(a) What is the escape speed on a spherical asteroid whoseradius is 520 km and w

Question

(a) What is the escape speed on a spherical asteroid whoseradius is 520 km and whose gravitationalacceleration at the surface is 2.6m/s2?
m/s
(b) How far from the surface will a particle go if it leaves theasteroid's surface with a radial speed of 1000 m/s?
m
(c) With what speed will an object hit the asteroid if it isdropped from 1000 km above the surface?
m/s
The hints he gave us were: Remember: a 1% error in a number that gets squared results ina 2% error and out of tolerance.
RE= 6375 km and g = 9.81 m/s2
Msol = 1.99 x 1030 kg
(a) What is the escape speed on a spherical asteroid whoseradius is 520 km and whose gravitationalacceleration at the surface is 2.6m/s2?
m/s
(b) How far from the surface will a particle go if it leaves theasteroid's surface with a radial speed of 1000 m/s?
m
(c) With what speed will an object hit the asteroid if it isdropped from 1000 km above the surface?
m/s
The hints he gave us were: Remember: a 1% error in a number that gets squared results ina 2% error and out of tolerance.
RE= 6375 km and g = 9.81 m/s2
Msol = 1.99 x 1030 kg

Explanation / Answer

(a) We know that : .       Escape velocity is : Ve   = 2gR   = ( 2 * 2.6 m /s2 * 520 * 103 m) .                                                            =   1.644 km / s . (b) We know that : .      m g = mv2 / r .        g   = v2 / r .        r    =   v2 / g   =   ( 1000)2 / 2.6 m/s2    =   --------- . (c)   Speed is : .         v   =   2 g H    =   (2 * 2.6 * 1000 *1000) m    =  -------- m/s . Solve the above. . Hope this helps u!

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