why earth attract lighter body towards it self and lighter body do not attarct the earth towards its centre?

Answer 1

The first responder, 'Helmut.' is confusing force and acceleration!

The gravitational attraction (a FORCE) between the Earth and a much less massive body is MUTUAL. That means that the STRENGTHS of the force each experiences is EXACTLY the same. Only their DIRECTIONS differ, being opposite from one another. This is how the gravitational acceleration between any two bodies operates.

However, because of Newton's 2nd Law,

F = ma,

the ACCELERATION produced by a given force F is INVERSELY PROPORTIONAL to the MASS it's operating on.

Let's look at how this happens, explicitly. Using M, A for Earth quantities, and m, a for the smaller mass (the suggestive notation is: big letters --- big thing; small letters --- small thing), we'd have

MA = F (= GMm/R^2) = ma, ......(1)

where GMm/R^2 is the strength of the mutual force , and I ignore a " - "sign that should strictly appear in one acceleration, for simplicity. Then

A = Gm/R^2, and a = GM/R^2. ......(2)

Notice that it's VERY TEMPTING to say "Oh, from eqns (2) I see that the acceleration A of the Earth must be 'caused' by the little mass m, since the formula for A has m in it," and likewise, "the acceleration a of the little mass must be 'caused' by the Earth's mass M, since the formula for a has M in it." That's very tempting, and indeed makes the result quite memorable, but scientifically that "obvious" conclusion ignores how BOTH of these results actually arise, together.

Eqns (1) show that FUNDAMENTALLY, BOTH of these eqn (2) results follow from the fact that there's ONE mutual force and that BOTH masses are simply subject to the same strength of that ONE mutual force.

Eqns (2) describe the CONSEQUENCES of having ONE mutual force. They should not be thought of as two quite INDEPENDENT statements of the type "A is attracting B by a very large amount" and "B is attracting A by a very small amount."

The attractions (forces) are the SAME, though the consequences (the ACCELERATIONS) may be VERY DIFFERENT.

It's always worth remembering that BOTH objects accelerate, but that from eqns (2),

A/a = m/M.

Very crudely, a 1kg mass m is 10^(-25) of the Earth's mass M. So, when the 1 kg mass drops towards the Earth at about 10m/s^2, the Earth is accelerating towards IT at

A ~ 10^(- 24)m/s^2.

It's hardly any wonder that one can't notice that!

Live long and prosper.

Answer 2

All gravitational forces have mutual attraction. The sun attracts the earth as the earth attracts the sun, but the difference in attraction and size is why the lighter object seems to only move.

Gravitational force is directly proportional to the mass of the object in question, the more mass it has the more of a gravitational force it exerts.

The question of why the lighter body doesn't seem to attract the earth toward it is a question of inertia. The more massive body requires more force to move in a specific direction than the lighter one.

An example of this would be you have 2 rockets in space, both exert the same amount of thrust. 1 is pushing a locomotive through space and the other is pushing a baseball. Both rockets fire their engines for 30 seconds. Which one moved further in the 30 seconds? The baseball did because it has a much lighter mass, therefore less inertia to overcome to induce motion.

Answer 3

It can be calculated in a simple way.

The mass of earth is 6 x 10^ 24 kg.

1kg object is pulled toward earth with an acceleration of ~10 m/s^2.

That is to say a force of 10 N acts on 1 kg object.

The same 10 N force pulls the earth toward its center.

The acceleration of earth is 10 / [6 x 10^ 24]

= 1.67 x 10^ (- 24) m/ s^2.
This shows that it is motionless.

Answer 4

Welcome my friend. I too, have been there. Enoch and Mohammad each ascended 7 heavens. I traveled backwards through 7 perspectives to reach the 8th. I say 'backwards' because my back was facing the direction of travel, but that's not right either, hmm...there was an effect of moving back as my peripheral view grew larger and larger. Each sky revealed it's mysteries and secrets. Each sky was more vast than the one before and I was able to get a better understanding of each by studying it from the next larger perspective. This is why I had the sense of moving backward. Knowledge of the 7 skies is hidden/woven within our everyday reality on earth. Each dimension speaks of all the others in it's own 'language'. Each sky is exponentially more vast than the one before. These are the 7 'days' of creation spoken of in Genesis. I will add more as the Spirit moves me.

Answer 5

How can you tell.They are both the same.In space you do no have any reference points(like land marks on earth) so all you see is the the earth and another body moving towards each other and because you are on the earth and move with it it looks like the lighter body is moving when fact they are both moving.

Answer 6

The attraction is mutual, but the force the Earth can exert is many orders of magnitude greater than the force s light body can exert.

Answer 7

or maybe, the earth is attracting lighter bodies toward its center AND lighter bodies are attracting earth toward its center?

::cues twilight zone music::

Answer 8

It does, and it can be worked out. However, the attraction is so laughably tiny that it is practically negligible.