# Why does JPL at NASA give two different values in astronomical units for planetary distances?

Why is it that JPL (Jet Propulsion Lab) at NASA gives astronomical unit values for the planets for two different time periods, namely 3000 B.C. to 3000 A.D., and 1850 to 2050?

• It would be helpful if you could provide more context for your question and also cite where J.P.L. reports these values. – David H May 27 '15 at 21:07
• Keplerian elements jpl put into google seems to get there – John Shanahan May 28 '15 at 6:44
• It seems to work by putting keplerian elements jpl into google – John Shanahan May 28 '15 at 6:51
• @JohnShanahan - You should put the links in your question. Don't make us search, and maybe find something else. – David Hammen May 28 '15 at 16:42
• Sorry but I am computer illiterate, I dont know how to do links! – John Shanahan May 28 '15 at 17:12

I believe the question is asking about the following tables, one for the period 1800 AD to 2050 AD, the other two for 3000 BC to 3000 AD. Note that in these tables, "EM Bary" refers to the Earth-Moon barycenter, the center of mass of the Earth-Moon system.

Table 1.

Keplerian elements and their rates, with respect to the mean ecliptic
and equinox of J2000, valid for the time-interval 1800 AD - 2050 AD.

a              e               I                L            long.peri.      long.node.
AU, AU/Cy     rad, rad/Cy     deg, deg/Cy      deg, deg/Cy      deg, deg/Cy     deg, deg/Cy
-----------------------------------------------------------------------------------------------------------
Mercury   0.38709927      0.20563593      7.00497902      252.25032350     77.45779628     48.33076593
0.00000037      0.00001906     -0.00594749   149472.67411175      0.16047689     -0.12534081
Venus     0.72333566      0.00677672      3.39467605      181.97909950    131.60246718     76.67984255
0.00000390     -0.00004107     -0.00078890    58517.81538729      0.00268329     -0.27769418
EM Bary   1.00000261      0.01671123     -0.00001531      100.46457166    102.93768193      0.0
0.00000562     -0.00004392     -0.01294668    35999.37244981      0.32327364      0.0
Mars      1.52371034      0.09339410      1.84969142       -4.55343205    -23.94362959     49.55953891
0.00001847      0.00007882     -0.00813131    19140.30268499      0.44441088     -0.29257343
Jupiter   5.20288700      0.04838624      1.30439695       34.39644051     14.72847983    100.47390909
-0.00011607     -0.00013253     -0.00183714     3034.74612775      0.21252668      0.20469106
Saturn    9.53667594      0.05386179      2.48599187       49.95424423     92.59887831    113.66242448
-0.00125060     -0.00050991      0.00193609     1222.49362201     -0.41897216     -0.28867794
Uranus   19.18916464      0.04725744      0.77263783      313.23810451    170.95427630     74.01692503
-0.00196176     -0.00004397     -0.00242939      428.48202785      0.40805281      0.04240589
Neptune  30.06992276      0.00859048      1.77004347      -55.12002969     44.96476227    131.78422574
0.00026291      0.00005105      0.00035372      218.45945325     -0.32241464     -0.00508664
Pluto    39.48211675      0.24882730     17.14001206      238.92903833    224.06891629    110.30393684
-0.00031596      0.00005170      0.00004818      145.20780515     -0.04062942     -0.01183482


Source: http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt

Table 2a.

Keplerian elements and their rates, with respect to the mean ecliptic and equinox of J2000,
valid for the time-interval 3000 BC -- 3000 AD.  NOTE: the computation of M for Jupiter through
Pluto *must* be augmented by the additional terms given in Table 2b (below).

