Problem 2.45 Relative to an earth-centered, non-rotating frame the position and velocity vectors of a
spacecraft are
r
03450ˆ
i1700ˆ
j7750 ˆ
k km
and
v05.4ˆ
i5.4ˆ
j1.0 ˆ
k km s
, respectively. (a) Find
the distance and speed of the spacecraft after the true anomaly changes by 82°. (b) Verify that the specific
angular momentum h and total energy
are conserved.
e.
r
Problem 2.46 Relative to an earth-centered, non-rotating frame the position and velocity vectors of a
spacecraft are
r
06320ˆ
i7750 ˆ
k km
and
v011ˆ
j km s
. (a) Find the position vector ten minutes lat-
er. (b) Calculate the change in true anomaly over the ten-minute time span.
Problem 2.47 For the sun-earth system, find the distance of the
L1
,
L2
and
L3
Lagrange points from
the center of mass of the system.
Problem 2.48 Write a program like that for Example 2.18 to compute the trajectory of a spacecraft us-
ing the restricted three-body equations of motion. Use the program to design a trajectory from earth to
earth-moon Lagrange point L4, starting at a 200 km altitude burnout point. The path should take the
coasting spacecraft to within 500 km of L4 with a relative speed of no more than 1 km/s
%}
end %rates
% ~~~~~~~~~~~~~
function output
% ~~~~~~~~~~~~~
fprintf(‘-———-————————–————-———-‘)
Command Window session:
