Tag Archives: Ephemerides

Weighing the Kuiper Belt

Hi there! Today, we are back to the Solar System, and more especially the Kuiper Belt. You know, all these small bodies, which orbit beyond Neptune. Instead of speaking of specific cases, like Pluto, Haumea or Sedna, we will see the Kuiper Belt as a whole.
The study I present, Mass of the Kuiper Belt, by E.V. Pitjeva and N.P. Pitjev, constrains its total mass with planetary ephemerides. This study has been recently published in Celestial Mechanics and Dynamical Astronomy.

The Kuiper Belt

I have presented the Kuiper Belt many times. These are objects, orbiting beyond the orbit of Neptune. This zone is named after the Dutch-American astronomer Gerard Kuiper, who hypothesized that it could have been a reservoir of comets, even if he thought that it would be almost clear. At that time, the only known Kepler Belt Object was Pluto. Now, more than 2,000 of them are known, and many more are probably to be discovered.
Most of these objects orbit between 30 and 50 AU (astronomical units) from the Sun.

This study wants to constrain the total mass of the Kuiper Belt, from the motion of the planets. For that, the authors built and used planetary ephemerides.

Planetary ephemerides

Planetary ephemerides give the location of the Solar System objects, especially the planets, at given dates. They have been of strategical importance during centuries for celestial navigation. Now, we still need them, for instance to identify potentially hazardous objects, to guide spacecraft, to detect new objects,…

I can cite 3 institutions, which provide ephemerides:

  • NASA’s JPL,
  • IMCCE, Paris Observatory, France,
  • Institute of Applied Astronomy, Russian Academy of Sciences.

JPL stands for Jet Propulsion Laboratory. It is located near Pasadena, CA, and is associated with the Californian Institute of Technology (CalTech). As part of NASA, it is associated with the American spacecraft.
The IMCCE, for Institute of Celestial Mechanics, is responsible for the French ephemerides. It has been founded in 1795 as the Bureau des Longitudes, in a context of rivalry between France and England. Its goal was then to assist France, to regain control of the seas.
And the Institute of Applied Astronomy, in Russia, is the place where this study has been conducted.

These 3 institutions provide their own ephemerides, i.e. solutions for the orbital motion of the planets, their satellites, the asteroids,… Now, let us see how to include the Kuiper Belt.

The Kuiper Belt as a ring

The orbital motion of planetary bodies come from the numerical integration of the gravitational equations, in which each body is perturbed by all the other ones… this makes many of them. So many that a common computer cannot handle that, when it comes to 2,000 of them. Moreover, there are probably many more Kuiper Belt Objects, which are not discovered yet, but which perturb the motion of the planets…

The authors by-passed this problem in modeling the Kuiper Belt as a ring. Not the whole Kuiper Belt actually. The 31 most massive of these objects are modeled as point masses, ans the remaining ones are embedded into a fictitious rotating ring, which mass perturbs the planets.

If you know the perturbation, you know the mass… Easy, isn’t it? Well, not that easy, actually…

As many data as possible

The authors maintain their ephemerides since many years, and each new version is enriched with new data. The current version, EPM2017, uses about 800,000 positional observations of planets and spacecraft, ranging from 1913 to 2015. Many of the observations of planets are Earth-based astrometric observations, while spacecraft observations include MESSENGER (mission to Mercury), Venus Express (to Venus), Cassini (to Saturn), and the Martian missions Viking-1 & 2, Pathfinder, Mars Global Surveyor, Odyssey, Mars Reconnaissance Orbiter, and Mars Express.

Very small objects like spacecraft are very sensitive to planetary perturbations, this is why their navigation data may be invaluable.

Observed and fitted parameters

Making ephemerides consists in fitting a dynamical model to data, i.e. observed positions. The dynamical model is mainly composed of the gravitational interactions between the planetary bodies, with some relativistic corrections (Einstein-Infeld-Hoffmann equations). These interactions use the masses of the objects as parameters.

When you want to fit the model to the data, you fit the initial conditions, i.e. the location of the objects at the beginning of the simulation, and some of the parameters. Why only some of them? It depends on how well you know them.

For instance, in this case, the mass of (1)Ceres is assumed to be accurately known, thanks to the Dawn mission (just finished, by the way). This means that fitting this mass would be counterproductive.

So, the authors have to make critical choices between what they fit and what they don’t, and also how they ponder the observations between each other.

A light Kuiper Belt

From formation models of the Solar System, the initial Kuiper Belt should be as massive as ten times our Earth. However,
fitting the ephemerides gives much smaller numbers. You can find below the outcomes of the previous studies and this last one, by the same team.

Year Kuiper Belt mass (in Earth mass)
2010 0.0258
2013 0.0263
2014 0.0197
2017 0.0228 ± 0.0046
2018 0.0197 ± 0.0035

As you can see

  • the current Kuiper Belt is by far much lighter than the original one. This means that this region of the Solar System has probably been depleted by the gravitational action of the main planets, only few objects remaining,
  • the numbers do not converge very fast, but they converge. In particular, each new measurement is consistent with the previous one, and the uncertainty tends to shrink. Slowly, but it shrinks.

This number of 0.02 Earth mass makes the Kuiper Belt about 2 orders of magnitudes (i.e. between 10 and 1,000) heavier than the Asteroid Main Belt, but some 3 orders of magnitude lighter than the proposed Planet Nine.

The Planet Nine would have a limited influence

You remember the Planet Nine? It is a yet undiscovered body, which is supposed to exist anyway. It should orbit far behind the orbit of Neptune, should be as massive as 10 Earth masses, and would be responsible for the clustering of the pericentres of the Trans-Neptunian Objects (the Kuiper Belt), and for the obliquity of the Sun.

In this study, the authors benefited from the very accurate navigation data of the space mission Cassini, which orbited Saturn until September 2017. And for Cassini, the Kuiper Belt has a much stronger influence than the hypothetical Planet Nine. This makes me think that the author believe that using such ephemerides is not a good strategy for constraining the Planet Nine.

Actually, the planetologists looking for the Planet Nine focus on the individual trajectories of the Kuiper Belt Objects, because these are the most sensitive to it.

The study and its authors

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

Locating Ultima Thule

Hi there! First I have to explain the title. Ultima Thule usually stands for any place beyond the known world… Actually, we will not leave the Solar System. Ultima Thule is an unofficial nickname for (486958) 2014 MU69, which is the next target of New Horizons spacecraft. Do you remember this spacecraft, which gave us outstanding images of Pluto and Charon in July 2015? That’s just the same one!
After having left Pluto, New Horizons changed its trajectory to 2014 MU69, which will be reached on January 1st, 2019. 6 months to wait then.
Interestingly, 2014 MU69 was unknown when New Horizons was launched in January 2006. Its primary mission was the binary Pluto-Charon and its satellites, and of course it was worth to extend the mission to another body. But choosing this second target was a difficult task, since the distant Solar System, here the Kuiper Belt, is very difficult to observe, and is pretty sparse. This is why observations programs of the Hubble Space Telescope (HST) were dedicated, and 2014 MU69 has been discovered in 2014.
Discovering an object is one thing, determining accurately its motion in view of a rendezvous with a spacecraft is another thing. This is the topic of the study I present today, High-precision orbit fitting and uncertainty analysis of (486958) 2014 MU69, by Simon Porter et al. This study has recently been published in The Astronomical Journal.

The New Horizons spacecraft

New Horizons is the first mission of NASA’s New Frontier program. It was launched in January 2006, and made its closest approach to Pluto in July 2015. Before that, it incidentally encountered the small asteroid (132524) APL at a distance of about 100,000 km in June 2006, and benefited from the gravitational assistance of Jupiter in February 2007.

The asteroid 132524 APL seen by New Horizons. © NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute
The asteroid 132524 APL seen by New Horizons. © NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute

It carries seven science instruments:

  • the Long-Range Reconnaissance Imager (LORRI), which images the encountered bodies,
  • the Solar Wind At Pluto (SWAP) instrument, which name is very explicit regarding its goal,
  • the Pluto Energetic Particle Spectrometer Science Investigation (PEPSSI), which supplements SWAP for the detection of high-energy particles,
  • Alice, which is an ultraviolet imaging spectrometer,
  • the Ralph telescope, which is a photographic instrument,
  • the Venetia Burney Student Dust Counter (VBSDC) measures dust. This instrument has been built by students of the University of Colorado,
  • and the Radioscience Experiment (REX), which measured the temperature and the atmospheric pressure of Pluto.

As you can see from some of the names of the instrument, Pluto-Charon was definitely the primary goal of New Horizons. Anyway, Pluto is now behind, and New Horizons is en route to 2014 MU69, also nicknamed Ultima Thule.

Ultima Thule

At this time, our knowledge of Ultima Thule is very limited. This body has been discovered in 2014, from a dedicated observation program on the Hubble Space Telescope, to identify potential targets for New Horizons. Finally, 2014 MU69 has been selected, partly for technical reasons, i.e. it is not so difficult to reach from Pluto.

It was discovered in June 2014, and has an apparent magnitude of nearly 27, and an absolute one of 11. We can guess its size from its magnitude, and its diameter should be smaller than 50 km. So, a very small body. A stellar occultation happening in 2017 has revealed that its diameter should be closer to 25-30 km, and its shape may be bilobal, or it could even be a contact binary.

