# Orbital Parameters Of Earth And Mars

729 Words Jun 17th, 2015 3 Pages
Question 5
It is assumed that Earth and Mars are in Circular orbits. The initial relative phase angle is stated to be 30o. Calculate the transfer orbit of a time of flight (TOF) 120 day. The orbital parameters such as ΔVs must be calculated. In addition, the propulsion considerations must be evaluated for the case when mission is to be Evaluate the orbital parameters, ΔVs and propulsion parameters when the mission is to be executed by a 500 kg spacecraft, which utilizes 450 s specific impulse propellant.
Assumptions:
Orbits are coplanar. Initial position of earth is taken as reference direction and epoch of the mission
Data:
2The total Time period of Earth = 365 days
1Hence, the time period of Mars = 365 x 1.881 = 686.565 days
3Distance of Earth from Sun = 149.5 x 106 kilometers
4Distance of Mars from Sun = 227.8 x 106 kilometers
5Initial position of planets: 7After 120 days position of planets:
8Change in position of Earth = 120/365 = 0.32876 = 32.876% of the complete orbit.
Change in angular position of Earth = 0.32876 x 360o = 118.356o
Final position of Earth with reference direction = 118.356 + 0 = 118.356o
Change in position of Mars = 120/686.56 = 0.17478 = 17.478% 0f the complete orbit.
Change in angular position of Mars = 0.17478 x 360o = 62.9219o
Final position of Mars with reference direction = 62.9219 + 30 = 92.9219o Transfer ellipse:
Now the transfer ellipse will be such that initial position of Earth will be the point of launch and perigee of the…