EPM2017 and EPM2017H
Overview
EPM2017 ephemerides contain coordinates and velocities of the Sun, the Moon, eight major planets, Pluto, three largest asteroids (Ceres, Pallas, Vesta) and 4 TNO (Eris, Haumea, Makemake, Sedna), as well as lunar libration and TTTDB. EPM2017 covers the timespan of more than 400 years (1787–2214).
EPM2017H ephemerides are the longer version of EPM2017, covering the timespan of more than 13100 years (10107 BC – AD 3036, H stands for “Holocene”). Within the EPM2017 timespan, EPM2017 and EPM2017H are practically equal with the only exception of the Moon.
Dynamical model
The dynamical model of EPM is based on the Parameterized PostNewtonian Nbody metric for General Relativity in the barycentric coordinate system (BCRS) and the TDB time scale.
The motion of the Sun, the planets (including Pluto), and the Moon (as pointmasses) obeys the EinsteinInfeldHoffmann relativistic equations, with additional perturbations from: solar oblateness, 301 largest asteroids and 30 largest transNeptunian objects (TNO), as well as two discrete annuli: the first for the asteroid belt, and the second for the Kuiper belt.
For improvement of the planetary part of EPM2017, about 270 parameters were determined:
 orbital elements of the planets and the 18 satellites of the outer planets;
 the value of the solar mass parameter (in accordance with the B2 resolution of 28 GA IAU which fixed the value of the astronomical units of length (au) equal 149597870700 m and proposed the determination of \(GM_\mathrm{Sun}\) in SI units);
 the ratio of the Earth and Moon masses;
 the Sun's quadrupole moment (J2) (has been defined from the MESSENGER data);
 the three angles of orientation with respect to the ICRF2 frame;
 the parameters of the rotation of Mars and topography of the inner planets;
 the masses of 30 asteroids and the mean densities of three taxonomic classes (C, S, and M) of asteroids, the masses of the asteroid and TNO rings;
 the total masses of the main asteroid belt and Kuiper belt;
 the time delay from the solar corona (the parameters of its model were determined from observations for different solar conjunctions);
 phase effects for outer planets; for Pluto it is the difference between the dynamical barycenter and light barycenter of the PlutoCharon system.
The model of orbital and rotation motion of the Moon in EPM [1] is based on the equations used in the JPL DE430 ephemeris [2] with combination of uptodate astronomical, geodynamical, and geo and selenophysical models.
The Moon is considered an elastic body having a rotating liquid core. The following equations are included in the model:
 perturbations of the orbit of the Moon in the gravitational potential of the Earth;
 torque due to the gravitational potential of the Moon;
 perturbations of the orbit of the Moon due to lunar and solar tides on the Earth;
 distortion of the Moon's figure as a result of its rotation and Earth's gravity;
 torque due to the interaction between the lunar crust and the liquid core.
Earth Gravitation Model 2008 (EGM2008 [3]) was taken for the gravitational model of the Earth, while GL660B [4] was used for the Moon. Common models recommended by IERS Convensions 2010 were used for the rotation of the Earth, displacement of stations and troposheric signal delay. Refinement of parameters was done basing on the lunar laser ranging (LLR) observational data in the time span of 19702016. Observations from the following stations were processed: Haleakala, McDonald/MLRS1/MLRS2, OCA, Apache, and Matera.
For the TTTDB conversion, the differential equation from [5] has been used, and TTTDB was obtained by numerical integration.
The parameters of the lunar and planetary parts of EPM2017 are in agreement with each other.
EPM2017 has been oriented to the ICRF2 with an accuracy better than 0.2 mas (3σ) by including into the total solution 266 ICRF2based VLBI measurements of spacecraft taken from 19892014 near Venus, Mars, and Saturn [6].
Changes in the “Holocene” version
The dynamical model used during the production of EPM2017H differs in two pieces. First, EPM2017H uses the model of the precession of the Earth valid over thousands of years [7]. Second, the lunar model of EPM2017H does not have friction between crust and core, to avoid exponential growing of the angular velocity of the lunar core in the past. That decision is similar to what has been done for the DE431 ephemeris model as compared to DE430. The lunar parameters of the solution were then refit to the EPM2017H model.
Changes since EPM2015
The most important changes in EPM2017 since the previous version of EPM are:
 inclusion of the LenseThirring acceleration into model;
 improved relativistic barycentre definition;
 modelling the acceleration of the Sun as a regular body;
 the new models of the asteroid belt and the Kuiper belt;
 recent estimates of masses and orbits of asteroids;
 usage of recent observations of spacecraft and LLR normal points that appeared after EPM2015 was released;
 the “Holocene” version of ephemeris, EPM2017H.
LenseThirring acceleration
where:

