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.

September

It’s not about my dog, this Puli is not barking at the Moon! At first because it hasn’t even born (just in scientists’ brain), and for the second time because the Puli is about to be a space probe. A group is organised – in which I participate as a consultant – where astronomers, physicists and, among many other great scientists, engineers are working for the goal that the Hungarian space probe, the Puli, reach the Moon, what is more, take a few step on it. This is not an easy task, and there is also a chance that we won’t succeed in few years. Of course our work won’t be useless, if we get to the solution of some part-tasks. It’s going to be the part of the Hungarian space research, in which many things can be built in the future. Though we believe we’ll be able to find sponsors, and money won’t be the obstacle of the realization. Furthermore we also believe that with our competence we are suitable for this unusual challenge.

The Moon – first in 1969 – was also reached by man. I’m sure you’ve heard about Neil Armstrong, who was the first human on the Moon. With him Edwin Aldrin also stood on our heavenly companion’s surface, and they returned back to the Apollo spaceship, which was orbiting around the Moon. Meanwhile the third member of the team, Michael Collins stayed in the spaceship. A rocket (like the Apollo spaceship), which is adequate to land on the Moon by man, was developed in one decade. The moon craft, which landed with the Apollo 11, was developed with the leadership of a great Hungarian engineer called Ferenc Pavlics. Of course there were technical preliminaries… Obviously, in few years we can not solve everything by ourselves, we lean on preliminaries, the available developed technical background, but everything else has to be bought. Though the Hungarian physicists have already proved in space research, they were always working for someone else. Now we imagine it in the opposite way: we are going to buy what we need, but what we can we are going to find out and create by ourselves. This is going to be real-Hungarian, like a good Hungarian Puli dog.

We know that the Moon is not really near. Average spaceships, space stations, space shuttles (moreover the most artificial Moons) are orbiting around the Earth, just a few kilometre away from it. Our planet’s diameter is almost 13 thousand kilometres, so these space tools are just right next to the surface of the Earth, around forty times higher, than the airliners. But the Moon’s average distance from the Earth is 384410 km. To take this distance the light, which moves the fastest, needs more than 1 (1,28) second. To the Moon we can put the Earth thirty times next to each other, so our heavenly companion is thousand times further than the most satellite. Moreover it is 30-40 times further the airliners flying above our heads, when they had already reached the travel height. But anyway, how can anything be sent to the Moon? As we know it’s not working like when we carry something on the surface of the Earth. Here, the transportation tools, when they are doing rectilinear uniform motion, are constantly consuming fuel, to overcome the friction and the drag. This is why most people believe that to the motion you need force. In the case of rectilinear uniform motion, the forces effecting the body equalize each other. For example the force which drives a car, equalizes with the opposite directional, but the same volume, friction and braking force. When the forces effecting the body don’t equalize each other, the body accelerates, the velocity vector changes. If the body slows down, it’s a negative acceleration. With ground transportation we can change the direction easily, even when we control a robot by a remote control. In the space there is no friction or drag, but the gravitation works: the heavenly bodies (like the Moon or the Earth) attract the other artificial celestial bodies towards themselves. Attention! This is a huge delusion that there’s no gravitation in the space. The space is full of gravity, because every celestial body attracts the others. Of course it really matters, how close we are to the bodies, because the gravitation increases when we are getting closer to the celestial body. In the opposite way, it weakens when we are going farther; moreover it is inversely proportional to the square of the distance. For example in the case of half distance it’s four times bigger, three times farther, nine times smaller, but in the case of ten times bigger distance it decreases to its hundredth part. The space tools don’t need rocket-drive constantly. The chosen tool is launched by a space rocket towards the appropriate direction and meanwhile we accelerate it to the required velocity – in this way we throw it where we want. If we would like to correct, specify the direction (orbit modification), we use a rocket again. Though the fuel is pretty expensive, and to place it in great distance/height is really costly. So it really matters how we aim the Moon from the Earth, which orbits around the Sun (with the Moon) at 30 km/sec (more than 100 thousand km/h) velocity and its peripheral speed at the Equator is more than a thousand km/h. The Moon orbits around our Earth quite fast too, approximately at 1 km/sec which is 3600 km/h. It also matters how large the orbit modification is going to be before landing. After that, if we want it not knock hard on the surface of the Moon, we have to slow it down before landing and while it’s falling – with the help of a rocket. Since the Moon has no atmosphere, we can not use braking shield.

I’m going to write the details of this story in the future. What you can do now is to contribute to our success, and your name can be launched to the Moon (see: www.pulispace.com )!

Zoltán E. Kovács
Abacus
Translation by Virág Váczi

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.