Question

need HELP ASAP

(a) What is the escape speed on a spherical asteroid whose radius is 284 km and whose gravitational acceleration at the surface is 0.254 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 310 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1575 km above the surface? (a) Number Units (b) Number Units (c) Number Units

Answer 1

Solution) (a) escape speed, Ve=? R = 284km = 284 x 10m a=0.254 m/s² a = GM , Ve=2GM = 7 AR= GM as ve a shar = 5 2 x 0.25m x 2P4 xlot Ve = 379.83 Sve = 379.83) mis (b) distance, d'= ? v= 310 mls KE = APE s 1 my²=-GM mu? - GMM - GMM - 1 mrt - GMM - - Gm (Ž - GM) = - GM GM - GM - 2 2 a GM=aR") aRe - 1 YER GM - = (0.256) (284x10²)2 = at & Ra 10.254) (284x10") - ((310) 8.5xlosm 1 = 1575 km = 1575x 10 m VE? I mv ² = GMM v² = 2GM Rth v² = 2 (aR²) = 2(0.254) 2 ath = 2(0.254) (284x103) ? 284 x 103 + 1575*103 v² = 22040.477 V= 22040.477 = 148.46 [v=148.46 fuls