Why are so many rocket launches done from Cape Canaveral in Florida? There are two main reasons. The first is energy.

Suppose I want to put an object in low-Earth orbit (about 300 km above the surface). There are two things to consider. How fast does it have to be in orbit so that it doesn't crash? How much energy would it take to get it there?

How fast do you need to be in orbit?

Here is the force diagram for an object in orbit around the Earth (not to scale):

The only force on the space object (rocket or whatever) is the gravitational force from the Earth. It can be expressed as a force with a magnitude:

For this case, the force is perpendicular to the velocity and only changes the direction. For an object moving in a circle, it has an acceleration towards the center of the circle and a magnitude of:

Putting these two together with Newton's Second law (everything is in the same direction - the r-hat direction and I will use positive to mean away from the center of the circle):

Note that r in this case is the distance from the center of the Earth to the object in orbit.

How much energy needed?

First, let me assume the Earth is not rotating (or that we are launching rockets from the North pole). This means that the rocket (or object or whatever) starts from rest. If I apply the work-energy principle and include the rocket plus the Earth as my system, then I get:

Remember that the gravitational potential energy has a negative sign in it. Also, (maybe it is obvious) R E is the radius of the Earth (where the object starts). So that work is the amount of energy you would need to put something in orbit.

But wait. There's more. What if the object is already moving? In this case the initial kinetic energy is not zero. How much kinetic energy would it have? Well, it depends on where it is on the Earth. You know the Earth spins, right? It's rotational rate is 1rpd (revolution per day). Actually, that isn't true. 24 hours is the time for the Sun to get back in the same position. It actually takes the Earth a little bit less time to rotate (Sidereal vs. solar day). Let me say the Earth has an angular velocity of ω. And suppose you are at a location on the Earth like this:

If you are at a latitude of θ degrees above the equator, then you are moving around the Earth in a circle of radius R E cosθ. This means that the object at that location would have a speed of:

This changes the amount of work needed to get the thing into orbit since the object will not be starting with zero kinetic energy. The new work-energy equation will be:

Ok. How about some graphs. Here is a plot of the energy needed to put something in low-Earth orbit (altitude of about 300 km) as a function of latitude. Oh, actually I will plot the energy per kg of mass to put in orbit.

Just a couple of values. The energy per kg at the equator is 3.25 x 107 J/kg compared to 3.26 x 107 J/kg at the North Pole. What about Cape Canaveral at a latitude of 28.5 degrees? The energy per kg for a launch from there would be 3.252 x 107 J/kg. This is 0.3% less than the energy per kg from the North Pole. Big deal, right?

What about cost? How much does it cost to get something in orbit? According to Wikipedia, the Space Shuttle has a payload price of $260/kg (in 1972 dollars). Odd that I don't find that value in today's dollars. Oh well. So if you have a payload of 20,000 kg that would be a payload cost of 5.2 million 1972 dollars. Using this conversion that would be 27.3 million 2010 dollars (and $1,366 per kg). Still seems low. But if you moved that launch to the North pole, it would cost about $800,000 more.

What about Canada, eh? Well, they would have to launch from a latitude of about 50 degrees. This would require an energy of about 3.256 x 107 J/kg. How does that compare to USA? To launch from this latitude would take 0.12% more energy (and I assume 0.12% more money). This means that it would cost about one more USD per kg to launch. It doesn't seem like much, but every little bit helps.

But why not southern California or something? The Earth is rotating in the direction of East (meaning if you look East, that is the direction you are moving due to the rotation of the Earth). You would want to launch in that direction to gain any benefit of the Earth's rotation. The difference between Florida and California is in what is to the East. Going East from Florida takes you over the Atlantic ocean. If you have to drop something, not really going to be a problem. However, from California going East takes you over stuff like Texas. Don't mess with Texas (I saw that on a bumper sticker, so it must be true).

I can't get this song out of my head:

It's these changes in latitudes, changes in attitudes

Nothing remains quite the same

With all of our running and all of our cunning

If we couldn't laugh we would all go insane

-Jimmy Buffet