A spherical asteroid has a radius of 545 km and a surface g of 3.0 m/s2. What is

Question

A spherical asteroid has a radius of 545 km and a surface g of 3.0 m/s2. What is the mass of the asteroid? What is the potential energy of a 1 kg object on the surface? What is the minimum speed at which an object* must be thrown upwards from the surface to never come back down? If a 1 kg object is thrown directly upwards from the surface with a speed of 1000 m/s, What is its initial kinetic energy upon launch? How high will it go above the asteroid's surface*? If a 1 kg object is dropped from rest 1000 km above the planet's surface: What is its initial potential energy when dropped? With what speed will the object hit the surface*? When the object has accelerated up to half its eventual impact speed, the object will have fallen to the asteroid's surface.

Explanation / Answer

a)let the mass of the asteroid be m.so,

GM/r^2=g

or 6.67*10^-11*M/(545*10^3)^2=3

or M=1.336*10^22 kg

b)potential energy=-GMm/R

=-mgR

=-1*3*545*10^3

=-1.635*10^6 J

c)conserving energy,

-GMm/R + 0.5mv^2=0

or -6.67*10^-11*1.336*10^22/(545*10^3) + 0.5*v^2=0

or v=1808.35 m/s

d)i)initial kinetic energy=0.5mv^2

=0.5*1*1000^2

=5*10^5 J

ii)conserving energy,

0.5*1000^2-6.67*10^-11*1.336*10^22/(R+545*10^3)=0

or R=1.237*10^6 m

e)i)initial potential energy=-GMm/h

=-6.67*10^-11*1.336*10^22*1/(545*10^3+1000)

=-1.632*10^6 J

ii)conserving energy,

-1.632*10^6+0.5*1*v^2=0

or v=1806.65 m/s

iii)more than halfway

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