Question

Fundamental Planetary Science problem 2.2 a) Calculate the minimum velocity at which a rock must leave Mars' at- mosphere for it to be on a trajectory that intercepts tje Earth's orbit? You can take into account the speed needed to escape from the Martian gravity but not the drag within the planet's atmosphere. You may also neglect planetary rotation and assume the planets' orbits are circular and coplanar. b) At what speed does this rock impact on the upper atmosphere of the Earth? c) Under tge same assumptions. calculate the minimum velocity for trans- fer from the top of the Earth's atmosphere to Mars. d) At what speed does this rock impact on the upper atmosphere of Mars? e) Qualitatively describe how planetary rotation and orbital eccentricity and inclinations may affect your results.

Answer 1

(a)�Minimum Velocity needed is equal to escape velocity. V_e = squareroot 2GM_mass/R_mass. M_mass = 6.4 times 10^23 kg R_mass = 3.39 times 10^6 m V_e = 5 times 10^3 m/s = 5 km/s (b) Applying conservation of Energy at Mass and earth's surface 1/2 mv^2_e GmM_mass/R_mass = 1/2 m v^2_0 -Gm M_earth/R_earth -GmM_mass /r V_0 rightarrow Velocity at earth's atmosphere r = 5.46 times 10^1 m V_0 squareroor 2G[M_earth/R_earth -M_mass/r] V_0 = 11.2 km/s (c) Escape velocity form Earth's surface V_e = 2G M_earth/R_earth M_earth rightarrow 6 times 10^24 kg R_earth rightarrow 6.4 times 10^6 m