As you walked on the moon, the earth’s gravity would still pull on you weakly and you would still have an earth weight. How large would that earth weight be, compared to your earth weight on the earth’s surface? (Note: The earth’s radius is 6378 km and the distance separating the centers of the earth and moon is 384400 kilometers.)
To determine how large your earth weight would be while walking on the moon, we need to calculate the gravitational force experienced at the surface of the moon and then compare it to the gravitational force experienced on Earth's surface.
The equation for calculating gravitational force is given by the formula:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the two objects (in this case, the mass of the person and the mass of the moon)
r is the distance between the centers of the two objects (in this case, the radius of the moon plus the distance between the centers of the earth and moon)
First, let's find the mass of the person (m1). We don't have the exact value, so for simplicity, let's assume a mass of 70 kilograms.
Next, let's find the mass of the moon (m2). The mass of the moon is approximately 7.34 x 10^22 kilograms.
Now, we need to calculate the radius (r) using the given information. The radius of the Earth is 6378 kilometers, and the distance separating the centers of the Earth and the moon is 384400 kilometers. Therefore, the radius (r) would be the sum of the moon's radius (1737 kilometers) and the distance between the centers of the Earth and moon (384400 kilometers).
r = 1737 + 384400 = 386137 kilometers
Converting the radius to meters:
r = 386137 kilometers * 1000 meters/kilometer = 386137000 meters
Now, we can plug the values into the gravitational force equation:
F = (6.67430 × 10^-11 N(m/kg)^2 * 70 kg * 7.34 x 10^22 kg) / (386137000 meters)^2
Calculating this equation will give us the gravitational force experienced at the surface of the moon.
Finally, we'll compare this force to the gravitational force experienced on Earth's surface. The acceleration due to gravity on Earth's surface is approximately 9.8 m/s^2. We can use this value to calculate the weight of the person on Earth:
Weight on Earth = (m1 * 9.8 m/s^2)
Now, divide the calculated gravitational force on the moon by the weight on Earth to find the large of the earth weight compared to the person's weight on Earth's surface.
0.11
2225
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, 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.
I think you should be able to get your answer yourself.