A spherical asteroid has a radius of 585 km and a surface g of 10.0 m/s 2 . a.)

Question

A spherical asteroid has a radius of 585 km and a surface g of 10.0 m/s2.

a.) What is the mass of the asteroid? 5.13e22kg

b.) What is the potential energy of a 1 kg object on the surface? ____ J

c.) What is the minimum speed at which an object* must be thrown upwards from the surface to never come back down? 3.43e3 m/s

d.) If a 1 kg object is thrown directly upwards from the surface with a speed of 1000 m/s,

i.) What is its initial kinetic energy upon launch? 5e5 J

ii.) How high will it go above the asteroid's surface*? ____ m

e.) If a 1 kg object is dropped from rest 1000 km above the planet's surface:

i.) What is its initial potential energy when dropped? ____J

ii.) With what speed will the object hit the surface*? _____m/s

Explanation / Answer

b) PE = -GMm/R = -(6.67*10^-11*5.13*10^22*1)/(585000)= - 5.85e+6 J

d) ii)KE + (-GMm/R) = (-GMm/(R+h))

5*10^5 - ((6.67*10^-11*5.13*10^22)/(585000)) = -((6.67*10^-11*5.13*10^22)/(585000+h))

?5.3490769e+6 = -3.42171e+12/(585000+h)

h = 54.6823347e+3 m


e)

i) PE = -GMm/(R+h) = ?2.1588076e+6 J

ii) -GMm/(R+h) = -GMm/R + (1/2)*m*V^2

-((6.67*10^-11*5.13*10^22)/(585000+1000000)) = -((6.67*10^-11*5.13*10^22)/(585000))+(1/2)m*V^2

?2.1588076e+6 = ?5.8490769e+6 + (1/2)*m*V^2

V = 2.7167147e+3 m/s

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