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THIS EBOOK WAS PREPARED AS A PART OF THE COMENIUS PROJECT WHY MATHS? by the students and the teachers from: BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS ( BELGIUM) EUREKA SECONDARY SCHOOL IN KELLS (IRELAND) LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY) GIMNAZJUM IM. ANNY WAZWNY IN GOLUB-DOBRZY (POLAND) ESCOLA SECUNDARIA COM 3. CICLO D. MANUEL I IN BEJA (PORTUGAL) IES LVAREZ CUBERO IN PRIEGO DE CRDOBA (SPAIN)

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- 1. Maths and Astronomy Maths and Astronomy
- 2. Page 2 THIS EBOOK WAS PREPARED AS A PART OF THE COMENIUS PROJECT WWHHYY MMAATTHHSS?? by the students and the teachers from: BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS ( BELGIUM) EUREKA SECONDARY SCHOOL IN KELLS (IRELAND) LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY) GIMNAZJUM IM. ANNY WAZWNY IN GOLUB-DOBRZY (POLAND) ESCOLA SECUNDARIA COM 3. CICLO D. MANUEL I IN BEJA (PORTUGAL) IES LVAREZ CUBERO IN PRIEGO DE CRDOBA (SPAIN) This project has been funded with support from the European Commission. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.
- 3. Page 3 II.. WWHHYY AASSTTRROONNOOMMYY?? IIII.. WWHHIICCHH IISS BBIIGGGGEERR?? IIIIII.. TTHHEE SSOOLLAARR SSYYSSTTEEMM -- TTHHEE CCOOMMPPAARRIISSOONNSS IIVV.. WWHHAATT TTIIMMEE IISS IITT?? TTHHEE MMAATTHHSS OOFF SSUUNNDDIIAALLSS VV.. DDIISSTTAANNCCEE UUNNIITTSS IINN SSPPAACCEE VVII.. HHOOWW TTOO CCAALLCCUULLAATTEE AACCCCEELLEERRAATTIIOONN DDUUEE TTOO GGRRAAVVIITTYY?? VVIIII.. WWEEIIGGHHTT OONN OOTTHHEERR PPLLAANNEETTSS VVIIIIII.. HHOOWW FFAASSTT DDOO TTHHEE PPLLAANNEETTSS MMOOVVEE?? IIXX.. HHOOWW OOLLDD AARREE WWEE OONN OOTTHHEERR PPLLAANNEETTSS?? XX.. HHOOWW TTOO CCAALLCCUULLAATTEE EESSCCAAPPEE VVEELLOOCCIITTYY??
- 4. Page 4 II.. WWHHYY AASSTTRROONNOOMMYY?? Astronomy is a science that studies celestial objects, such as moons, planets and stars. It involves other sciences, like physics, chemistry and mathematics, in order to explore the history and evolution of these celestial objects. It is one of the oldest sciences, but one of the most important ones nowadays. The connection between Maths and Astronomy is very important, in order to calculate the volume, density, distance to Earth, to know the orbits and other useful information about the objects in the universe. ! Astronomy is a fascinating science, from the distances to and inter- workings of stars and planets. Most of mathematical skills are grade school level arithmetic skills, so it is not needed to be a mathematics major to understand the mathematical concepts necessary to do well in an introductory astronomy class. One of the first mathematical challenges we find ourselves facing in astronomy is dealing with very large numbers, Basic arithmetic rules of manipulation for addition, subtraction, multiplication, and division apply to numbers written in scientific notation.
