EPM2021 and EPM2021H

Download EPM2021

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.

Download EPM2021H

Long version of EPM2021 (13199 BC — AD 17191).

EPM User Manual

List of software to access the EPM ephemeris in SPICE and other formats.

Online Ephemeris Service

Interactive web tool for obtaining ephemeris tables according to various EPM versions, including EPM2021.

Overview

EPM2021 ephemeris contains coordinates and velocities of the Sun, the Moon, eight major planets, Pluto, five asteroids (Ceres, Pallas, Vesta, Iris, Bamberga) and 4 TNO (Eris, Haumea, Makemake, Sedna), as well as TT-TDB and Euler angles for lunar physical libration. EPM2021 covers a time span of more than 400 years (1787–2214).

EPM2021H ephemeris is the longer version of EPM2021, covering a time span of more than 30000 years (13199 BC — AD 17191). Within the EPM2021 time span, EPM2021 and EPM2021H are practically equal with the only exception of the Moon. EPM2021H uses the model of the precession of the Earth from (Vondrák et al. 2011). Also, the lunar model of EPM2021H does not have friction between crust and core.

Observations

The planetary and lunar solutions or EPM2021 used the observational data of EPM2017 with the following additions:

• Optical observations of natural satellites of outer planets made in Pulkovo Observatory in 2016–2018 (Ershova et al. 2016, Narizhnaya et al. 2018a, Narizhnaya et al. 2018b).

• Optical observations of Triton made at the Sheshan station of the Shanghai Observatory in 2003–2009 (Qiao et al. 2007, Qiao et al. 2014).

• Optical observations of Triton made at Yunnan Observatory in 2014–2019 (Wang et al. 2017) and optical observations of Uranian satellites made at the same observatory in 2014–2016 (Xie et al. 2019).

• 4 normal points of the Jovian orbiter Juno obtained in 2016–2017.

• 780 normal points of Mars Reconnaissance Orbiter (MRO) obtained in 2014–2017 and 3226 observations of Mars Odyssey obtained in 2014–2017.
  The data were kindly provided by Dr. William Folkner of NASA JPL.

• 1211 LLR normal points from the Apache Point Observatory in NM, USA, covering the timespan from late 2016 to late 2020.

• LLR data from the Côte d'Azur Observatory in Grasse (Chabé et al. 2020): 3789 normal points obtained with the 1024-nm laser (September 2017 — present) and 262 normal points obtained with the 532-nm laser (September 2017 — 2020).
  The data were taken from NASA CDDIS.

• LLR data from the Matera observatory in Italy: 261 normal points (September 2017 — July 2021), also taken from NASA CDDIS.

• LLR data from the Wettzell Observatory in Germany (Eckl et al. 2019): 101 normal points (2018 — present) taken from the EDC archive.

• Historical LLR data from Crimean Astrophysical Observatory (Tryapitsyn et al. 2021): 25 normal points (1982–1984).

Dynamical model

The dynamical model of EPM2021 is for the most part the same as that of the previous public release, EPM2017. It includes all planets, Pluto, the Moon, the Sun, selected asteroids, the discrete uniform 180-point asteroid annulus (Pitjeva & Pitjev, 2018a), selected Trans-Neptunian objects (TNOs), and the discrete uniform 160-point TNO ring (Pitjeva & Pitjev, 2018b). Sixteen bodies (the Sun, the planets, Pluto, Ceres, Pallas, Vesta, Iris, Bamberga) obey Einstein–Infeld–Hoffmann equations of motion. Other bodies are modeled as interacting with those 16 bodies with only Newtonian forces and not interacting with each other. Apart from point-mass interactions, the model includes additional accelerations from solar oblateness and Lense–Thirring effect. Earth also gets “point mass–figure” accelerations that come from the Sun, Venus, Mars, Jupiter, and the Moon. The Moon is modeled as an elastic body with a rotating liquid core (Pavlov et al. 2016, Pavlov 2020).

With EPM2021, changes to the list of point masses were introduced:

• Two point masses were added representing Greeks (in the L₄ Lagrange point of Jupiter) and Trojans (in L₅)
• The inner and outer radii of the discrete astroid annulus were changed to 2.2 au and 3.0 au, respectively; the middle radius is 2.74 au.
• The list of individual asteroids was completely revised and now has 277 asteroids (see below).

Determination of asteroid masses

The initial list of asteroids was compiled by merging 343 asteroids of the DE430 model (Folkner et al. 2014) and 287 asteroids from (Kuchynka et al. 2009). The resulting list contained 379 asteroids. A priori estimates, known either from precise measurements or infrared observations, were used to determine the masses of all asteroids via Tikhonov regularization scheme, following the approach proposed by Kuchynka & Folkner (2013). 102 masses that were determined negative (always within uncertainty) were excluded from the model. The final list contains 277 asteroids.

Reductions of spacecraft ranging observations

Two improvements were made to reduce systematic errors in the residuals of Martian orbiters MRO and Odyssey who provide Earth–Mars ranges (normal points) of sub-meter accuracy. One is accounting for measurement biases that come from miscalibrations on radio observatories. Following the decision from (Kuchynka et al. 2012), two sets of biases were determined for Deep Space Network (DSN) stations: one for Mars Global Surveyor (MGS) and Odyssey spacecraft, another for the MRO spacecraft.

The second improvement concerns the delay of the radio signal due to the free electrons in the solar plasma. In EPM2021, there is only one determined solar plasma parameter for 1999–2017. The model of the solar plasma electron density is the following: $$N_{\mathrm{e}} = C \, \frac{N_1(t)}{r^2},$$ where the function \(N_1(t)\) is equal to the smoothed in situ measurements of the electron density near Earth obtained from the NASA/GSFC's OMNI dataset, and \(C\) is a factor determined from observations. The reference value of \(C\) is 1.

Technical improvements

A new numerical integrator, ABMD (Aksim & Pavlov, 2020), was developed for EPM. It is an extension of the multistep Adams–Bashforth–Moulton scheme capable of handling time-delayed terms in the dynamical equations of the tidal response of the Moon.

Constants and determined parameters