I'm not one of the 'gravity is only a theory' crowd or a flat earther that thinks gravity is fake and that down is always down. but thinking about gravity and what has been put forward by many great thinkers. The strength of an objects gravitational pull is in proportional to its sizeand as such the gravity on the moon is lower than that of the gravity on earth, and as such the gravitation effect of the sun is of such power that it keeps all the planets of the solar system in check(orbit) and blackholes have a gravity greater than any thing else in the observable universe. my question is that given that the suns gravity is significantly higher than that of the earth ( because ofits size) and that despite the distance between us and the sun it still has enough of an effect to keep the earth in its orbit. so why is it that the moon hasn't yet been drawn away from earth and to sun ( or is that happening but at such a minute amount that it's taken longer than the length of human recorded history for any perceptible change in the distance between earth and moon is there a range at which gravity from object Y has a greater effect on another object than the gravitational pull of object X ( eve though object X should in theory have the greater gravitational pull.
3 Answers
so why is it that the moon hasn't yet been drawn away from earth and to sun
You might ask, why is it that the earth hasn't been drawn to the sun? In the absence of drag, objects can remain in stable orbits. The gravity of the sun allows the earth to orbit once a year.
Well, the earth and the moon orbit each other, but both simultaneously orbit the sun as well. If the sun were pulling on just one of the two, they would be ripped apart. But since it is pulling on both, they can remain together. Neither is "sucked in".
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Two objects fall equally fast in a vacuum . Even if they are of different sizes and masses. Armstrong famously dropped a hammer and a hawk feather on the moon and they fell and hit the ground simultaneously. This can be explaining from combining the law of gravitation,
$$F_g=G\frac{Mm}{r^2},$$
With Newton's 2nd law of motion:
$$\sum F=ma \quad\Leftrightarrow\quad G\frac{M}{r^2}=a.$$
You can see that the mass of the object that we are considering the motion (acceleration) of has cancelled out. The fall speed does not depend on the mass of the falling object. Everything falls equally fast.
So, which ever relationship or interaction two falling objects had before hand will not be altered during a fall.
In the solar system, the earth and moon are both falling "towards" the sun. (They are "falling" around the sun, tracing out an orbit). But they fall equally fast as explained above - even though they are positioned quite far from each other, the difference between their respective $r$ values, which is their distances to the sun's centre, is still insignificant in relation to the enormous distances, so we can to a very good approximation consider them as positioned equally far from the sun at any moment.
During their "fall" around the sun, they are simultaneously interacting with each other causing them to orbit one another (that is, the Earth's orbit around the moon is so tiny that we might rather call it an insignificant wobble). This interaction is not altered during their fall. The moon's orbit around the earth won't be meddle with from the moon being pulled in by the sun, because the earth also is being pulled in with equal effect.
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A helpful way into understanding this: calculate the acceleration due to gravity for the Earth due to the Sun and for the Moon due to the Sun. They're roughly the same, because it doesn't depend on the masses of either the Earth or the Moon and the distance between the Earth and Moon rounds to zero in the face of the distance from the Earth to the Sun. If you and a friend are on the road in adjacent cars, have roughly the same speed, and then start accelerating at roughly the same rate, do you see them move behind/in front of you, or do they stay right by your side?
The Earth is in orbit of the Sun, and the Moon is in orbit of the Earth, but if you look from the Sun's rest frame, the Earth and Moon move at pretty close to the same speed. We say that the Moon stays in an orbit around the Earth instead of its own orbit around the Sun because it is close enough to the Earth to be within the Earth's "sphere of influence", which is a very loosely-defined term that sort of defines where one gravitational field dominates all others. That is to say, it's close enough to the Earth that the acceleration the Moon feels due to Earth's gravitation is much greater than that due to the Sun, so much so that you can call the Moon an object that's just in orbit of the Earth instead of the Sun.
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