----+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8
GRVTIM1 -2.5D-11
----+----0----+----0----+----0----+----0----+----0----+----0----+----0----+----0
COLUMNS FORMAT DESCRIPTION DEFAULT VALUE & UNITS
1-6 A6 GRVTIM - Requests application and/or
adjustment of time dependent gravity
coefficients. The geopotential coefficients
may be given a linear rate and/or up to nine
periodic terms. The epoch time for this
option is set with the GRVEPO option.
7 I1 C or S geopotential coefficient designator.
=1 C coefficient indicator.
=2 S coefficient indicator.
8 I1 Defines the content of the fields
in columns 25-80 as follows:
Columns Columns Columns Columns
25 - 44 45 - 59 60 - 72 73 - 80
=1 Linear Rate Rate sigma [NOTE 2]
=2 A B Period
=3 A sigma B sigma
15-17 I3 Degree of C and S coefficients (n index) 0
18-20 I3 Order of C and S coefficients (m index) 0
21-22 I2 # of period for this coefficient 1
(a number between 1-9)
25-44 D20.8 This field contains geopotential linear rate per year
or rate sigma information as defined by the
values selected in columns 7 & 8.
col 8=1 Cdot or Sdot (linear rate).
DEC 1999
9912.0
GLOBAL SET
GRVTIM (cont)
COLUMNS FORMAT DESCRIPTION DEFAULT VALUE & UNITS
45-59 D15.3 This field contains geopotential rate sigma,
amplitude (A), or amplitude (A) sigma
information as defined by the values selected
in columns 7 & 8.
col 8=1 Standard deviation for Cdot or
Sdot. A non zero sigma indicates
that this parameter will be adjusted.
col 8=2 Amplitude (A) of cosine term.
col 8=3 Standard deviation for amplitude
(A). A non zero sigma indicates
that this parameter will be adjusted.
60-72 D12.8 This field contains geopotential amplitude
(B), or amplitude (B) sigma information as
defined by the values selected in columns
7 & 8.
col 8=2 Amplitude (B) of sine term.
col 8=3 Standard deviation for amplitude
(B). A non zero sigma indicates
that this parameter will be adjusted.
73-80 D8.3 This field contains the period for the
periodic option. The frequency will be years
computed as frequency=2*pi/period.
DEC 1999
9912.0
GLOBAL SET
GRVTIM (cont)
NOTE 1: See next page for the time dependent gravity formulation.
The cards specifying the apriori periodic terms MUST precede the
cards which carry the accompanying sigma information, as in
the following example. In the following example the coefficient
C21 has two periodic terms.
GRVTIM12 2 0 0.0 0.0 1.0
GRVTIM13 2 0 1.0D-07 1.D-07
GRVTIM12 2 1 1 0.0 0.0 1.0
GRVTIM13 2 1 1 1.0D-07 1.D-07
GRVTIM12 2 1 2 0.0 0.0 1.0
GRVTIM13 2 1 2 1.0D-07 1.D-07
GRVTIM12 2 2 0.0 0.0 1.0
GRVTIM13 2 2 1.0D-07 1.D-07
GRVTIM22 2 2 0.0 0.0 1.0
GRVTIM23 2 2 1.0D-07 1.D-07
NOTE 2: Coefficient rates should be normalized in case of application
of time dependent gravity.
IF CARD OMITTED: Time dependent gravity will not be applied.
DEC 1999
9912.0
GLOBAL SET
GRVTIM (cont)
The formulation for the time dependent gravity implementation follows:
1#1 + Cdot(n,m)*(t-t0) + 2#2*(t-t0))
+ 3#3*(t-t0))
4#4 + Sdot(n,m)*(t-t0) + 5#5*(t-t0))
+ 6#6 *(t-t0))
7#7 - Normalized geopotential C and S coefficients.
Cdot, Sdot - Linear rates for the geopotential coefficients.
t0 - Start time for application of time dependent gravity.
(See GRVEPO option for setting the start time.)
t - Current time. Time at which time dependent gravity
will be computed.
Aci ,Asi - Amplitude of the cosine term for the C or S coefficient
for application of a periodic gravity effect.
Bic ,Bsi - Amplitude of the sine term for the C or Scoefficient
for application of a periodic gravity effect.
Omegai(n,m) - Frequency for the periodic gravity effect for the
(n,m) coefficients. (Where Frequency=2*pi/period)
8#8