\(\mathbf{r}_i\) is the barycentric position of the \(i\)th body

\(\mathbf{r}_{iS}\) is the heliocentric position of the \(i\)th body

\(r_{ij} = \mathbf{r_j}  \mathbf{r_i}\)

\(\mathbf{z} = (0, 0, 1)\)

\(R_\mathrm{Sun}\) — rotation matrix from \(\mathbf{z}\) to the Sun's pole. The following value is used: \(R_\mathrm{Sun} = \mathrm{R}_z(16^{\circ}.13)\mathrm{R}_x(26^{\circ}.13)\)

\(G\) is the gravitational constant

\(S_\mathrm{Sun}\) is the angular momentum of the Sun. Following the decision from [8], we take \(S_\mathrm{Sun} = 190\times 10^{39}\ \mathrm{kg\ m}^2/\mathrm{s}\)
Relativistic barycentre definition
The relativistic barycentre of pointmasses \({\mu_i}\), where \(\mu_{i} = GM_i\) is the \(i\)th body's gravitational parameter, is defined as
where \(\mathbf{r}_i\) is the position of the \(i\)th body, while \(\mu_i^{*}\) is the body's relativistic gravitational parameter:
Initial positions and velocities of the bodies are equally adjusted so that the position of the center of mass and the momentum are zero:
In previous versions of EPM, the \(\dot{\mu_i^{*}}\) was neglected.
Modelling the acceleration of the Sun as a regular body
In earlier versions of the EPM, the Sun was explicitly placed to keep the barycenter at the origin. In EPM2017, the Sun obeys the EinsteinInfeldHoffmann equations of motion as all the other bodies. Similar approach has been taken in DE ephemeris starting from DE430 [2] and INPOP ephemeris starting from the first release INPOP06 [9].
The perturbations from solar oblateness and LenseThirring effect act not only on planets, but on Sun, too, following Newton's third law.
The mutual influence of the astroid belt and the Kuiper belt to the orbit of the Sun, neglected in previous versions of EPM, is properly taken into account in EPM2017.
Numerical roundoff errors in the integration cause the barycenter, initially placed at the origin, to drift at a slow pace. In the timespan of 19002020, the displacement of the barycenter from the origin is less than 0.03 mm.
The new models of the asteroid belt and the Kuiper belt
The largest 301 asteroids and 31 TNO (including Pluto) are directly included in integration in EPM ephemeris. However, in order to take into account gravitational influence of other smaller asteroids and TNO, their perturbations were modeled as perturbations from uniform rings.
The first model [9, 10] consisted of a onedimensional asteroid ring with estimated mass and radius, and a onedimensional TNO ring of radius 43 au with estimated mass. Both rings lie in the ecliptic plane. Due to large correlation between radius and mass of the asteroid ring, later it was replaced with a “twodimensional ring” (annulus) [5].
But these models did not quite reflected the mutual interactions between moving bodies of the belts and ordinary pointmasses (Sun and planets). To remedy this shortcoming, a new discrete rotating models have been has been proposed.
In EPM2017, the asteroid and the Kuiper belt are modeled by a system of uniformly distributed pointmasses lying in the plane of the ecliptic on three circular lines each. That also allows to model their influence to the orbit of the Sun (unlike previous versions of EPM) and planets.
The asteroid belt is approximated with 180 points with equal masses (60 points on each circle). The two border circles (inner and outer) lie on R1 = 2.06 au and R2 = 3.27 au that correspond to the average distances for orbital resonances 1:2 and 2:1 with the motion of Jupiter. The middle cicle lies on Rmid = 2.67 au.
The Kuiper belt is approximated with 160 points with equal masses. The two border circles, 40 points each, lie on R1=39.4 au and R2=48.7 au—the average distances of orbital resonances 3:2 and 2:1 with the motion of Neptune. The middle circle (80 points), approximating the dense core of the Kuiper belt, lies on Rmid = 44 au.
The belt points don't interact each other, only with other bodies of the Solar system. At the inital moment of the integration, the velocities of the points correspond to a circular motion.
The total masses of the belts were the fitted parameters that were determined from processing and fitting the spacecraft observational data.
