constant: RA = 132.993°, DEC = -6.163°.

plu055.bsp:
Ephemeris for Pluto's satellites updated to include New Horizons data. This ephemeris is the basis of the work reported at the 2015 DPS meeting.

• +1 Very interesting, thank you! My guess is that this is the geometrical libration that comes from whatever values SPICE uses for Charon for inclination (relative to Pluto's equator) and eccentricity, which are both going to be very small. My guess is that it assumes that any residual rocking back and forth after locking first started has long since damped out which is probably quite reasonable.
– uhoh
Jul 15, 2020 at 2:04
• I noticed that Charon's inclination and eccentricity listed in Wikipedia are different than those in this answer (which are probably newer; after New Horizons' flyby). Are you able to see what values are used by SPICE for this plot?
– uhoh
Jul 15, 2020 at 2:06
• @uhoh Added some info in the "Edit". For the inclination and the eccentricity, they are not hardcoded in a file, they need to be calculated starting from the state vector, but I get e= 0.12 for Charon. Jul 15, 2020 at 8:30
• The image "Table 1" says "Mean orbital elements (semimajor axis, orbital period, eccentricity, and inclination) for Charon are Plutocentric", but it's wrong because if I do the calculations with Charon barycentric state vector I get e from 0.000057 to 0.000260 (it's not clear the epoch of the elements in that table). Jul 15, 2020 at 8:38
• The GIF of our Moon's libration removes the movement in the sky leaving only the libration (apparent tilting and rolling of the surface due to constant rotation but variable orbital velocity, and inclination) and variation in size due to variation in distance. Is it possible to address libration at all? I think the 0.05 degree azimuth variation plus some similar triangles in the rotating frame suggests about the same amount of libration, and the eccentricity gives the apparent size variation, but not sure yet.
– uhoh
Nov 25, 2020 at 23:19

Here is a paper with information on Pluto and Pluto's moons. I believe much of the info comes from the New Horizons mission. S. A. Stern, the P.I. for New Horizons, is listed as lead author.

Here's a screen capture from the top of page 3 of this pdf:

0 inclination as well as near zero eccentricity.

There'd be no bobbing and weaving like in your gifs of our Moon. Charon would hover quite motionless in Pluto's sky. And Pluto who hover frozen in Charon's sky.

Body Semimajor axis(km) Period(days) Eccentricity Inclination Radius(km) GM($$\frac{km^{3}}{s^{2}}$$) Density($$\frac{kg}{m^{3}}$$)
Pluto 6.3872 1187 ± 4* 869.6± 1.8 1860 ± 13
Charon 19,596 6.3872 0.00005 0.0° 606 ± 3* 105.88 ± 1.0 1702 ± 21
Styx 42,413 20.1617 0.00001 0.0° 1.8 to 9.8† 0.0000 ± 0.0001
Nix 48,690 24.8548 0.00000 0.0° 54 × 41 × 36‡ 0.0030 ± 0.0027
Kerberos 57,750 32.1679 0.00000 0.4° 2.6 to 14† 0.0011 ± 0.0006
Hydra 64,721 38.2021 0.00554 0.3° 43 × 33‡ 0.0032 ± 0.0028
• I'm thinking that when an object first becomes just barely tidally locked it still oscillates by almost +/- 90 degrees, and these oscillations continue to slowly damp. This kind of rocking could have a period much longer than 6 days and so by itself New Horizons' flyby images may not be enough to rule it out.
– uhoh
Jul 14, 2020 at 6:36
• I am missing any information about "how locked they are?" So New Horizons' flyby images dont give us enough information to rule out a remaining oscillation?.
– Uwe
Jul 14, 2020 at 9:14
• @uhoh why +/- 90? shouldn't it be +/- 180deg? Jul 15, 2020 at 4:41
• @qqjkztd yes I think you are right! I had to fix that here as well
– uhoh
Jul 15, 2020 at 5:25
• An eccentricity of 0.00005 means the distance varies by approximately 2km for anyone wondering. One part in ten thousand. Oct 1, 2020 at 23:50

Charon was discovered by United States Naval Observatory astronomer James Christy, using the 1.55-meter (61 in) telescope at United States Naval Observatory Flagstaff Station (NOFS).[19] On June 22, 1978, he had been examining highly magnified images of Pluto on photographic plates taken with the telescope two months prior. Christy noticed that a slight elongation appeared periodically. The bulge was confirmed on plates dating back to April 29, 1965. The International Astronomical Union formally announced Christy's discovery to the world on July 7, 1978.

Charon's discovery at the Naval Observatory Flagstaff Station as a time-varying bulge on the image of Pluto (seen near the top at left, but absent on the right). Negative image.

If we see only this small bulge when we look for Charon from Earth, how should we know about How "locked" are Pluto and Charon? There are better ground based and Hubble images showing both objects as separated dots but without surface details.

Is it possible to determine how locked they are using the images taken by New Horizons during a short flyby? Do we need the images of a orbiter of the dual system Pluto-Charon?

Quotes and image from Wikipedia.

• With four decimal points of precision on Charon's eccentricity I think there is more information available than these fuzzy images. New Horizons took some data on approach example. Look at the level of precision in all of it's orbital parameters for example: en.wikipedia.org/wiki/Charon_(moon) I Think there is a lot more known that your answer suggests.
– uhoh
Jul 13, 2020 at 16:40
• There are better pictures of Pluto and Charon available Jul 13, 2020 at 16:51
• Also Pluto, Charon and the other moons are resolved in HST images taken during the New Horizons pre-approach campaign to look for debris, rings and other satellites. Additional information on the orbit and the bodies themselves was also obtained during the Pluto-Charon mutual events in 1985-1990 Jul 13, 2020 at 17:46
• @matteol : These images are better but they do not show how locked Pluto and Charon are.
– Uwe
Jul 13, 2020 at 20:16