Question

Spacecraft orbit Initial orbit radius (km) 7000 Comet properties semi major axis (Au) 1.5 eccentricity 0.2 inclination (deg) 10 argument of perihelion (deg) 60 Comet mass(kg) 3E16 Consider the requirement to transfer a satellite, initially in an elliptical orbit about the Earth that is to be to be placed in orbit about a Comet. You should note from the data that is provided to you that this target Comet orbit is neither circular nor a coplanar orbit with the initial orbit and you should therefore consider carefully the way you undertake your calculations.

A) Draw a diagram of the Comet’s orbit indicating clearly where this orbit intersects with the ecliptic plane and the two distances (ie as Comet approaches the Sun and then where it is moving away from the sun) from the Sun at these points. Calculate the Sun – Comet distances at these points of interception.

B) Calculate the minimum values of ΔV (in km/s) that would be required to take the satellite from its orbit about the Earth so that it could intersect the orbit of the Comet at the two locations where the Comet crosses the Ecliptic plane. In this calculation you should explain clearly each step of your calculations in words linked with another diagram as well as writing down the appropriate equations.

C) Calculate the ΔV (magnitude and direction) that would be required to change the velocity of the spacecraft as it intersects the cometary orbit, so that it could then fly alongside the Comet in the same orbit as the Comet. You should take particular care concerning the fact that the orbits are not coplanar prior to this manoeuvre, but will need to be so after the manoeuvre, and the intersection will not occur at periapsis of the comet’s orbit. Again you should explain in words as well as writing down the equations, what manoeuver would be performed and whether there are any options that could affect the magnitude of the ΔV.

D) Calculate how close your spacecraft will need to approach the comet in order for the spacecraft motion to be dominated by the comet rather than the being dominated by the gravitational field of the sun.

E) Consider the results obtained in section C and compare which mission profile results in the lowest overall ΔV in respect to whether your solution for section B provides this overall minimum ΔV for the mission. Comment upon these findings. Extend your discussion regarding the mission selection by consideration of other features not considered thus far including other mission profiles, supported by appropriate calculations in order to establish which of these may influence the final mission selection.

Answer 1