Orbital Mechanics 1. Consider an interplanetary mission from Earth to Mars. The interplanetary orbit is tangent to the Earth orbit. The true anomaly at Mars encounter is 170 deg. Evaluate (a) the semi-major axis and eccentricity of the interplanetary transfer, the radial component and transverse (horizontal) component of the spacecraft the heliocentric velocity at the Mars encounter, the magnitude of the excess of hyperbolic velocity of the probe at Mars encounter, (d) the aiming radius and the semi-aperture of the hyperbolic orbit about Mars, (a) the velocity increment required for inserting the spacecraft in a circular orbit of 250km altitude around Mars. Provide a schematic graphical representation of the trajectory. Sun Earth Mars Gravitational parameter, [km/sec] Orbit radius, R [km] Radius of Planet 1 [km] 1.327e11 1 398600.4 149.5*10^6 6378.136 42824.0 227.8*10^6 3390