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 *M*_{1} and *m*_{2} are the masses of the two objects, and *G* is the gravitational constant with a value of 6.67 x 10^{-11} N × m^{2}/kg^{2}. 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 10^{24} kg, and the broom is 6.38 x 10^{6} 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 10^{11} meters. Since Venus has a mass of 4.87 x 10^{24}, 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.