Gravity Day is September 8th (9/8) which represents the constant g = 9.8 N/kg. Clearly, we should celebrate. Here are some interesting things regarding g.
What is g?
You might hear people call this the “acceleration due to gravity”. That’s not really wrong, but it might be a bit misleading. I prefer to call g the magnitude of the local gravitational field with units of Newtons per kilogram. Why? Well, if you place a book on a table and it’s just sitting there what is the acceleration? The acceleration isn’t -9.8 m/s2. No, the acceleration is zero. However, the gravitational force is still acting on the book. So, the best thing is to call this the gravitational field.
Oh, just so you know a Newton per kilogram is the same as a meter per second squared. Using these units makes the gravitational field look more like the electric field which has units of Newtons per Coulomb.
π squared is approximately g.
This cool. If you take π and square it you get 9.689 (no units with π). This is pretty close to the value of g at 9.8 N/kg.
This isn’t a magical coincidence. If you use different units (like feet per second squared for g), it doesn’t work since in that case g = 32.2 ft/s2. So, why does this mostly work with units of m/s2 (or N/kg)? It has to do with the original definition of the meter. One of the early ways to determine the length of a meter was to make a pendulum such that it had a period of 2 seconds. For small oscillations, a pendulum has a period of:
So, a length of 1 meter gives a period of about 2 seconds. Why don’t we still use this? It turns out that the gravitational field at different locations varies slightly. That makes this method not so great as a standard for a length measurement.
The Earth’s spin makes a difference in how much you think you weigh.
Yup. If you are at the equator, you are moving around in a circle the size of the Earth at a rate of 1 rotation per day. Since you are turning in a circle, you are accelerating (just like when you make a turn in your car). Of course this acceleration isn’t very large.
If you stand at the equator, there are essentially two forces acting on you. There is the gravitational force pulling down and the ground pushing up. These two forces do NOT cancel. Instead, the the ground pushes up with a smaller force so that the net force is towards the center of the Earth. This net force is what you need to accelerate as you move in a circle.
How about this? If the Earth was spinning 50 times faster, the gravitational force would not be enough to hold people on the surface. They would get flung off.
Gravity in Angry Birds
If you look at the Angry Birds game, they birds move with a constant vertical acceleration (just like they would on Earth without air resistance).
If you assume this game takes place on Earth with the same gravitational field, then you can calculate the size of these birds. They are HUGE. The red bird would be about 70 cm tall.
Gravity in space
As you move farther away from the surface of the Earth, the gravitational force decreases. However, at the orbital distances of the International Space Station, this value isn’t all that small it’s just about 90% the value on the surface.
But why are astronauts weightless in orbit? They aren’t. Instead they “feel weightless” because they are accelerating. All the details are are in this older post.