- 5. Page 5 II.. WHICH IS BIGGER? Jupiter or the Sun? Jupiter is the biggest planet on the Solar System and the Sun is the biggest star. But which one of them is bigger? To do that, I will calculate the volume of the two celestial objects. Although Jupiter and the Sun are not perfect spheres, I will calculate the volume of them as if they were. To calculate the volume of a sphere, we use the mathematical expression: where R represents radius. So, we need the radius of Jupiter and Saturn. Jupiter radius: 71,492 km Sun radius: 696,342 k Jupiter volume: Sun volume: How many times is the Sun bigger than Jupiter? To do that, we just need to do a simple division equation - we divide the Sun volume (the bigger one) by the Jupiter volume The sun is approximately 928 times bigger than Jupiter. How many Europes fit in the Sun? To calculate how many Europes fit in the Sun, we need to calculate the area of the Sun and of Europe. The area of Europe is 10180000, and we calculate the area of the Sun. To calculate the area of a sphere, we use the mathematical expression:
- 6. Page 6 Now, we just divide the area of the Sun by the area of Europe.! Almost 60000 Europes fit in the Sun. How many days it would take if I wanted to go to the Moon by plane? Imagine is planes could fly on space - how many days it would take to get to the Moon? To calculate that, we need the distance between the Earth and the Moon and the average speed of the plane. Distance between Earth and Moon: approximately 400000 km Average speed of a Boeing 747: 920km/h In order to calculate the days, we need to convert the hours to days:
- 7. Page 7 IIIIII.. TTHHEE SSOOLLAARR SSYYSSTTEEMM -- TTHHEE CCOOMMPPAARRIISSOONNSS Here we compare all the numbers and the statistics about the characteristics of the planets, the Moon and the Sun but as The sun has big numbers, sometimes it doesn't appear in the graphs. RADIUS Looking at the radius we know which is the biggest, and as we can see it's Jupiter. The planets which are close to the Sun, are smaller than the planets which are far from the Sun. MASS Now its time to compare the mass of all the planets. Jupiter has the biggest mass. The mass of Jupiter is twice that of all the other planets combined. Mercury has a mass of 3.301023 kg, making it the lightest planet in our Solar System.
- 8. Page 8 AGE All solar system was formed at the same time so all the planets have the same age; four and a half million years. SURFACE The data about the radius is similar to the surface's data because to calculate the surface we need the radius. The surface shows us which is the biggest and the smallest planet. And as we can see Jupiter is the largest one and Mercury the smallest one. DISTANCE TO THE SUN As we know, Uranus and Neptune are very far from the Sun. Here we have the distance to the Sun in kilometers. DISTANCE OF ALL PLANETS FROM EARTH
- 9. Page 9 MOONS NUMBER In this graph we can see how many moons different planets have, for example Mercury and Venus have no moons. The Earth has only one moon. Uranus, Neptune and Saturn have a lot of moons and Jupiter is the planets with more moon's number with 67 moons. TRANSLATION MOVEMENT Neptune has a longest translation movement, his duration is 60000 Earths days. ROTATION MOVEMENT A day is the length of time it takes for a planet to complete one rotation on its axis 360. Since all of the planets rotate at different speeds, the length of a day on each one differs. Compared to Earth, Mercury has a very long day. A day on Mercury takes 58 days and 15 hours in Earth days. Venus is the slowest moving planet. Venus has the longest day of any planet in our Solar System. It is about 225 Earth days for the planet to orbit the Sun.
- 10. Page 10 DENSITY Density ( symbol) is a scalar relating to the quantity of mass in a given volume of a substance. The average density is the ratio of the mass of a body to its volume. Just like the size of the planets, the density of the planets varies widely. All of the 4 inner planets the planets closest to the Sun are much denser than the four outer planets. GRAVITY Gravity is an attracting force that is present in all objects in the universe. It differs depending on what planet we are on. This is because the planets vary in size and mass. In our solar system, the planet with the greatest gravity is Jupiter. and lowest gravity planet is Mercury. ESCAPE VELOCITY Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravity well. The escape velocity is determined by the gravity of the planet which in turn is determined by the mass and size of the planet. The escape velocity from the moon is so much smaller than from the earth that it's no wonder that the moon can't keep an atmosphere.
- 11. Page 11 MAX. AND MIN TEMPERATURE Many people know that most of the planets in our Solar System have extreme temperatures unsuitable for supporting life. Mercury is the planet closest to the Sun, so one would assume that it is a burning furnace. While the temperature on Mercury can reach 465C, it can also drop to frigid temperatures of -184C. Venus, the second closest plant to the Sun, has the highest average temperatures of any planet in our Solar System, regularly reaching temperatures over 460C. Venus is so hot because of its proximity to the Sun and its thick atmosphere. With temperatures dropping to -218C in Neptunes upper atmosphere, the planet is one of the coldest in our Solar System. ELEMENTS NUMBER The numbers of elements that form the different planets. The Moon has 25 elements
- 12. Page 12 IIVV.. WWHHAATT TTIIMMEE IISS IITT?? TTHHEE MMAATTHHSS OOFF SSUUNNDDIIAALLSS The sundial is the oldest known device for the mea