Given that the earth is 81 times heavier and 4 times larger in size as copared to moon. Determine the velocity requried by a spacceraft to escape the graavitational force of the moon.

Explanation

Given `M_(e)=81M_(m)`
i.e. , `M_(m)=(M_(e))/(81)`
`R_(e)=4R_(m)"i.e.",R_(m)=(R_(e))/(4)`
To find : Escape velocity on moon `(v_(m))`
Formual : `v_("esc")=sqrt((2GM)/(R))`
Calculation : Using formula for earth ,
`V_(e)=sqrt((2GM_(e))/(R_(m)))`
`"and for moon ", v_(m)=sqrt((2GM_(m))/R_(m))`
`therefore" " (v_(m))/(v_(e))=sqrt((2GM_(m))/(R_(m))xx(R_(e))/(2GM_(e)))`
`therefore" " (v_(m))/(v_(e))=sqrt((4M_(e))/(81R_(e))xx(R_(e))/(M_(e)))`
...... `(thereforeM_(e)=81M_(m)andR_(e)=4R_(m))`
`thereforev_(m)=(2)/(9)v_(e)`
The escape velocity on the surface of moon will be `(2)/(9)` times that on surface of earth .