I've been thinking... objects don't really fall at the same rate. I don't think so anyway. I'm not talking about air resistance or any of that crap - I'm talking bona fide, Newton-destroying DIFFERENCES in the rate at which objects of different masses fall. "Surely not," you gasp. But it is true. I am smarter than Sir Isaac Newton. Or I am mistaken. YOU DECIDE.
Let's start at the beginning. Acceleration due to gravity is g. F=mg, that is, the force pulling an object down equals the mass in Kg, times g.
Also, F=GMm/d^2, where M is the planet mass, m is the object mass, and d^2 is the distance between the object and the centre of the earth (i.e. the radius of earth), squared.
So! mg=F=GMm/d^2. Canceling m, you get g=GM/d^2.
G is the universal gravitational constant, 6.67 * 10^-11.
M is the mass of the earth, 5.9742 * 10^24 Kg.
d is the radius of the earth, 6,378,100 metres.
Plug it all in and you get a gravitational acceleration of about 9.8 ms^-2, for an object of any mass. So that's basic physics, right? Newtonian stuff. Old stuff.
BUT! This doesn't take into account the movement of the earth. Now, when an object is falling, it does so because of attraction between it and the earth. The object accelerated easily because it is small. The earth doesn't move, right? Wrong. The earth is not "fixed" in space. It's just as influenced by forces, but its mass is so immense compared to, say, a tennis ball, that its acceleration is negligible. However, because its mass is constant, more force equals more acceleration (remember Newton's second law, F=ma).
The upshot is that heavier objects pull the earth towards them oh-so-slightly faster, and therefore they fall faster (relative to the earth) than small objects.
So that's sorted out.
"But," you say, puffing on your pipe thoughtfully, "if objects can pull the earth, doesn't that mean we can alter its orbit by throwing things up in the air?" If his were true, I would immediately order everybody to throw lots of things up in the air at night time, so the airborne objects pull the earth away from the sun, counteracting global warming, allowing us to emit all the CO2 we want and assuring me a Nobel prize (although I should get one anyway for this ground-breaking paper).
But it's not true. Let us imagine that I heave a '62 Buick into the air with my bulging, manly muscles. Pause on that thought... OK. Now we have to the law of conservation of momentum. This Buick is launched effortlessly into the air by yours truly, and the momentum transferred into the car in the upward direction is equalled by the momentum transferred into the earth in the opposite direction. The earth and the '62 Buick drift away from each other for a bit, then come together due to our friend gravity. They impact with an impressive crash and, if a Hollywood director is filming it, a huge fireball. Anyway, the impact halts them both and we're back where we started.
But that's fairly obvious, so I don't really know why I diluted my ground-breaking paper with it. Why do you have to ask such stupid questions? Altering the fucking orbit...
EDIT: As a strange addendum to this post, I came across this website for
World Jump Day, the day after I did this post disproving its principles! It really is an amazing coincidence.
Labels: articles
