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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Present and Future Ephemerides: Requirements and
Limitations
E. M. Standish
Caltech/Jet Propulsion Laboratory, Pasadena, CA, USA
Introduction
JPL continues to develop planetary and lunar ephemerides in support of its
spacecraft navigation. Over the years, the requirements for increasingly sophisti­
cated navigation have called for higher and higher accuracy; that trend is expected
to continue into the future. It is therefore mandatory that JPL maintains a state­
of­the­art program for the maintenance and improvement of its ephemerides. This
paper discusses various aspects of the planetary and lunar ephemerides at JPL.
First, the question of the independent variable of the ephemerides is reviewed:
JPL's long­time use of ``T eph '' vs. the IAU's newly­defined ``T CB''. Next, the pa­
per mentions the navigational requirements of past missions and those expected
in the future. A brief description follows of modern observational accuracies, of
present­day ephemeris uncertainties, and of the effects of the asteroids upon the
ephemerides. Lastly, the plans for future ephemerides are presented.
Independent Variable of the Ephemerides
Since the mid­1960's, JPL navigation, including the ephemeris creation effort,
has included general relativity in all of its dynamical calculations as well as in
the reductions of the observational data. Even though the IAU defined both the
variables, ET and TDB, the JPL ephemerides have never used either as they were
defined; the strict IAU definitions of give variables that are not physically real. On
the other hand, as shown by Standish (1998), the time argument used in the JPL
ephemerides since the mid­1960's, ``T eph '', is a true relativistic coordinate time,
rigorously equivalent to TCB, which is the time variable most recently defined
by the IAU and which differs from T eph only by a rate and an offset.
Contrary to what has been said in the literature, a conversion to TCB would
not allow an increase in accuracy for the JPL ephemerides. One can show that
working in T eph is equivalent to working in TCB; the resultant ephemerides would
be equivalent.
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There has been an immense amount of sophisticated and detailed software
produced over the past number of decades throughout the astronomical commu­
nity and within the aerospace industry. The mere suggestion that this software
be converted from the present T eph into TCB is unacceptable: a conversion to
TCB would involve a tremendous cost, time, and effort, and the chance of sig­
nificant error involved with such a conversion would be virtually guaranteed and
unavoidable. There are many applications which don't even have to consider the
difference between TT and T eph , since those two time scales never differ by more
than 2 milliseconds of time; in contrast, the difference between TT and TCB
grows at 0.5 seconds per year!
What is the benefit in converting to TCB? Absolutely nothing. Furthermore,
it is a trivial matter to convert T eph units provided by the JPL ephemerides into SI
units using TCB. This involves simply the scale factor, 1\GammaL B = d(T eph )=d(TCB),
applied to T eph , the independent argument of the ephemerides, to the distances,
and to the GM values.
Spacecraft Navigation : Accuracy Requirements
Planetary spacecraft navigation continues to become more and more sophis­
ticated, requiring ever higher accuracy. For example, the numbers and sizes of
necessary mid­course corrections are significantly reduced with accurate naviga­
tion, leading to significant savings in the onboard thruster propellant. Accurate
navigation also allows the immediate entry of a spacecraft into a planet's at­
mosphere, a process which requires an extremely accurate entry angle, thereby
taking advantage of aerobraking, and avoiding the fuel­consuming process of or­
bit insertion. Even greater accuracy is demanded when a small landing area on
the surface of planet is specified, as will undoubtedly be the case in the future as
the planetary terrains become better known.
One of the major contributing sources of navigation uncertainty has been and
continues to be the uncertainties associated with the planetary ephemerides. For
this reason, JPL has been supporting the maintenance and improvement of the
ephemerides since the mid­1960's and is expected to continue to do so into the
future, as the navigational requirements become even more demanding. For the
Viking mission in 1976, the ephemeris requirements for going into Mars orbit
were on the level of 50 km; by the time of the direct entry (and subsequent use
of a parachute) of Pathfinder, the requirements had shrunk below 5 km; for the
future Mars Exploration Rovers, launching in 2003, the demand is for no more
than a 1 km error.
Observations, Ephemeris Accuracies and Effect of Asteroids
The planets may be split into two groups when discussing the observational
data and the resultant accuracies.
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For the four inner planets, the ephemerides are dominated by two types of
data:
ffl ranging measurements, whether radar reflections from a planetary surface
or return signals from a transponder aboard a landed or orbiting spacecraft,
and
ffl \DeltaVLBI measurements of an orbiting or landed spacecraft, taken with re­
spect to the International Celestial Reference Frame (ICRF).
