This isn't new, but it is popular: Balancing a broom on its brushes. Cool trick, but the big problem is what people say.
"Hey, today is special because the planets are aligned and you can balance a broom!"
Well, today may indeed be special (maybe it's your birthday or something), but the position of the planets has nothing to do with it. As we'll see in a moment, they're much too far away to have any real effect. But there is a cool physics explanation for why this works.
One note: I'm almost certain that others have shown calculations very similar to what I will show—I just can't remember where. If I had to guess, I would say it was Ethan at Starts With a Bang. But all of this has happened before, and all of it will happen again.
Let me start with gravity. Not your dad's "mass times g" gravity, no, the REAL stuff—Newton's gravity. (Of course, if your dad was Newton, these are the same thing.) People think of gravity as an interaction with the Earth, but that's only the most obvious example. It's really an interaction between any objects having the property of mass.
Suppose I have two objects, mass 1 and mass 2, that are separated by a distance r (as measured from the centers of the objects).
The magnitude of the gravitational force between these two would be:
where M1 and m2 are the masses of the two objects, and G is the gravitational constant with a value of 6.67 x 10-11 N × m2/kg2. Yes, both masses have the same force acting on them, because forces are an interaction between two objects.
Let me look at the broom and estimate its mass at around 1 kg. What objects could be interacting with this broom? Well, obviously the Earth. Earth has a mass of 5.97 x 1024 kg, and the broom is 6.38 x 106 meters from the center (the radius of the Earth). Using these values, the gravitational force on the broom from the Earth is:
You know why that looks the same as your "mass times g" formula? Because it is. Where do you think g = 9.8 N/kg comes from?
Now, how about a couple of planets? Right now, Venus is fairly bright in the night sky. But how far away is it? This is a perfect job for WolframAlpha. It says the distance to Venus is 1.292 x 1011 meters. Since Venus has a mass of 4.87 x 1024, this means the magnitude of the gravitational force on the broom will be 1.94 x 10-8 newtons. That's tiny compared to the gravitational force from the Earth. Why? Because the mass of Venus is about the same as Earth's, but it's MUCH farther away.
OK, how about a planet with a little more mass. What about Jupiter? It has a mass of 1.90 x 1027 kg and is currently 8.29 x 1011 meters away. This will create a gravitational force of 1.8 x 10-7 newtons—still minuscule.
One more object. What is the gravitational force between YOU and the broom? Let's say you have a mass of 65 kg with a distance of maybe 0.3 meters between your centers. This would create a gravitational force of 4.8 x 10-8 newtons. Yes, this is also tiny. But look: The gravitational force from you is greater than the gravitational force from Venus. So here is your answer. How could the alignment of the planets matter when there are people around the broom that matter as much or even more?
Really, there are two important things: First, the shape of the broom. Since the bristles are at the bottom and are bigger than the handle, the broom's center of mass is low. Here is a picture of me with my hands at the center of mass.
(As a quick note, finding the center of mass for objects is fun and simple. Here is a demo of how you can do that.) What does the center of mass have to do with it? Well, if an object's center of mass is not directly over its base of support, it will fall over. But in this case, the brush provides a pretty wide support area. And because the center of mass is low, the broom can tilt quite a bit without moving its center of mass very much.
There is another thing that is probably important. The brushes bend and act like a springy-type restoring force. This means you don't have to get the thing exactly balanced before you let go. You just have to be close. Let's describe a similar situation. Suppose you have a perfectly spherical bowl turned upside down. Try to balance a marble on the top of this inverted bowl and you will find it quite difficult. I guess it's theoretically possible, but it will be tough. Now imagine a marble on top of an inverted bowl that looks like this:
I know, not my best drawing. Sorry, I will try better in the future. But here you can see that there are several places you can put this marble such that it will stay near the top. Of course, you can't put it just anywhere. The broom is sort of like this. That is why it can stay up. I guess the next thing would be for me to plot the restoring force on the broom as a function of angle. Maybe someday.
