Thinking Problem Down Here?

Question

Somewhere between the earth and the moon, gravity from these two bodies on a space pod would cancel. Is this location nearer to the earth or to the moon?
2.- SECOND PROBLEM
The earth and the moon are atracted to each other by gravitational force. Does the more massive earth attract the less massive moon with a force that is greater, smaller, or the same as the force with which the moon attracts the earth?.

PLEASE SPECIFY WHICH ANSWER IS FOR WHAT QUESTION

Answer 1

1. Closer to the moon, of course.

2. Actually the force is a result of the two bodies in Harmony with each other. You cannot have a gravitational force with a single massive body, so the question really isn't valid.

Answer 2

Closer to the moon, as most answerers have said. This results from W = M(g/R^2) and w = M[(1/6)g/r^2]; where M is the mass of something between the Earth, with gravitational acceleration g/R^2 where R is the distance from Earth; and r is the distance from the moon of the body weighing w.

The 1/6 in the moon's equation reflects its smaller mass which results in a gravitational accleration 1/6 that of Earth's (g) at its surface. The squares in the distances reflect that the force of gravity diminishes as the square of the distance between the source of gravity and the affected body.

To solve for the place where the pod would be acted on by equal force start with W = w, the weight caused by the Earth is offset by the weight caused by the moon. The M and g in each weight cancel out leaving 1/R^2 = (1/6)/r^2; so that r^2 = (1/6) R^2 and r = R sqrt(1/6); so that we can say r < R, which clearly shows that the pod's weight cancels out when it is closer to the moon.

For the SECOND PROBLEM think of the force of gravity on the two bodies (Earth and moon) as being like the tension force on a rope as the moon revolves around the Earth. Clearly that force has to be the same throughout the distance along that imaginary rope. Otherwise, the rope length would be moving (getting bigger or smaller). This results when there is a net force on something and that net force causes that something to accelerate (as in F = Ma).

Because the distance between the Earth and moon is not changing, our imaginary rope is staying the same length, we can safely say all the forces on that rope add up to zero. That is, the Earth is tugging on that rope with the same force the moon is tugging on that rope. In fact, there is an equation F = GMm/R^2 saying that the force between two masses (M and m) is equal to some constant (G) times the masses and divided by the square of the distance (R) between them.

To help you understand how such a big mass M can be exerting the same force as a small mass m, think of you pushing on a building with force f. What force F is the building exerting? It's f, the same force you're exerting. Why? Because if the building were exerting more force than you are, it would be displacing you backward. You'd be moving because F - f = ma > 0 and you'd be accelerating back away from the bulding. But clearly you are not; so F - f = ma = 0 and the only way for that to be true is for a = 0 which results when your force is exactly offset by the building's.

Answer 3

The zero gravity point between the earth and the moon is real close to the moon.

The attraction is the same between the moon and the earth because the equation is the same.

Answer 4

Gravitational neutral point is over 200,000 miles from Earth, less than 40,000 miles from moon. Earth's attraction for moon is 80 times greater than moon's attraction for earth (ratio of masses).

Subsequent responder makes an interesting point. You can view the matter either from the point of view of the graviational field (which is my point), or of the total gravitational attraction (responder's point). There is usefulness in both views, depending on what you are trying to figure.

Answer 5

1. No, it won't cancel out, coz gravitational force is attractive in nature and one more strong reason is, if they cancelled out, then at a point in the orbit of the moon, the moon doesn't follow its orbit, in a better sense for ex: two positve numbers don't cancel out each other and hence two attractive force won't cancel each other ( U might h've confused this with the electrostatic forcre)


2. Earth attracts the moon with a greater force coz, the greater mass of earth and Newton's II law shoes that force = mass* accln. and hence force is directly proportional to mass, hence force exerted by earth is more compared to that of the moon