a              e               I                L            long.peri.      long.node.
AU, AU/Cy     rad, rad/Cy     deg, deg/Cy      deg, deg/Cy      deg, deg/Cy     deg, deg/Cy
------------------------------------------------------------------------------------------------------
Mercury   0.38709843      0.20563661      7.00559432      252.25166724     77.45771895     48.33961819
0.00000000      0.00002123     -0.00590158   149472.67486623      0.15940013     -0.12214182
Venus     0.72332102      0.00676399      3.39777545      181.97970850    131.76755713     76.67261496
-0.00000026     -0.00005107      0.00043494    58517.81560260      0.05679648     -0.27274174
EM Bary   1.00000018      0.01673163     -0.00054346      100.46691572    102.93005885     -5.11260389
-0.00000003     -0.00003661     -0.01337178    35999.37306329      0.31795260     -0.24123856
Mars      1.52371243      0.09336511      1.85181869       -4.56813164    -23.91744784     49.71320984
0.00000097      0.00009149     -0.00724757    19140.29934243      0.45223625     -0.26852431
Jupiter   5.20248019      0.04853590      1.29861416       34.33479152     14.27495244    100.29282654
-0.00002864      0.00018026     -0.00322699     3034.90371757      0.18199196      0.13024619
Saturn    9.54149883      0.05550825      2.49424102       50.07571329     92.86136063    113.63998702
-0.00003065     -0.00032044      0.00451969     1222.11494724      0.54179478     -0.25015002
Uranus   19.18797948      0.04685740      0.77298127      314.20276625    172.43404441     73.96250215
-0.00020455     -0.00001550     -0.00180155      428.49512595      0.09266985      0.05739699
Neptune  30.06952752      0.00895439      1.77005520      304.22289287     46.68158724    131.78635853
0.00006447      0.00000818      0.00022400      218.46515314      0.01009938     -0.00606302
Pluto    39.48686035      0.24885238     17.14104260      238.96535011    224.09702598    110.30167986
0.00449751      0.00006016      0.00000501      145.18042903     -0.00968827     -0.00809981
------------------------------------------------------------------------------------------------------

Table 2b.

for Jupiter through Pluto, 3000 BC to 3000 AD, as described
in the related document.

b             c             s            f
---------------------------------------------------------------
Jupiter   -0.00012452    0.06064060   -0.35635438   38.35125000
Saturn     0.00025899   -0.13434469    0.87320147   38.35125000
Uranus     0.00058331   -0.97731848    0.17689245    7.67025000
Neptune   -0.00041348    0.68346318   -0.10162547    7.67025000
Pluto     -0.01262724
---------------------------------------------------------------
`

Source: http://ssd.jpl.nasa.gov/txt/p_elem_t2.txt

It's important to note that the above tables are approximations. More accurate techniques exist.

For details on how to use these tables, and on the errors that result, see http://ssd.jpl.nasa.gov/txt/aprx_pos_planets.pdf and http://ssd.jpl.nasa.gov/?planet_pos .

The latter shows the errors in the two: $$\begin{matrix} &&1800&\text{to}&2050 && 3000\ \text{BC}&\text{to} & 3000\ \text{AD} \\ \\ \text{Planet} &\ & \text{RA} & \text{Dec} & \text{r} &\quad& \text{RA} & \text{Dec} & \text{r} \\ && \text{arcsec} & \text{arcsec} & \text{km} &\quad& \text{arcsec} & \text{arcsec} & \text{km} \\ -----&&---&---&---&&---&---&---\\ \text{Mercury} && 15 & 1 & 1 && 20 & 15 & 1\\ \text{Venus} && 20 & 1 & 4 && 40 & 30 & 8\\ \text{Earth-Moon} && 20 & 8 & 6 && 40 & 15 & 15\\ \text{Mars} && 40 & 2 & 25 && 100 & 40 & 30\\ \text{Jupiter} && 400 & 10 & 600 && 600 & 100 & 1000\\ \text{Saturn} && 600 & 25 & 1500 && 1000 & 100 & 4000\\ \text{Uranus} && 50 & 2 & 1000 && 2000 & 30 & 8000\\ \text{Neptune} && 10 & 1 & 200 && 400 & 15 & 4000\\ \text{Pluto} && 5 & 2 & 300 && 400 & 100 & 2500 \end{matrix}$$ Source: http://ssd.jpl.nasa.gov/?planet_pos

Note that the errors are considerably greater for tables 2a and 2b than they are for table 1, even with the extra complexity involved with using tables 2a and 2b. This says you should use table 1 if the time point of interest is between 1800 AD and 2050 AD, tables 2a and 2b if the time point of interest is outside that interval but between 3000 BC and 3000 AD.

