A space probe of mass m=680 kgm = 680\text{ kg}m=680 kg is sent to study Saturn's moon Titan. The probe is placed in a stable circular orbit at an altitude hhh above Titan's surface. Titan has a mass MMM and a radius RRR.
Useful data:
Show that the angular speed ω\omegaω of the orbital probe is given by:
ω=GM(R+h)3 \omega = \sqrt{\frac{GM}{(R+h)^3}} ω=(R+h)3GMCalculate the orbital period TTT of the probe when its altitude h=1.42×106 mh = 1.42 \times 10^6\text{ m}h=1.42×106 m.
Calculate the gravitational potential energy of the probe when in this orbit.
