A satellite in an areostationary orbit around the planet Mars appears to remain at the same point in the sky when viewed from the planet's surface.
State one orbital condition required for an orbit around Mars to be areostationary.
Calculate the orbital radius of this areostationary satellite.
Mass of Mars M=6.4×1023 kg \text{Mass of Mars } M = 6.4 \times 10^{23} \text{ kg} Mass of Mars M=6.4×1023 kg Rotational period of Mars T=8.9×104 s \text{Rotational period of Mars } T = 8.9 \times 10^4 \text{ s} Rotational period of Mars T=8.9×104 s Gravitational constant G=6.67×10−11 m3 kg−1 s−2 \text{Gravitational constant } G = 6.67 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2} Gravitational constant G=6.67×10−11 m3 kg−1 s−2A satellite of mass m m\,m is in a circular orbit of radius r r\,r around a planet of mass MMM.
By considering the centripetal force required for orbit, show that the kinetic energy Ek E_k\,Ek of the satellite is equal to half the magnitude of its gravitational potential energy EpE_pEp, where Ep=−GMmr\displaystyle E_p = -\frac{GMm}{r}Ep=−rGMm.
A small robotic probe of mass 2.0 kg is launched from rest from the surface of Mars into a low Martian orbit.
Calculate the minimum total energy that must be supplied to the probe to place it in this orbit.
