F = gravitational force between the earth and the moon, G = Universal gravitational constant = 6.67 x 10^(-11) Nm^2/(kg)^2, m = mass of the moon = 7.36 × 10^(22) kg M = mass of the earth = 5.9742 × 10^(24) and r = distance between the earth and the moon = 384,402 km F = 6.67 x 10^(-11) * (7.36 × 10^(22) * 5.9742 × 10^(24) / (384,402 )^2 F = 1.985 x 10^(26) N
The above all i took from http://in.answers.yahoo.com/question/index?qid=20071109190734AATk6NV
Age of Moon 4.53 billion years (From google)
So Earth has been producing a force of 1.985 x 10^(26) N for 4.53 billion years I do not know how to calculate the total energy spent so far(Please some one do the favor) from force and time but it must be very huge. if E = mc^2 then atleast some of the mass of earth must have disappeared in producing this energy or where did the energy come from ?
Somewhere some one has answered if we place a ball above earth then during that time we did the work and when it fell down to the earth that work changed into kinetic energy ok accepted but the moon is being pulled towards earth for unlimited time where does the earth get the energy from to do so ?
@Emilio Pisanty Thanks for your reply.
"it needs to move the object in the direction that the force acts in"
Even though the force applied by earth is perpendicular to the direction of motion the moon's direction is definitely changed because of the force applied by the earth and the moon is moving a little towards earth from the straight line otherwise the motion would be a straight line. If earth did no work on moon why would the moon not go in straight line escaping earth's gravity. Even if we accept that earth does no work and spends no energy in making the moon orbit around it,By newton's law any body which accelerates needs force and since the moon keeps accelerating all the time(changing its direction of movement)where does moon gets this force continuously for such a long time.