Recent masses and orbits of some asteroids
Some asteroid data were updated. In particular, the new mass value was obtained during the approach of the Dawn spacecraft to Ceres [10]. The masses of 30 large asteroids (not including 13 double and multiple asteroids) were improved from observations of different spacecraft (their values are given below). Masses of other 255 asteroids were calculated from their diameters and densities.
Recent aditional observations
The planetary part of EPM2017 ephemerides has been fitted to about 800000 observations of different types, spanning 19132015, from classical meridian observations to modern planetary and spacecraft ranging.
However, spacecraft ranging near planets are correlated with each other on each tracking pass, so there is effectively only one independent range point for each pass. Based on this, Dr. Folker formed normal points of JPL spacecraft ranging; the normal points for other spacecraft ranging were formed by authors. Moreover, the points near solar conjunction were deleted due to large solar plasma effects, as Dr. Folker did with the MESSENGER data. The new radar data were obtained due to the courtesy of William Folkner (JPL) and Agnes Fienga (IMCCE) via private communication, a NASA JPL webpage “Observational Data for Planets and Planetary Satellites”, and a Geoazur “Astrometric Planetary Data” webpage.
The fouryear MESSENGER (20112015) [8] observations were added in EPM2017. As a result, the Mercury ephemeris has become significantly more accurate than it was in EPM2015.
New LLR data that appeared after EPM2015 release (till the end of 2016) was added into EPM2017 solution—most notably, the new high quality infrared data from the OCA observatory.
Software
Processing of observations, fitting of parameters, and numerical integration of EPM2017 were performed with a software package ERA8 (Ephemeris Research in Astronomy) developed at IAA RAS [11].
Availability
EPM2017 can be found on the FTP server of the IAA RAS. While IAA binary and ASCII formats, originally used for EPM, are still supported, users are encouraged to use the SPK and PCK formats, also known as the SPICE formats [12, 13]. The list of provided software to access the EPM ephemeris in SPICE and other formats is given in the User manual.
IAA RAS provides an interactive web tool for obtaining ephemeris tables according to various versions of ephemerides (including EPM2017).
Constants and determined parameters
Selected constants:
JD 2446000.5 (27.10.1984)  date of the starting epoch of the integration 
JD 2374000.5 (10.09.1787)  left boundary date 
JD 2530000.5 (22.10.2214)  right boundary date 
299792.458 km/s  the speed of light 
149597870700 m  the Astronomical Unit in meters 
81.300568886  the EarthMoon mass ratio 
2.0321572×10^{4}  dynamical form factor of the Moon 
6.310179×10^{4}  lunar (CA)/B (beta) 
2.277292×10^{4}  lunar (BA)/C (gamma) 
2.41×10^{2}  lunar k2 
9.3×10^{2} day  lunar tide delay 
2.366×10^{7}  solar oblateness 
1.0  PPN parameter β 
1.0  PPN parameter γ 
0.0  the variation of the gravitational constant 
R1 = 2.06 au, R2 = 3.27 au  the radii of the asteroid annulus 
R1 = 39.4 au, R2 = 48.7 au  the radii of the TNO annulus 
The following masses were estimated in EPM2017: the solar mass parameter (\(GM_\mathrm{Sun}\)) from ranging data, masses of the Earth and the Moon from ranging and LLR data, masses of 30 asteroids and the mean densities of three taxonomic classes (C = 1.270 g/cm^{3}, S = 1.714 g/cm^{3}, and M = 3.383 g/cm^{3}) of asteroids. Those mean densities were taken to determine the masses of 255 asteroids whose diameters were taken from IRAS and MSE surveys. The masses of 13 asteroids (from 301) having satellites, as well as Vesta, Ceres, and Eros exploring by spacecraft, are known well and have been fixed (marked by * in the table below).
The masses of planets (except the Earth) and TNO in EPM2017 are equal to their EPM2015 counterparts.
Masses (in the TDB timescale) of barycenters of systems of planets with their satellites:
GM in 10^{15} au^{3}/day^{2}  GM in km^{3}/sec^{2}  

