# Is there any ephemeris generator that gives you accurate distances between Earth and other bodies?

I've tried JPL's HORIZONS ephemeris generator and while it gives accurate celestial coordinates for an object it doesn't give the geocentric distance.

JPL's Solar System Simulator gives the distance to an object at a certain time however only down to a few digits.

Is there an accurate tool that generates exact (meaning down to the meter) geocentric distances between Earth and another Solar System body over increments of time?

• Down to the metre? I don't think such data exists for most of the Solar System. From ssd.jpl.nasa.gov/?horizons_doc#limitations "Uncertainties in major planet ephemerides range from 10cm to 100+ km in the state-of-the-art JPL/DE-431 ephemeris, used as the basis for spacecraft navigation, mission planning and radar astronomy". I vaguely remember reading somewhere that the current uncertainty in Saturn's orbit is ~1 km. – PM 2Ring Nov 25 '20 at 7:33
• But anyway, the Earth's mean orbital speed is ~29.78 km/s, so there's no point in calculating geocentric distances to metre precision unless your times have sub-millisecond precision. – PM 2Ring Nov 25 '20 at 7:34
• @PM2Ring I believe that your comments warrant an answer (even when it's not the one the OP wants to hear) – planetmaker Nov 25 '20 at 9:50
• And as additional nicety: if you want sub-millisecond or metre precision... you will have to take into account the speed of light to calculate interactions precisely. It cannot be stressed enough that one should always pay attention to the accuracy of the data at hand and to be aware of that. More than once I had to deduct points for exagerated yet unwarranted precision which is not available due to the (lack of) precision of the input data :) – planetmaker Nov 25 '20 at 12:56

JPL HORIZONS gives the distance from the observer to the target as delta. In Table Settings this option is 20. Observer range & range-rate. For asteroids and comets, it can also give distance uncertainty (39. Range & range-rate 3-sigmas) as RNG_3sigma. You can choose units of au or km.

For example, with Table Settings: QUANTITIES=1,20,39; range units=KM, the geocentric ephemeris for asteroid (153201) 2000 WO107 around its 2020-11-29 close approach to Earth looks like:

 Date__(UT)__HR:MN     R.A._____(ICRF)_____DEC            delta      deldot RNG_3sigma RNGRT_3sig

2020-Nov-29 03:00     08 48 22.83 +14 26 33.8 4.3065970451E+06  -1.1137937   143.5915  0.0000166
2020-Nov-29 04:00     08 43 44.11 +14 51 56.9 4.3035317776E+06  -0.5890828   144.6349  0.0000171
2020-Nov-29 05:00     08 39 04.01 +15 17 00.3 4.3023570178E+06  -0.0635364   145.6159  0.0000175
2020-Nov-29 06:00     08 34 22.78 +15 41 42.1 4.3030745286E+06   0.4621549   146.5331  0.0000180
2020-Nov-29 07:00     08 29 40.62 +16 06 00.2 4.3056835832E+06   0.9872992   147.3852  0.0000185


In other words, at 05:00 UT, the asteroid is 4,302,357 ±49 km from the center of Earth. Though its orbit is determined well enough for a permanent number designation, even 1 km precision would be unreliable. Its perihelion distance q is only known to ±8.7 km and perihelion time tp to ±1.7 s. New observations may improve this.

Update: new observations of (153201) 2000 WO107 improve its q to ±6.9 km, tp to ±0.3 s, and distance at 2020-11-29 05:00 UT to 4,302,522.2 ±1.1 km. That precision is largely due to radar data, which are not always available.