The reason for two tables is that a narrow span of time around the present is of interest to most people, but a broad span of time is of interest to some.

These tables were constructed using some kind of optimal fit (e.g., least squares) that best matched a set of observations. It is very bad form to extrapolate an optimal fit outside of the region over which the estimation was performed. The errors that result from using table 1 (1800 AD to 2050 AD) on the span 3000 BC to 3000 AD would be immense. Never extrapolate curve-fit data!

The data used to generate table 1 was based on (somewhat) modern instrumentation. The measurements are much more accurate and much more plentiful than the older data needed to generate the long ephemeris. The narrow time span combined with plentiful, accurate measurements is what makes the 1800 AD to 2050 AD table considerably more accurate than the long ephemeris.

Some of that older data goes back to 2800 BC. Chinese, Babylonian, and Egyptian astrologers granted immense powers in the stars and planets to influence kings and calamities such as war, famine, drought, and disease. That irrational behavior led to great record keeping. Those ancient astrological observations (particularly solar eclipses) provide a fantastic anchor for long ephemerides.

• Could you, by chance, explain what EM Bary is, in this data? It seems to take Earth's place in the list of planets but Google returns nothing for the phrase.. – Seth Oct 22 '17 at 3:23
• @Seth - It refers to the Earth-Moon barycenter. I updated the answer to incorporate this. – David Hammen Oct 22 '17 at 14:48

Because "the expected positions and distances of objects at an established time are calculated (in au) from these laws, and assembled into a collection of data called an ephemeris". According to Description of JPL Solar System Ephemeris "the computer calculations have been extended as far as 3000 BC to 3000 AD, but positions for the 1850-2050 range are the most accurate, of course... one needs to be very careful about comparing observations reduced on the basis of different ephemerides and coordinate systems."

There is a separate issue with the astronomical unit itself. Until 2012 IAU (International Astronomical Union) defined astronomical unit as the mean distance from the earth to the sun, and their best 2009 estimate "was still derived from observation and measurements subject to error, and based on techniques that did not yet standardize all relativistic effects, and thus were not constant for all observers." This should not be relevant anymore because in 2012 IAU finally saw the light, and "simply used the 2009 estimate to redefine the astronomical unit as a conventional unit of length directly tied to the meter (exactly 149597870700 m) and assigned it the official symbol au". The meter is currently tied to the speed of light in the vacuum, so that is as ironclad as it gets. But... stay tuned for JPL to get up to speed.

On Physics SE David Hammen describes a previous standardization "war" between JPL and Europeans, over relativisitic time measurements, which affected the astronomical unit under the old definition, by the way. "Relativistic religious wars were fought over this issue. Europeans (Russia and France, the only other countries with a stake in the game) wanted to use a (theoretical) clock far removed from the Sun. One second on that clock would always tick faster than an Earth-based clock. JPL's ephemeris time is essentially that far-removed clock, scaled to tick at Earth rate (on average). JPL won that religious war, but perhaps only because they got slightly better results than did the Russian Academy or the Paris Observatory."

• Is it generaliy true that over millions of years as the Sun loses mass and the planets gain somewhat, that they all move further away from the Sun? – John Shanahan May 28 '15 at 7:13
• @John Shanahan Sun does lose mass in emitting radiation, which causes planetary orbits to expand and speeds to decrease, this was one of the reasons IAU changed the definition of astronomical unit. newscientist.com/article/… However, this effect is not enough to explain observed 15cm/year drift of earth away from the sun, tidal repulsion was also suggested, the same effect that moves moon away from earth newscientist.com/article/… – Conifold May 28 '15 at 21:03