mandyaero
Newbie level 1
The angular position E along the elliptical orbit of a spacecraft is given by the following nonlinear equation:
f(E)=nt-E+esinE=0 (1)
where t is the time (in seconds) at which E is required, e is the eccentricity of the ellipse and u is the mean motion defined as:
u=(m/(a^3))^1/2
with being the gravity constant of the planet and a is the semi-major axis of the ellipse.
Use the Newton iteration:
Ek+1=Ek-f(Ek)/f'(Ek)
to find a solution to Eq. (1), where f'(Ek)=df(Ek)/dE, for different values of e in the
interval [0.1, 0.5]. Take Eo=nt , a = 14000 km, t = 10000 s and m = 3.9860E+5 km3/s2
(the gravity constant of the Earth). Plot the value of f as a function of the number of
iterations k for each value of e on the same plot.
f(E)=nt-E+esinE=0 (1)
where t is the time (in seconds) at which E is required, e is the eccentricity of the ellipse and u is the mean motion defined as:
u=(m/(a^3))^1/2
with being the gravity constant of the planet and a is the semi-major axis of the ellipse.
Use the Newton iteration:
Ek+1=Ek-f(Ek)/f'(Ek)
to find a solution to Eq. (1), where f'(Ek)=df(Ek)/dE, for different values of e in the
interval [0.1, 0.5]. Take Eo=nt , a = 14000 km, t = 10000 s and m = 3.9860E+5 km3/s2
(the gravity constant of the Earth). Plot the value of f as a function of the number of
iterations k for each value of e on the same plot.