Observations of its dynamics revealed that it is a cold, classical Kuiper Belt object. Its eccentricity and inclination are limited, since they are not excited by any resonance with the giant planets. So, it belongs to a region of the Solar System, which is quiet from a dynamical point of view.

As I previously said, discovering it is not enough if you want a spacecraft to reach it. You must know its motion accurately, and for that you need more data. And Ultima Thule can be observed only with the Hubble Space Telescope.

Hubble Space Telescope data

The authors disposed of 5 observations of 2014 MU69, by the Wide Field Camera 3 (WFC3) of the HST. Even with the HST, imaging 2014 MU69 requires 6 minutes of exposure, i.e. you need to accumulate photons reflected by 2014 MU69 during 6 minutes to have enough signal.

The detection of 2014 MU<sub>69</sub>. © NASA, ESA, SwRI, JHU/APL, and the New Horizons KBO Search Team
The detection of 2014 MU<sub>69</sub>. © NASA, ESA, SwRI, JHU/APL, and the New Horizons KBO Search Team

Another difficulty comes from the number of stars in that region of the sky. This is due to the galactic latitude of 2014 MU69, which is close to 0, i.e. close to the Galactic plane. The images have to be treated, to remove their incoming light. This is not just a pixel, but a diffraction spot, which needs to be modeled to be properly removed.

Once you have these data, you can start to determine the orbit of 2014 MU69, i.e. make ephemerides.

From astrometry to orbit

When you catch a body on a 2-dimensional image of the sky, you get two coordinates. Basically, these coordinates translate into a right ascension, and a declination. And to build ephemerides of a body, you need to integrate the equation ruling the orbital motion. This equations is a second-order 3-dimensional ordinary differential equation.

The motion is ruled by the gravitational perturbation of the Sun and the major planets, and for the problem to be solved, you need initial conditions. These are a position and a velocity of 2014 MU69 at a given date, which you derive from your astrometric observations, i.e. the 5 couples (right ascension, declination).

Easy, isn’t it? No, it’s not! Because of the uncertainties on the measurements, your 10 data, i.e. 5 right ascensions and 5 declinations, do not exactly correspond to an initial condition. So, you have to make a fit, i.e. determine the initial condition, which best fits the observations.

There are many potential sources of uncertainties: the accuracy of the positioning of the HST, the accuracy of the coordinates of 2014 MU69 (remember: this is not a pixel, but a diffraction spot), the duration of the exposure… and also the location of the stars surrounding 2014 MU69 in the field of view. To make absolute astrometry, you need to know precisely the location of these stars, and you get their locations from a star catalogue. Currently, the astrometric satellite Gaia is making such a survey, with a never reached accuracy and comprehensiveness. The Gaia Data Release 2 has been released in April 2018, and gives positions and proper motions (i.e. you can now consider that the stars move from date to date) of more than 1 billion stars! The authors had the chance to use that catalogue. This resulted in predictions, which were accurate enough, to predict a stellar occultation, which has been observed from the Earth.

Predicting stellar occultations

When a Solar System body occultates a star, you can indirectly observe it. You observe the star with your telescope, and during a few seconds, the star disappears, and then reappears, because of this object, which light is too faint for you. Multiple observations of a stellar occultation give information on the motion of the object, and on its dimensions. The rings around Chariklo and Haumea have been discovered that way.

For 2014 MU69 (or Ultima Thule), an occultation has been successfully predicted. It has been observed 5 times on 2017 July 17, in Argentina, giving 5 solid-body chords. This permitted us to infer that 2014 MU69 could be bilobal, or even a contact binary.

A stable orbit

And from these astrometric data, the authors propagated the orbit of 2014 MU69 over 100 million years, in considering the uncertainties on the initial positions. The outcomes of the simulations safely state that 2014 MU69 is on a very stable orbit, with a mean semimajor axis of 44.23 astronomical units (39.48 for Pluto), and an orbital eccentricity smaller than 0.04. This results in an orbital period of 294 years, during which the distance to the Sun barely varies.

We are looking forward for the encounter in 6 months!

The study and its authors

And that’s it for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter, Facebook, Instagram, and Pinterest.

Where is Triton?

Hi there! Today’s post is on the location of Triton. Triton is the largest satellite of Neptune and, of course, we know where it is. The paper I present you, entitled Precise CCD positions of Triton in 2014-2016 using the newest Gaia DR1 star catalog, aims at assisting an accurate modeling of its motion. This is a Chinese study, by Na Wang, Qing-Yu Peng, Huan-Wen Peng, H.J. Xie, S. Ma and Q.F. Zhang, which presents observations made at the Yunnan Observatory. This study has recently been published in The Monthly Notices of the Royal Astronomical Society.

Triton’s facts

Triton is by far the largest satellite of Neptune, with a mean radius of 1,350 km. It was discovered almost simultaneously with Neptune, i.e. 17 days later, in 1846. It orbits Neptune in a little less than 6 days, and rotates synchronously.

Surprisingly, its orbit is very inclined with respect to the equator of Neptune (some 24°), and it is retrograde… which means that the inclination should not be given as 24° but as 180-24 = 156°. Usually the satellites have a very small inclination, since they are supposed to have been formed in a nebula which gave birth to the planet. Such a large inclination means that Triton has probably not been formed in situ but was an asteroid, which has been trapped by Neptune. Since then, it loses some orbital energy, which has resulted in a circularization of its orbit and a fall on Neptune.

Triton has been visited by the Voyager 2 spacecraft in 1989, which covered about 40% of its surface. It revealed an atmosphere of nitrogen and evidences of melting, which indicate a geological activity, probably resulting in a differentiated body. It could even harbor or have harbored a subsurface ocean.

Astrometry in the Solar System

The goal of the paper I present today is to give accurate positions of Triton. This is called astrometry. The idea is this: measuring accurately the position of a body at a given date requires to take a picture of the satellite. Stars must be present in the field since the satellite will be positioned according to them. The result will then be compared to the predictions given by dynamical models, called ephemerides. Since we observe only in 2 dimensions, i.e. on the celestial sphere, which is a surface, then an astrometric position consists of two coordinates: the right ascension and the declination.

The positions of the stars surrounding the satellite, actually its image projected on the celestial sphere, since the stars are much further, are known thanks to systematic surveys. The satellite Gaia is currently conducting the most accurate of such surveys ever performed, and the first data were released in 2016, in the Gaia Data Release 1 (DR1, see this post, from October 2016). The accuracy of Gaia lets us hope very accurate future astrometry, and even past, since old observations could be retreated in using Gaia’s catalog.

But why making astrometry? For improving the ephemerides, which would give us a better knowledge of the orbital motion of the satellite. And why improving the ephemerides? I see at least two reasons:

  1. To help future space missions,
  2. To have a better knowledge of the physical properties of the bodies. Some of these properties, like the mass and the energy dissipation (tides), affect the orbital motion.

Potential difficulties

This study presents Earth-based observations, which are affected by:

  1. Diffraction on the CCD chip. When you observe a point as a light-source, you actually see a diffraction disk, and you have to decide which point on the disk is the position of your object. You can partly limit the size of the diffraction disk in limiting the exposure time, this prevents the chip from being saturated. If this results in a too faint object, then you can add several images.
  2. The anisotropy of the light scattering by the surface of the body (here Triton). When we see Triton, we actually see the Solar light, which is reflected by the surface of Triton. Since the surface could be pretty rough, since the limb is darker than the center because of a different incidence angle, and since Triton is not seen as a whole disk (remember the lunar crescent), then the center of the diffraction disk, i.e. the photocentre, is not exactly the location of the body.
  3. The refraction by the atmosphere. The atmosphere distorts the image, which makes the satellite-based images more accurate than the Earth-based ones. This distortion depends on the location of the observatory, and the weather. Some systems of adaptive optics exist, which partly overcome this problem.
  4. The aberration. The relative velocity of the observed object with the observer (the Earth is moving, remember?) alters the apparent position of the objects.
  5. The seeing. When you have some wind, the locations of the stars present some erratic variations.
  6. The inhomogeneity of the CCD chip. An homogeneous lightning will not result in a homogeneous response, because of the positions of the pixel on the image (you have a better sensitivity in the center than close to an edge), and some technical differences between the pixels. A way to overcome this problem is to normalize the light measurement by a flat image, which is the response to a homogeneous lightning. This is usually obtained in taking a picture in the dome, or from the averaging of many images.

This paper

This paper presents 775 new observations, i.e. 775 new positions of Triton at given dates, between 2014 and 2016. The images were taken with a 1-meter refractor at the Yunnan National Observatory, Kunming, Yunnan, China. The residuals, i.e. observed minus predicted positions, are obtained from the ephemerides made by the Jet Propulsion Laboratory in California, USA. The authors obtain mean residuals of a few tens of milli-arcsec, i.e. some thousands of kilometers. Something interesting is the dispersion of these residuals: the authors show that when the stars are positioned with Gaia DR1, the residuals are much less dispersed than with an older catalog. The authors used the catalog UCAC4, released in August 2012 by the US Naval Observatory, for comparison.

These new observations will enrich the databases and permit the future improvements of ephemerides.

Some links

That’s all for today! Please do not forget to comment. You can also subscribe to the RSS feed, and follow me on Twitter.