Question

Eris, the largest dwarf planet known in the Solar System, has a radius R = 1200 km and an acceleration due to gravity on its surface of magnitude g = 0.77 m/s2.
(a) Use these numbers to calculate the escape speed from the surface of Eris.
1360 m/s correct answer.

(b) If an object is fired directly upward from the surface of Eris with one third of this escape speed, to what maximum height above the surface will the object rise? (Assume that Eris has no atmosphere and negligible rotation.)

Answer 1

PE at the surface: GMm/r but you are given

g=Force/mass=GM/r^2 =.77

PE at Surface then=GMm/r*r/r=mgr

escape velocity for KE=PE
1/2 mV^2=mgr

Vescape= sqrt (2gr)
checking book answer Vesc=sqrt(2*.77*1.2E6)=text answer.