Basics of Moving Around in Space
To figure out how to get from Earth to another planet, and to figure out how much fuel will be needed in various cases, we need to start with Newton's laws of motion, again:
Newton's First Law: A body will remain at rest or in motion in a straight line unless acted upon by a force.
Newton's Second Law: Change in motion is proportional to the applied force and parallel to it.
Newton's Third Law: To every action there is an equal and opposite reaction.
By Newton's first law, two things are really cheap: Coasting and sitting still. Out in space, sitting still is a little hard to define - do I mean compared with the Sun, or Mars? Also, most of the time we are in an orbit of some sort, so sitting still doesn't really make sense. What we need to think about is how to change from one kind of orbit to another kind of orbit.
Newton's Third Law contains the "secret" of rocket propulsion for space travel. See the figure below. If A exerts a force on B, then B exerts an equal and opposite force on A. Or, in the case of space travel, if a mass (m) of fuel is pushed out the exhaust of a rocket, then the rocket will accelerate in the opposite direction the direction the exhaust fuel went.
In this animation, we put in some imaginary space dust to help you visualize the motion. When the animation begins, the dust and the rocket are orbiting in the same orbit, so the dust appears to be at rest. When we fire the jets the rocket accelerates relative to the dust.
Coasting is Free
Once a spacecraft has fired its engines for some amount
of time, the ship accelerates from rest and reaches some planned speed.
When the engines cut off, there is a total lack of any force acting
on the spacecraft (this is, again, assuming that the spacecraft is in
deep space and not near any planets).
While the engines are firing, the spacecraft accelerates. When it has reached its planned speed, the rockets are turned off. This means it is now in some sort of orbit around Earth or around the Sun. It will stay in this orbit until its rockets are fired again. Its speed will be constant except for very slow changes that are part of its orbital motion.
After you have worked through the question above, you should now see that coasting, as a result of Newton's first law, is a vitally important aspect of space travel. The reason this is the case is because it means that astronauts only need to fire their engines for a brief time to then coast their way to a planet. But what happens when they get to a planet? If they don't slow down they could crash their ship into the planet.
The easy answer to the last question is that a spacecraft must use fuel to slow down as well as tospeed up. When a spacecraft is moving forward, using Newton's laws again, the astronauts must fire their rockets in that direction to create an opposing force.
In a later unit we will look at this in more detail, but for now: To get to another planet, we need to use enough fuel to get us into a big orbit that reaches all the way to the planet. Once we arrive at the planet we will need to use more fuel to slow down again. In general, the faster we get from Earth to the other planet, the more fuel we will need at both ends.
Speed and velocity
One of the words that appears in this discussion, "velocity," is a special word to which you should pay careful attention. In everyday English, the word "velocity" is used as another way of indicating speed. Therefore, "high velocity" means "high speed." But in the context of Newton's laws, it is important to keep in mind the technical definition of velocity.
Velocity is a vector indicating both speed and direction of motion.
So, what are the implications for moving around in space? By Newton's second law, a force is required in order to change the direction of motion of a spacecraft, even if its speed stays constant. This is a very important thing to remember in the discussion of orbits in the next section.
We have created a game that demonstrates some of the topics covered
in this section. It is not a perfect simulation of docking the shuttle,
because that would be too frustrating without a computer to help with
the process. So we introduced just a little friction that would not
really be there to keep the game from being too hard. We hope you find
it interesting and fun and will ask you to tell us what you thought
of it in the exercises following Unit 5.