References in celestial mechanics

I've found lots of books in the local library that explain how orbits of
planets work. However none I can find specifically explain how to calculate
the positions of planets at specific times. Searching the web I've found
Keplarian elements for the planets, and also references to Jean Meeus's
Astronomical Elements. I've also found some negative reviews of that book.

So what does everyone reckon the best references are in this field? There
doesn't seem to be a huge amount on the web. So I'm assuming it will all be
in hard to find books.... Thanks,

David

Just in case I haven't made it clear, I'm talking about the level of
accuracy required for spacecraft trajectory design. Thanks,

David

"David Findlay" wrote in message
. au...
I've found lots of books in the local library that explain how orbits of
planets work. However none I can find specifically explain how to calculate
the positions of planets at specific times. Searching the web I've found
Keplarian elements for the planets, and also references to Jean Meeus's
Astronomical Elements. I've also found some negative reviews of that book.

So what does everyone reckon the best references are in this field? There
doesn't seem to be a huge amount on the web. So I'm assuming it will all be
in hard to find books.... Thanks,

Any time you're dealing with more than two large bodies in
a gravitational system, except for contrived configurations,
the method used is integration of the equations of motion.

An "integrator" in this sense is a programmed numerical
method that takes the equations of motion for a system
along with a starting state (position and velocity of the
component bodies) and evolves the state forward or
backward in time.

There are any number of integrators in use for different
mechanical systems or systems of equations. For following
planetary orbits and spacecraft, depending upon the
accuracy required and the total time for the integration
one can use simple "leapfrog" or Verlet algorithms,
Runge-Kutta, or more sophisticated ones.

For planet positions, NASA/JPL have already done the
integrations for +/- many years from present. The positions
have been reduced to multi-term series of sine and cosine
terms, and a user only need download the data files and
code up a program to read them and apply the algorithm.

One integration that NASA/JPL did is called DE406. The
results of the integration were reduced to a series form
known as VSOP87 Theory by Bretagnon and Francou. VSOP87
is a very practical way to obtain accurate planet positions.
The data files are freely available, along with sample
programs to read and apply them. Jean Meeus, in his book
Astronomical Algorithms, includes truncated data tables and
the mathematics of the algorithm to be applied for each
planet.

A web search on VSOP87 Theory will turn up scads of
related materials.

On Sat, 27 Sep 2003 21:04:20 +1000, David Findlay
wrote:

Just in case I haven't made it clear, I'm talking about the level of
accuracy required for spacecraft trajectory design. Thanks,

David

Nowadays, spacecraft trjectories are planned on the basis of
numerically integrated ephemerides. Depending on the accuracy
required, special ephemerides may be prepared for specific missions.
The method used is described in _The Explanatory Supplement to the
Astronomical Almanac_, and Steve Moshier, who occasionally posts here,
has put up some C code to perform the computations he

http://www.moshier.net/

Look for de118i and examine the sources to see how you might want to
modify them in terms of time intervals and such to get the accuracy
you need.

Al Moore

In article ,
David Findlay wrote:

I've found lots of books in the local library that explain how orbits of
planets work. However none I can find specifically explain how to calculate
the positions of planets at specific times. Searching the web I've found
Keplarian elements for the planets, and also references to Jean Meeus's
Astronomical Elements. I've also found some negative reviews of that book.

So what does everyone reckon the best references are in this field? There
doesn't seem to be a huge amount on the web. So I'm assuming it will all be
in hard to find books.... Thanks,

On my web site (URL below) you'll find an explanation on how to
compute the positions of the major planets with an accuracy of
approximately one minute of arc. If you require more accuracy than
that, I also give links to sites containing FORTRAN code for very
high precision positions, using the VSOP87 end ELP2000 theories.

--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://www.stjarnhimlen.se/
http://home.tiscali.se/pausch/

In article ,
David Findlay wrote:

Just in case I haven't made it clear, I'm talking about the level of
accuracy required for spacecraft trajectory design. Thanks,

The VSOP87 should provide enough accuracy. However, if you want to
also compute the trajectory of the spacecraft itself, you must resort
to numerical integration. If you do a web search for "de118i" you'll
find free C code for hig-accuracy numerical integration of the major
planets in the solar system. You can modify that code and add your
own bodies, if you wish.

--
----------------------------------------------------------------
Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://www.stjarnhimlen.se/
http://home.tiscali.se/pausch/

In article ,
David Findlay wrote:

Just in case I haven't made it clear, I'm talking about the level of
accuracy required for spacecraft trajectory design. Thanks,

The VSOP87 should provide enough accuracy. However, if you want to
also compute the trajectory of the spacecraft itself, you must resort
to numerical integration. If you do a web search for "de118i" you'll
find free C code for hig-accuracy numerical integration of the major
planets in the solar system. You can modify that code and add your
own bodies, if you wish.

Thanks for that information.

David

Nowadays, spacecraft trjectories are planned on the basis of
numerically integrated ephemerides. Depending on the accuracy
required, special ephemerides may be prepared for specific missions.
The method used is described in _The Explanatory Supplement to the
Astronomical Almanac_, and Steve Moshier, who occasionally posts here,
has put up some C code to perform the computations he

http://www.moshier.net/

Look for de118i and examine the sources to see how you might want to
modify them in terms of time intervals and such to get the accuracy
you need.

Thanks for the information.

David

A web search on VSOP87 Theory will turn up scads of
related materials.

Thanks,

David