Improved Planetary Ephemeris Model for Interplanetary Mission Studies

Paper number

IAC-09.C1.11.3

Author

Dr. Rajesh Arora, Indian Space Research Organization (ISRO), VSSC, India

Coauthor

Mr. Abhay Kumar, Vikram Sarabhai Space Centre (VSSC), India

Year

2009

Abstract

The accuracy of interplanetary design parameters such as launch date and Delta-V 
will  depend  upon  how  accurate  is  the  planetary  ephemeris  models.  Using  planetary 
ephemeris models, one gets position and velocity vector of departure and arrival planets. Using  this  data,  one  then  solves  the  Lambert’s  problem  to  get  the  design  parameters. Often  a  grid  search  procedure  is  desired  where  these  steps  are  repeated  for  different launch dates  and  transfer durations. From  these  searches,  launch date  corresponding  to minimum Delta-V  is  selected. These  studies  form  the basis  for detailed analysis, where numerical integration of trajectories is made for proper capture at the targeted orbit of the 
arrival planet.  
The planetary ephemeris model developed by Meeus  [1991]  is extensively used 
for preliminary design of  interplanetary  trajectories.  In  this model,  the orbital  elements are stored  in a polynomial form as a function of corrected Julian centuries. The position and velocity vector of a planet is then computed using simple transformations. For a ten year period ranging from 2010 to 2020, error in position and velocity of all the planets is quantified when using  the Meeus model. The  reference  ephemeris used  for quantifying the errors  from Meeus model  is JPL’s DE405. Large errors  in state vector are observed for the outer planets when Meeus model is used.
The objective of  this paper  is  to retain  the simplicity of  the expressions given  in Meeus model and yet give accuracy that is close to JPL ephemeris. During interplanetary trajectory design and optimization studies, where planetary ephemeris model  is called a number of  times,  simplified model helps  in  saving  significant amount of computational time. The polynomial coefficients  in  the Meeus model are optimized  so as  to minimize the  maximum  error  obtained  from  this  model.  For  example,  there  are  about  20 coefficients that need to be optimized for the Jupiter planet. These design variables are to 
be  determined  by  the  optimization  algorithm  so  as  to minimize  the maximum  error  in position  in  the  span  of  years  ranging  from  2010  to  2020.  A  quadratic  programming methodology  is used  for  the purpose of optimization. Without  changing  the number of polynomial coefficients as in the Meeus model, the optimization strategy from the present analysis resulted  in upto one order  improvement  in  the position error with simultaneous reduction  in  velocity  error,  for  some  of  the  outer  planets.  The  improved  planetary ephemeris model  is proposed for Mars, Jupiter and Saturn planets with new polynomial coefficients.

Abstract document

IAC-09.C1.11.3.pdf

Manuscript document

(absent)