The ranging measurements provide all relative angles and distances between
the earth and the other three innermost planets, thus locking the whole system
together. The ranging measurements also provide accurate mean motions of the
planets with respect to inertial space. The \DeltaVLBI are angular measurements
which serve to orient the whole inner system onto the background ICRF.
Typically, radar­ranging has in inherent accuracy of 100 meters or less, though
topography tends to add signatures to the observations. The uncertainties of
spacecraft­ranging can be as low as 2--3 meters when the solar corona is calibrat­
ed using dual frequency signals or when the single frequency is high enough or
when the planet is not near to solar conjunction. VLBI to an orbiting or landed
spacecraft relate the planet to the background radio sources at a level of a few
milliarcseconds.
No matter how good the observational data are, the planetary motions can not
be perfectly known, for the planets are perturbed by many asteroids whose masses
are quite poorly known. It is not possible to solve for the individual asteroid
masses, other than for the biggest few, because there are too many for their
relatively minor signatures to be uniquely recognizable in the observational data.
Consequently, as shown by Williams (1984) and by Standish and Fienga (2002),
the ephemerides of the inner planets, especially Mars, will deteriorate over time.
If, as in the case of Mars, the most accurate observations are separated by long
stretches of time (15 years between Viking and Pathfinder), then the attempts
to fit all of the observational data, at the level of its inherent accuracy, result in
effectively smoothing out the perturbations. The result is that the ephemerides
are no more accurate than 1--2 km over the span of the observations and that the
uncertainties grow at a rate of a few km/decade outside that span.
There has been a great deal of effort to model the asteroid perturbations as
well as possible. The orbits are sufficiently known; the masses are not. Studies
of the estimations of the masses for the most relevant 300 or so asteroids have
been made by Fienga (2001) and by Krasinsky et al. (2001); modeling of a ring
to represent the perturbations from the remaining thousands of small asteroids
is described by Krasinsky et al. (2002).
Certainly, any improvement in our knowledge of asteroid masses in general will
provide a corresponding improvement in the computed dynamics of the planetary
motions.
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For Jupiter, a number of spacecraft observations exist, allowing Jupiter's
ephemeris to be known at the level of about 50 km (0.''01 -- 0.''02). For the out­
ermost four planets, the problem is not the asteroids; it is the fact that the
observations are only optical and the planets have not gone through a full orbital
period since the most modern optical techniques were developed. Consequently,
these ephemerides are accurate to only about 0.''1 -- 0.''2.
Future JPL Ephemerides
There is a choice to be made in creating ephemerides; the choice involves
mainly the ephemerides of Mars and the Earth and is due to the uncertainties
imposed by the perturbations of the asteroids.
ffl One may fit all of the observations as well as possible, thereby smoothing
out the perturbations and creating a ``long­term'' ephemeris which is as
accurate as possible over extended periods of time. However, some of the
perturbations have periods exceeding the time­spans of the modern obser­
vations. The result can be biases, especially in the mean motions.
ffl One may concentrate on fitting only the most recent observations so that
present­day accuracy is as high as possible. Hopefully, extrapolation into
the near future (a year or two) will be good enough for these ``accurate
now'' ephemerides, but certainly, the accuracy will decline over longer time
spans.
For future JPL planetary ephemerides, the independent variable will continue
to be T eph . The ``long­term'' ephemerides will continue to be available to the gen­
eral public, while the ``accurate now'' ephemerides will be created for navigational
purposes and for specific scientific studies.
References
1. Fienga A. G. private communication, 2001.
2. Krasinsky G. A., Pitjeva E. V., Vasilyev M. V., Yagudina E. I. Estimating
Masses of Asteroids. 2001, Communications of IAA RAS, No. 139.
3. Krasinsky G. A., Pitjeva E. V., Vasilyev M. V., Yagudina E. I. Hidden mass
in the asteroid belt. Icarus, 2002, 158, 98--105.
4. Standish E. M., Fienga A. G. Accuracy limit of modern ephemerides imposed
by the uncertainties in asteroid masses. Astronomy and Astrophysics, 2002,
384, 322--328.
5. Williams J. G. Determining Asteroid Masses from Perturbations on Mars
Icarus. 1984, 57, 1--13.
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