Reaction due to gravity

Question

There is a reaction to the gravity of the earth on us but the earth does not move due to its huge mass. But what if I combine the weight of all humans and other things on Earth? Is it not enough to move the earth from its position(even a bit)? What if (imagine) the bio population suddenly increases? I think that we are not being taught the complete thing in school$(a\propto\frac{1}{m}$, when $F$ is constant). Is there anything more to gravity than just this?Please explain.

Answer 1

According to Google the mass of the earth is around $5.972 \times 10^{24}$ kg (presumably that figure includes its 7 billion human inhabitants plus everything else were meant to be sharing with). If we take the average weight for a human as given by WolframAlpha as 62 kg this gives humanity a combined weight of $4.34 \times 10^{11}$ kg - so our share in the distribution of mass in/on the planet is approximately only 1 part in $1.4 \times 10^{13}$!

Now while in theory if we shipped everyone on the planet to one of the poles and then got them all to jump at EXACTLY the same time there would be a minute blip on the position of the earth in relation to where it's normal trajectory would take it, we would all resume the same course once everyone's feet touched ground again.... As to how big this 'blip' would be - I doubt it is worth the time of calculating it (unless somebody else reading this is bored).

As for if the bio-population were to increase this would have no effect since until we start breading people in space the population will always be just a minute fraction of the relatively fixed mass of the planet (the mass of the planet as a relatively closed system [incoming space dust and outgoing atmosphere] isn't effected no matter how many of it's constituent rocks are transformed into other arrangements that just happen to breath).

And finally, as to

I think that we are not being taught the complete thing in school

You are 100% correct! What we get taught in school is always a simplification due to necessity considering that any one branch of enquiry is usually more than enough to keep multiple humans busy for there entire academic career.

Answer 2

Is it not enough to move the earth from its position (even a bit)?

For all practical purposes, nope. Think of it in the following manner:

The (Earth + All the Humans) can be viewed as one system, and in this case, the gravitational force exchanged between any one person (e.g. you), and the Earth, is an internal force of this system. And internal forces can not produce a net motion of the center of mass of a composite system, since they will always cancel in pairs, and therefore, make no difference to center-of-mass. The argument can be generalized to include N other human beings, even with this, the internal forces can not make a net difference to the situation. And of course, if you feed in the numbers, the center of mass of the (Earth + All Humans) system, will more or less be at the center of the Earth, due to its large mass ($6 \times 10^{24}$kg). In comparison, the world population is about 7.2 billion, and if one ascribes an average weight of 80 kg to each, it is still lesser by orders of magnitude. And of course, the 7.2 billion are distributed (inhomogeneously) over the entire world, an not concentrated as a bunch. Thus, for all practical purposes, the center of mass is the center of the Earth.