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# Ballistic Motion

Ballistic motion is an important concept in our path to understanding how rockets get up into orbit. Really, there are a few types of rockets: (1) rockets that just go up and then come right back down, otherwise known as ballistic missiles; (2) rockets that put something into orbit; and (3) rockets that take something away from the Earth and put it on a trajectory to somewhere else.  Each of these requires more energy than the last one, with the ballistic missile requiring the least amount of energy.

But, what is ballistic motion?  It is the motion that something feels when the “only” force acting on it is gravity. (I say “only” because often atmospheric drag is acting on it also, but we will ignore this for now.)

Let’s take a person throwing a baseball as an example.  Figure 1 illustrates a person getting ready to throw a ball.  (My son Alan drew most of the images again!)

The person then moves their arm forward, accelerating the ball up to some speed.  Typically, this speed is roughly parallel to the ground. Figure 2 illustrates the person’s hand accelerating the ball (wow, that is a beautiful hand!)  When the ball leaves the person’s hand, it is moving with a velocity of Vx parallel to the ground.  In addition, gravity is acting on the ball, so it starts, immediately, to accelerate towards the ground at a rate of 32 feet/sec per second.  The ball will follow an arched trajectory, with the velocity towards the ground growing and growing all of the time, but with the velocity parallel to the ground (Vx) staying the same all of the time.

Because I am in America, where we are lovers of guns (although I am not), we should use a gun example! Imagine a person shooting a bullet towards a target.  If the person is far enough away from the target, or the bullet is slow, gravity will have enough time to pull the bullet down, and the person could miss the target.  A person far away from a target with a low-muzzle-velocity gun, has to aim upwards to compensate for gravity.

A much better example, in my opinion, is a catapult, which has an extremely slow speed, so that all objects need to have a very large upward velocity, in order to actually get the object to where you want it to go.

Ballistic missiles (or InterContinental Ballistic Missiles, ICBMs) operate on exactly the same principle as the baseball, catapult, or bullet.  Each goes through an acceleration phase, in which something is giving it an initial velocity (the rocket engine, which thrusts for a short amount of time). Then, the force cuts out, and the “only” force left is gravity. Gravity acts to decrease the upwards velocity down to zero, then causes the object to fall at faster and faster speeds. Just like the catapult.

ICBMs are not the only types of ballistic missiles being developed right now.  There are many companies that want to take “space tourists” on a very fast ride (like 5 minutes).  These companies are creating reusable rockets that have a ballistic trajectory, taking the tourists to about 60 miles into the air, and bringing them back down safe and sound.

The rockets work exactly the same as ICBMs, in that they accelerate for a short amount of time (maybe 100 seconds), and then go into a free fall phase, where the only force acting on the rocket is gravity.

In reality, what happens next is that the rocket, which is well above the breathable part of the atmosphere, keeps going up for a while, reaches its maximum altitude, comes down, and re-enters the atmosphere.  At this point, the rocket is moving at very fast speeds, and starts to feel an incredible drag force.  The people inside the rocket actually have to lay down, since the forces acting on their bodies become so large.  The rocket is slowing down at such a fast rate that the people weigh about 3 times their normal weight.  Gravity is still acting to pull them down towards the ground, but the drag force is rapidly slowing them down.

The space tourists get a large force on them as they take off, and an even larger force on them when they re-enter the atmosphere.  It is truly a wild ride!

## 2 thoughts on “Ballistic Motion”

1. So again…wonderful article…but again the forces that are acting upon ALL of these objects is INERTIA not gravity.

In the case of throwing an object like a baseball the tendency for the ball is to go UP not down based upon the motion of the THROW and not through some mystical “falling force” What causes a baseball to literally “fall” is both the fact that it is losing velocity immediately (failure to fight inertia) and “flight characteristics” of the ball itself (curveball, knuckleball) thus cause in the case of a knuckleball “dramatic deceleration” (ideally at point where said ball is to be caught.)

And of course the same is true of a bullet.

While it will fall immediately upon leaving the barrel the “round”(it’s actually a point sphere) will “sail” (meaning suddenly and dramatically move higher in flight again just as with the baseball “upon release” the bullet wants to “fly” or go UP not down.

Obviously what prevents this is the barrel of the rifle…INITIALLY…but again no matter gun and bullet the tendency is to have the round “overshoot” the target…not to suddenly drop to the ground.

As with the baseball the bullet will “regain inertia” as it loses velocity causing it to…yes..”fall”…but unlike a sphere the conical shaped bullet flies “ballistically” because of the motion imparted to it by the barrel and the fact of its conical shape. (Imparting lift like an aeroplane.)

I don’t really understand why a rocket going straight up then falling is considered a “ballistic” trajectory as you so accurately describe as in fact a rocket is merely a lifting body with at most a 180 degree rotation of the body.

“Orbital mechanics” therefore is merely the study of your speed relative to the Earth’s speed…about 22,000 miles an hour…and your object’s “speed” (final velocity) relative to that.

For example the ISS travels at 17,000 miles an hour meaning it is literally falling back to Earth…like the baseball, like the bullet…but not in an absolute sense but in a relative sense. This fact requires the ISS to be “lifted” from time to time not so that it stops falling but so that it doesn’t “suddenly fall” like our aforementioned “knuckle ball.” This latter is exacting what happens when your rocket deorbits though…it literally falls immediately…so “good luck catching that’!!

Anything faster than Earth is leaving it.

Getting that object to ever slow down again is actually very difficult.

But that is for another story…

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1. Thanks for your comments. It is an interesting way to look at ballistic motion!

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