# Orbital Mechanics

Space probes and other long-distance vehicles are designed with small rockets to allow for mid-course corrections. An orbit can be defined by ro and vo . If a satellite is launched in a direction parallel to the surface of the earth with a velocity of 36000 km/h from an altitude of 500 km. Apply the principles of conservation of energy and conservation of angular momentum to the orbit insertion point and the point of minimum altitude to determine:

Velocity of the satellite at any point around the elliptical orbit. (i.e. from θ = 0 deg to 360 deg. with an increment of 30 deg.) and magnitude of the position vector of the satellite at any point around the elliptical orbit. (i.e. from θ = 0 deg to 360 deg. with an increment of 30 deg.). (use EXCEL or MATLAB to generate and tabulate the data.)

a) Velocity of the satellite at any point around the elliptical orbit. (i.e. from θ = 0 deg to 360 deg. with an increment of 30 deg.)

b) Magnitude of the position vector of the satellite at any point around the elliptical orbit. (i.e. from θ = 0 deg to 360 deg. with an increment of 30 deg)

c) Maximum allowable orbit insertion angle error (see below) at any point around the elliptical orbit. (i.e. from θ = 0 deg to 360 deg. with an increment of 30 deg.)

d) Determine the minimum and maximum velocity of the satellite and their corresponding θ.

e) Calculate the period of the orbit.

f) Plot the velocity of the satellite versus time. (e.g. from 0 sec to the orbital period with an increment of 1s).

g) Plot the position of the satellite versus θ, with an increment of 1 deg)