Sun  295912208289.8587  132712440043.85333 
Moon  10931.8945  4902.80008 
Mercury  49124.8045  22031.78000 
Venus  724345.2333  324858.59200 
Earth  888769.2447  398600.43552 
Mars  95495.4870  42828.37521 
Jupiter  282534582.5972  126712764.13345 
Saturn  84597060.7325  37940585.20000 
Uranus  12920265.7963  5794556.46575 
Neptune  15243573.4789  6836527.10058 
Pluto  2175.0991  975.50118 
Asteroids  
*Ceres1  139.6418  62.62736 
Pallas2  30.3058  13.59173 
Juno3  4.1238  1.84947 
*Vesta4  38.548027  17.288245 
Hebe6  1.3284  0.59578 
Iris7  1.8658  0.83676 
Flora8  1.0298  0.46185 
Metis9  0.4020  0.18028 
Hygiea10  11.7734  5.28020 
Parthenope11  0.8442  0.37861 
Egeria13  1.8018  0.80807 
Irene14  1.4314  0.64198 
Eunomia15  4.9508  2.22034 
Psyche16  4.7941  2.15009 
Fortune19  1.3907  0.62372 
Massalia20  0.4277  0.19180 
*Kalliope22  1.1846  0.53127 
Thalia23  0.2537  0.11377 
Amphitrite29  0.9840  0.44129 
Euphosyne31  4.2720  1.91592 
*Daphne41  0.9390  0.42115 
*Eugeria45  0.8617  0.38644 
Doris48  2.4123  1.08189 
Europa52  2.7672  1.24104 
Cybele65  1.5472  0.69388 
*Sylvia87  2.1995  0.98646 
Thisbe88  2.6142  1.17245 
*Antiope90  0.1235  0.05540 
*Minerva93  0.5209  0.23360 
Aegle96  1.6885  0.75726 
Artemis105  0.3689  0.16543 
*Camilla107  1.6668  0.74752 
*Hermione121  0.7396  0.33171 
*Elektra130  0.9822  0.44050 
Juewa139  0.7809  0.35022 
*Kleopatra216  0.6905  0.30969 
*Emma283  0.2054  0.09211 
Bamberga324  1.6437  0.73718 
Diotima423  1.9738  0.88521 
*Eros433  0.00099490317  0.0004462 
Patientia451  2.4679  1.10681 
Davida511  4.6674  2.12167 
Herculina532  1.9482  0.87375 
*Alauda702  0.9014  0.40426 
Interamnia704  5.3123  2.38250 
*Pulcova762  0.2083  0.09344 
Largest TNO  
Eris136199  2485.2618  1114.60477 
Haumea136108  596.1650  267.37157 
Sedna90372  148.8180  66.74277 
Makemake136472  446.4540  200.22830 
Quaoar50000  210.3840  94.35425 
84522  223.2270  100.11415 
Orcus90482  94.3510  42.31509 
Varuna20000  55.0630  24.69498 
Ixion28978  44.6450  20.02265 
307261  76.1670  34.15982 
2006 QH_181  69.7520  31.28279 
55565  61.0150  27.36436 
208996  78.8740  35.37387 
225088  415.8790  186.51585 
Salacia120347  64.8850  29.10000 
Other  
Asteroid annulus (does not include 301 asteroids)  15.0024  6.72837 
TNO ring (does not include 30 TNO)  9846.5489  4416.03791 
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Elena Pitjeva, email evp@iaaras.ru,
Dmitry Pavlov, email dpavlov@iaaras.ru,
Institute of Applied Astronomy RAS, St. Petersburg, Russia
7 November 2017.