# The Force of Gravity on object with mass of 200 kg

#### trex

##### New member
I need to calculate the force of gravity on earth of an object that has a mass of 200 kg.

#### stapel

##### Super Moderator
Staff member
trex said:
I need to calculate the force of gravity on earth of an object that has a mass of 200 kg.
What formula did they give you? How far have you gotten in applying it?

Please be complete, including clear definitions for all of the variables. Thank you! Eliz.

#### TchrWill

##### Full Member
trex said:
I need to calculate the force of gravity on earth of an object that has a mass of 200 kg.

Try F = Gmm/r^2 where G = the universal gravitational constant, M = the earth's mass, m = the mass of the object and r = the distance between the centers of each mass.

#### trex

##### New member
Hello, That is all of the problem that they gave me to work with. Any idea's? Thank You

F = mg

#### TchrWill

##### Full Member
I need to calculate the force of gravity on earth of an object that has a mass of 200 kg.

The earth's gravity reaches out forever but the force of attraction on bodies at great distances would be extremely small depending on the mass of the body. The Law of Universal Gravitation states that each particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Expressed mathematically,
F = GM(m)/r^2
where F is the force with which either of the particles attracts the other, M and m are the masses of two particles separated by a distance r, and G is the Universal Gravitational Constant. The product of G and, lets say, the mass of the earth, is sometimes referred to as GM or mu (the greek letter pronounced meuw as opposed to meow), the earth's gravitational constant. Thus the force of attraction exerted by the earth on any particle within, on the surface of, or above it, is F = 1.40766x10^16 ft^3/sec^2(m)/r^2 where m is the mass of the object being attracted = W/g, and r is the distance from the center of the earth to the mass. The force of attraction which the earth exerts on our body, that is, the pull of gravity on it, is called the weight of our body, and shows how heavy our body is. Thus, our body, being pulled down by by the earth, exerts a force on the ground equal to our weight. The ground being solid and fixed, exerts an equal and opposite force upward on our body and thus we remain at rest. A simple example of determining this force, or our weight, is to calculate the attractive force on the body of a 200 pound man standing on the surface of the earth. Now the man's mass is his weight divided by the acceleration due to gravity = 200/32.2 = 6.21118 lb.sec^2/ft. The radius of the surface from the center of the earth is 3963 miles x 5280 ft/mile = 20924640 feet. Thus the attractive force on his body is 1.40766x10^16(6.21118)/20924640^2 = 200 pounds. What do you know? The mans weight.

Now, the attractive force on the 200 lb. man 1000 miles above the earth would only be 1.40766x10^16(6.21118)/26204640 = 127 pounds and half way to the moon, only .22 pounds.