Question

At what distance from the earth does the moon's gravitaitional foce cancel that of the earth? What is the sign and magnitude of the gravitational potential enrgy of the earth-moon system? Use G=6.67*10^-13 nt m^2/kg^2, Mg=6.0*10^24kg, Re-m=3.8*10^8m, and Mm=7.3*10^22 kg.

Answer 1

let at x distance from the earth's surface the moon's gravitaitional foce cancel.

let m is the mass of the object that is placed

G*Me*m/x^2 = G*Mm*m/(Rem - x)^2

Me/x^2 = Mm/(Rem - x)^2

(Rem - x)^2/x^2 = Mm/Me

(Rem - x)/x = sqrt(Mm/Me)

(Rem - x)/x = sqrt( (7.3*10^22)/(6*10^24))

(Rem - x) = x*0.1103

Rem = 1.1103*x

==> x = Rem/1.1103

= 3.8*10^8/1.1103

= 3.42*10^8 m <<<<<<<-------------Answer

the gravitational potential enrgy of the earth-moon system,

U = -G*Me*Mm/Rem

= -6.67*10^-11*6*10^24*7.3*10^22/(3.8*10^8)

= -7.7*10^28 J <<<<<<<-------------Answer