Solution to Newton’s Cannon problem I proposed earlier, explained in this nice YouTube video.
Let’s revisit Sir Isaac Newton’s cannon.
In the above mentioned article we had placed a level on the cannon and shot the cannonball at 1440 feet per second parallel to the ground until it fell and bounced and rolled and came to a stop.
We didn’t want to shoot it up in the air in a big arc to see how far we could get it to go because we knew if we shot the cannonball up in the air in an arc, it would go much further. Naturally. We were simply interested in the effect of gravity on a projectile as it moves forward and we chose to level the cannon and shoot straight out.
So now let’s do just that, but because we know the cannonball can only go so fast, we’ll do it with a rocket. We’ll shoot the thing up in the air into a big arc and see where it comes down.
Roar! We launched. The burning rocket fuel accelerates our rocket faster and faster until it’s going 20 times the speed of sound. That’s Mach 20. Pretty lickedy-split I dare say. It’s going faster than any jet plane that I ever flew in went. In fact, it’s going so fast that every second it travels almost 5 miles (4.9 miles to be precise). I’d be scared out of my wits if I was riding that thing.
Okay, so this rocket just goes so fast and so far, and then you know what happens? Well, it runs out of fuel of course. It can’t burn forever. We only put so much of that rocket fuel inside of it, so once we light it and run to the side and it roars to the sky it’s going to run out of fuel after awhile.
So now here it is, way up in the sky. It went so high, so fast, that it actually went higher than the air. The sky around the rocket went dark, the stars came out and it got really quiet.
Yet it’s still going forward in that big arc even though we’ve run out of fuel, because essentially we threw something up in the air really fast.
Technically we didn’t even need rocket fuel, we could have used a slingshot if we could have achieved that speed. Alas, trial and error has shown me that unless you give it that extra boost as it goes up, it’s never going to go 4.9 miles per second. I’ve been through a lot of slingshots as a kid and never managed to shoot a projectile going that fast. Good thing, too! My neighbors would have been upset.
As our burned out rocket shell continues to move upward, it’s going to slow because of gravity. After all their’s no more rocket flames to boost it any higher. When it reaches the top, we call that the Aphelion, it levels out and slowly starts to curve down toward the Earth. Wherever it hits, somebody’s going to get really upset.
Except it’s so high and going so fast, that as it arcs downward toward the ground, accelerating faster and faster, it completely misses the planet! It just goes zooming right by planet Earth, it’s course warped by gravity, and whipped all the way around to the other side and then flung out into space again.
Marvelously, this happens again and again, much to our amazement. It doesn’t look like that rocket’s going to crash down at all! It’s in what they call an elliptical orbit.
That my friend, is another example of what keeps things in orbit. The speed one needs to achieve orbital velocity is 4.9 miles per second, or 7.9 kilometers per second. At that speed things go up, then free-fall to the earth, miss the earth, and keep going round and round.
Sometimes the orbit is highly elliptical, or if you’re very clever, you can make it almost round. The Earth’s orbit around the sun is elliptical, and the moon’s orbit around the Earth is also elliptical (that’s what a super moon is all about, when the moon is both full and closer to the Earth).
I’m sorry, Sir Isaac. Your cannon didn’t cut it this time. Had to make a rocket. If you want to see how this works, click here!
Because of Joe’s ball, the Earth may fall into the sun and the moon may fall from the sky.
Meet Joe. Joe has a ball, and his ball is a great problem for the whole world.
Because of Joe’s ball, the Earth may fall into the sun and the moon may fall from the sky. That’s a big problem for a small ball in Joe’s hand.
The problem is that Joe drops his ball and then tosses it to the side (see illustration at right).
You see, when Joe drops his ball it accelerates at a spectacular rate of 32.2 feet per second per second.
Joe’s ball, as does any falling object, doesn’t just drop. It drops faster and faster, whether he just drops it, or tosses it to the side! If he tosses it to the side, it will hit the ground at the same time as if he just dropped it. The forward movement of the ball doesn’t slow down the downward acceleration of the ball toward the ground. (We are assuming here, that there’s no wind or air to slow it down, okay? Just leave that out for now.)
Now, Let’s say Joe has a bullet in his hand and drops his bullet. Like the ball, the bullet’s gonna fall to the ground at the same rate the ball did.
Let’s next give Joe a gun, and have him shoot the bullet. The bullet is going forward, just like the ball that Joe tossed. But the forward movement of the bullet from the gun barrel doesn’t slow the downward acceleration of the bullet as it falls to the ground. It just falls to the ground a ways off because the bullet was going fast.
Finally, Sir Isaac Newton shoots a cannon. And his cannon is very powerful. The cannonball goes so fast, so far, that as it falls to the ground, the ground curves away underneath it, and it goes around the world in an orbit.
But why? Both the ball and the bullet fall to the ground at 32.2 feet per second per second. They accelerate toward the ground, but Isaac Newton’s cannonball doesn’t. Satellites stay in orbit, the moon stays in orbit, the Earth stays in orbit, and they don’t accelerate toward the ground. How come?