The force of attraction between the earth and some object is called the weight of that object. The law of gravitation states, then, that the weight of an object is inversely proportional to the square of its distance from the center of the earth. If a person weighs 120 lb on the surface of the earth (assume this to be 3960 mi from the center), how much will he weigh 1300 mi above the surface of the earth?

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, M, is sometimes referred to as GM or µ (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.

To solve this problem, we can use the inverse-square law of gravitation. According to the law, the weight of an object is inversely proportional to the square of its distance from the center of the earth.

Let's denote the weight of the person on the surface of the earth as W1 and the weight of the person 1300 miles above the surface of the earth as W2.

Using the inverse-square law, we can set up the following proportion:

(W1/W2) = (d2^2/d1^2)

Where:
W1 = Weight of the person on the surface of the earth
W2 = Weight of the person 1300 miles above the surface of the earth
d1 = Distance from the center of the earth to the surface (3960 miles)
d2 = Distance from the center of the earth to 1300 miles above the surface (3960 + 1300 miles)

Now we can substitute the known values into the equation:

(W1/W2) = (d2^2/d1^2)

(120/W2) = ((3960 + 1300)^2)/(3960^2)

Simplifying the equation:

120/W2 = (5260^2)/(3960^2)

Cross multiplying:

120 * (3960^2) = W2 * (5260^2)

Solving for W2:

W2 = (120 * (3960^2))/(5260^2)

Calculating the value of W2:

W2 ≈ 89.15 lb

Therefore, the person will weigh approximately 89.15 lb when 1300 miles above the surface of the earth.

To find out how much a person will weigh 1300 mi above the surface of the earth, you need to use the equation for the law of gravitation.

The law of gravitation states that the weight of an object is inversely proportional to the square of its distance from the center of the earth. Mathematically, this can be represented as:

W = k / r^2

Where:
W is the weight of the object,
k is a constant, and
r is the distance from the center of the earth.

In this case, we know that a person weighs 120 lb on the surface of the earth, which is approximately 3960 mi from the center. We can use this information to find the value of k.

W = k / r^2
120 lb = k / (3960 mi)^2

To find the value of k, we can rearrange the equation:

k = 120 lb * (3960 mi)^2

Now that we have the value of k, we can use it to calculate the person's weight 1300 mi above the surface of the earth.

W = k / r^2
W = k / (3960 mi + 1300 mi)^2

Substituting the values, we get:

W = (120 lb * (3960 mi)^2) / (5260 mi)^2

Simplifying the equation, we have:

W = (120 lb * 15681600 mi^2) / 27667600 mi^2

Calculating, we find that:

W ≈ 67.97 lb

Therefore, a person would weigh approximately 67.97 lb 1300 mi above the surface of the earth.