Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
Howard D. Curtis 545 Copyright © 2013, Elsevier, Inc.
Problem 12.46 Solve Problem 12.45, neglecting solar radiation pressure and including only the per-
turbing effect of lunar gravity.
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
rm s
æ
ö
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Problem 12.47 Solve Problem 12.45, retaining the effect of solar radiation pressure and adding that of
lunar gravity as well.
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
ˆ
r=r
r
ˆ
w=r´v
r´v
ˆ
s=ˆ
w´ˆ
r
ˆ
w´ˆ
r
Compute the position of the moon relative to the satellite:
rm s =rm–r
.
Compute the perturbing acceleration of the moon:
pmoon
m
r
m s
rm s
3r
m
rm
3
(Equation 12.117).
Compute the sun’s geocentric equatorial position vector
rS
by means of Algorithm 12.2, and the
earth-to-sun unit vector
ˆ
uSr
Sr
S
.
Calculate the value of the shadow function
n
from
r
and
rS
using Algorithm 12.3
Compute the solar radiation perturbation
psun
S c
CRAsm
ˆ
uS
(Equations 12.97 and 12.98).
Calculate the total perturbing acceleration,
ppmoon psun
.
Compute the components of the perturbing acceleration along the rsw axes:
pr=piˆ
rps=piˆ
spw=piˆ
w
Use Equations 12.84 to calculate the components of
f
in Equation j.
The procedure is implemented in the following MATLAB code, after which the plots of the variations are
shown.
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
function problem_12_47
% This function solves Problem 12.47 by using MATLAB‘s ode45 to integrate
% Equations 12.84, the Gauss variational equations, for lunar
% gravitational and solar radiation pressure perturbation.
%
% User M–functions required: sv_from_coe, lunar_position, solar_position,
% los
% User subfunctions required: rates
%
% The M-function rsmooth may be found in
% Garcia, D., 2010, “Robust smoothing of gridded data in one and higher
% dimensions with missing values.” Computer. Stat. Data Anal. 54,
% 1167–1178.
%
% The M-function toptitle may be found in
% Marchand, P. and O. T. Holland, 2003, Graphics and GUIs with MATLAB,
% 3rd Edition. Chapman & Hall/CRC.
% –———––—––—–––——––––—–————–––——––––————–—–––——–––—–
global JD %Julian day
%...Preliminaries:
close all
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
Solutions Manual Orbital Mechanics for Engineering Students Third Edition Chapter 12
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~