Question

according to newtons law of gravitation all objects in the earth attracts one another.then, in the case of an airoplane. when airoplane in an accident it will fell down on earth. why the earth do not go there?

Answer 1

It does! However, we have to take into consideration how the force will acting on the object will cause it to move.

Newton's 2nd Law states:\[\sum_{}^{}F=ma\]

Newton's 3rd Law tells us that the gravitational force of the earth on the plane is equal (but opposite in direction) of the gravitational force of the plane on the earth. Just because the earth and plane have the same force on them does not mean they will move in the same fashion.

When we solve Newton's 2nd law for acceleration, to see how the objects will move, we get\[a = \sum_{}^{}F / m\]

The plane having a small mass will have a large acceleration. However, the earth being so massive will end up having an acceleration so small that it realistically will be to small to measure. Theoretically though, the earth does accelerate upwards towards the plane as it falls downward. Hope that helps.

Answer 2

The previous answer is correct but if you actually add numbers you can see exactly how small the number is.

Answer 3

I'm not sure if the previous answer is completely correct. As can be seen in the second equation posted by simplephysics, we need to take into account all the forces affecting both the plane and the Earth. So, I think the Earth doesn't move not only because the acceleration is small, but also because the resultant force is not pointing to the plane. Does that make sense?

Answer 4

An easy way to imagine the forces involved is to think about which is easier: To push a tricycle toward a car, or to push a car toward a tricycle. The car has more Inertia, (it's harder to start moving,) than the tricycle, although both have wheels.

Answer 5

bergo, the explanation is of course an over simplification. It is aimed at an introductory level at which the question was asked, and imagines a system of only the earth and airplane. The example is to over emphasize the point for understanding.

Answer 6

Without a defined level of study, then the answers will vary. This is where physics, engineering and mathematics come apart or come together. In the most strict definition the Earth will move. The number is finite and not exactly equal to zero in math terms. What one observes relative to their measurement scale or the level the professor depends on the class. In an introductory level high school class for very low level learners or complete novices you may start with the Earth does not move but as the level rises and the math rises one sees a finite number will exist. How close one can measure will create the approximation in physics and engineering problems in asking; to the first order approximation in physics or the tolerance level allowed in an engineering problem. I believe low level questions like this make it very confusing for novice physics students that only take one or two semesters of physics versus earning a PhD or a MS in physics.
What would greatly help when answering the question is the level of the class of physics; examples say high school physics in the USA ,or year 2 in physics at MIT, or physics for business majors at Rice university, or so on.
I can prove my answer the Earth will move using Newton's over simplified universal gravitation equation using the body Earth and a single 747 airplane. If you do not like my 747 plane, give me your mass in kg of your plane and I can still do the problem. Please note that the instruments available to measrure the distance the Earth moves may only be done with fine tuned x-rays or laser beams.

Answer 7

the earth will move towards the plane but the displacement is negligible.