October

I've mentioned in the previous issue the first would-be Hungarian Moon probe, the Puli. Our goal is to send in a few years a – privately funded! – rover to the  Moon: that is the challenge of the international competition called Google Lunar X-Prize (GLXP). Our team, Puli Space Technologies also plans that our rover will send back pictures and videos to the Earth and will travel at least 500 meters (1600 ft) on the rugged terrain of the Moon. What's more, it will try to make geological measurements too. And the Puli intends to bring the names of everybody who supports us with at least 1000 Forints (5 $) to the Moon. When Armstrong stepped to the Moon, he said “small step for a man, one giant leap for mankind”. Today, everybody can join the Small Step Club (pulispace.com): five bucks is is small step for a man but put together, it is a great opportunity for the Puli, the Hungarian science and culture! (Besides, all members will receive a personal certificate and – if the mission succeeds – a photograph of the Moon, and after the registration of the team ended, we will give away gifts too.) The rover will reach the Moon atop a big rocket and will descend to it alone, breaking with a smaller rocket to avoid to hit the surface too hard. (We can't use parachutes as the Moon has essentially no atmosphere.)

The Puli wants to do public outreach and education too so I want to continue to expand your astronomy-space-physics knowledge, dear Reader. Since the most important constituents for the Puli to reach the Moon are rockets, I want to tell you how rockets work first.

A rocket doesn't work with air (or other gases in the atmosphere) like common airplanes in the Earth's atmosphere but with the accelerated gas that exits it, making it capable to get faster or slower on it's own even in space.

I've implied last time that movement itself doesn't need a force. I you are for example sliding on ice, you keep almost all of you speed for a while. After you accelerated to that speed, you will move on on your own, no force is needed anymore (- or rather no more would if there were no friction and air resistance at all: but ice is not entirely frictionless, so the force of friction is going to stop you, and even without that, the resistance of air would slow you down bit by bit).

A force is capable to change a body's state of movement which is described with the velocity vector. (Velocity or speed – just like force – has not just magnitude but direction too. A vector expresses both properties through the length and direction of the arrow you draw.) Velocity can zero too, of course. If a body stays still, then this is the state of it's “movement”, it has no speed. The state can be changed with a force vector: it can be accelerated to a specific direction and speed through a force. The forces acting on the body will compensate each other after a while (like the force driving a car and roll friction slowing the car) and the velocity vector will not change anymore. (Neither the speed not it's direction.) The force vectors acting on the body determine it's state of movement together. If we sum them as vectors (see the rules of vector summation!) the resultant sum vector will tell us he direction and magnitude of the acceleration (or deceleration) of the body. When you will be older, you will learn Newton's second law of motion which is exactly about that. (Actually, Newton's first law – the state of movement of a body will remain unchanged if the vector sum of the forces acting on it cancel out each other – could be the special case of this. But it is important to know in what coordinate system do we measure the speed, to what do we relate to. Velocity has to be described differently in accelerating reference frames than in so-called inertia frames – but I will tell about that another time. It is enough to know now that Newton's first law isn't an actual law because it isn't true in all reference frames in the same form but exactly that “law” make it possible to define inertia frames.)

It is useful to know Newton's third law too to get to know rockets: if a body exerts some force on another, the other body exerts a force with the same amount – but opposite direction – on the first. (For example, the Moon pulls the Earth with the same gravitational force the Earth is pulling the Moon towards itself.)

Now, let's play a rocket and think! Assume (or try, gingerly, on roller skates) that two of you are skating. Let you be the “rocket” and your friend the “fuel”. You face each other. Ask your friend to hold his/her hands steady as you're going push him. Launch the “rocket”: push your friend away from you! This way, leaning against him/her – you will start to move. (You – and of course your friend – will start slowly move backwards, getting away from each other.) This simple “rocket-play” demonstrates the basics of the rocket principle. Your friend replaced the gas particles shooting out from a real rocket. Think through all this: the forces required to change the states of movement and the results of these forces! We will get back to it and we will discuss the processes inside the rocket, how the gas particles poke each other pushing the rocket forward, the next time.

Zoltán E. Kovács

Abacus

Translation by László Molnár

Abacus magazine on Mathematics for ages 10-14

http://www.mategye.hu/?pid=abacus

This paper is maintained by the János Bolyai Mathematical Association and the Foundation for Children Talented in Mathematics. The 14 sections of this magazine deal with interesting topics and competitions about maths and natural sciences. Founder: Sándor Róka, 1994.

The following articles are the works of Zoltán E. Kovács from the monthly issue of the magazine, and deal with the Puli project and and many related topics in a clear and easy to read style. The articles are only presented in Hungarian, please refer to the Hungarian version of this page for more details.