Answers to Last Issue's Do You Know? 1. The lunar transfer of Chandrayaan-1 was done with an elliptic orbit which touches an orbit of Earth as well as an orbit of the Moon. Who thought of this idea? Has it been done before by other spacecraft? Vladimir Petrovich Vetchinkin, a Soviet scientist in the field of aerodynamics and aeronautics, suggested the idea of the elliptical transfer. Walter Hohmann, a German engineer actually worked out this orbit, although Vetchinkin did not get the credit until much later. Both of them did their work in the early part of the 19th century. Minimising the amount of fuel that the spacecraft had to carry is an an important consideration of interplanetary space-flight. Hohmann plotted a number of orbits until he found the one that needs the least energy and that now bears his name: Hohmann transfer orbit. The Hohmann transfer orbit is one half of an elliptic orbit that touches both the orbit that one wishes to leave (labeled 1 on diagram) and the orbit that one wishes to reach (3 on diagram). The transfer (2 on diagram) is initiated by firing the spacecraft's engine in order to accelerate it. This makes it leave the smaller circular orbit and move into an elliptical (transfer) orbit. This adds energy to the spacecraft's orbit. When the spacecraft has reached a point (at the top of the diagram) where it touches the destination orbit, its engines are fired again to accelerate it to the required velocity so that its new orbit is circular. Instead of just firing twice, sometimes, the engine is fired several times. The timing is carefully done so that the initial circular orbit is slowly enlarged until it finally moves into the destination orbit. While it takes longer, the engine need not generate as much thrust as only a small acceleration is achieved in each step. Hohmann transfer orbits also work to bring a spacecraft from a higher orbit into a lower one. In this case, the spacecraft's engine is fired in the opposite direction to its current path, decelerating the spacecraft and causing it to drop into the lower-energy elliptical transfer orbit. The engine is then fired again in the lower orbit to decelerate the spacecraft into a circular orbit. 2. What is reverse swing bowling? Who thought of this idea? Former Pakistani international cricketer Sarfraz Nawaz is the founder of reverse swing during the late 1970s. The cricket ball often moves in the air towards or away from a batsman when a pace bowler is bowling. It is this deviation most fast bowlers strive for because of the problems it causes batsmen. Batsmen are used to facing ordinary swing - which happens when the ball is still relatively hard and new in the first 10 to 15 overs. However, over the past 20 years fast bowlers have developed a new method of making the ball move in the air with the older ball called 'reverse swing'. Both swing and reverse swing (to obtain any sort of movement of the ball in the air) depend on aerodynamics: the difference of flow of air over rough and smooth surfaces). There are a number of factors to consider. 1. Rubbing the ball only on one side: This helps to maintain a smooth, shiny side with the other side being much rougher. 2. The seam position: This is the prominent stitch at the centre. All fast bowlers hold the ball along the stitch. So one side is shiny and the other is smooth. The ball swings to the right or left depending on which side is rough (see the figure). After the ball has lost its shine and hardness it is difficult to swing the ball in this way (and mostly spin bowlers take over at this point!) Once the ball becomes older and more worn, it will begin to move in the opposite direction to where it would usually swing with no great change in the bowling grip. However, the ball needs to be bowled at least at a speed of 130 km/hr. This is called reverse swing. Also, the ball tends to swing very late on in the delivery, making it difficult for the batsman to pick up the changes in the air. In fact, when the Pakistani bowlers learned this technique, and used it effectively in the 1980s-1990s, many people thought they were cheating in some way. Many theories are there about how this happens. One popular theory is that after some time the rough side becomes so rough that it has no more variations. So it becomes like the smooth side! So the inswinger becomes the outswinger and vice versa; hence the name reverse swing. 3. What is a prime number? Is there any way of finding out how many primes there are between 1 and 1,000? Or 1 and 10,000? A prime number is any number that can be divided only by 1 and itself leaving no remainder. Simple prime numbers are 3, 5, 7, etc. For instance, 12 can be divided by 1, 2, 3, 4, 6 and 12 so it is very composite. It is known that there are infinite number of primes. There is no formula that gives you the number of primes between 1 and 1000 (or any two numbers). This is one of the most important problems in mathematics today. However, there is a simple and very old method to actually find out which numbers are primes by going through the list of numbers one by one. This is called the Sieve of Eratosthenes. A sieve is like a strainer that you use to drain spaghetti when it is done cooking. The water drains out, leaving your spaghetti behind. Eratosthenes's sieve drains out composite numbers and leaves prime numbers behind. To use the sieve of Eratosthenes to find the prime numbers up to 100, make a chart of the first one hundred positive integers (1-100): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 1. Cross out 1, because it is not prime. 2. Circle 2, because it is the smallest positive even prime. Now cross out every multiple of 2; in other words, cross out every second number. 3. Circle 3, the next prime. Then cross out all of the multiples of 3; in other words, every third number. Some, like 6, may have already been crossed out because they are multiples of 2. 4. Circle the next open number, 5. Now cross out all of the multiples of 5, or every 5th number. Continue doing this until all the numbers through 100 have either been circled or crossed out. You have just circled all the prime numbers from 1 to 100! Don't you want to do this for the first 1000 numbers and see what you get?! 4. Many biologists use Petri dishes in their experiments. What are they and why are they used? A Petri dish is a shallow glass or plastic cylindrical lidded dish that biologists use to culture (grow) cells. It was named after German bacteriologist Julius Petri who invented it when working as an assistant to the famous scientist Robert Koch. Glass Petri dishes can be re-used by sterilization (for example, dry heating in a hot air oven) while plastic Petri dishes must be disposed of after one use. For microbiology, agar plates are very frequently used. The dish is partially filled with warm liquid agar along with a particular mix of nutrients, salts and amino acids and, optionally, antibiotics. After the agar solidifies, the dish is ready to receive a microbe-laden sample that grows comfortably on the agar block (see picture). Modern Petri dishes often have rings on the lids and bases which allow them to be stacked so that they do not slide off one another. Multiple dishes can also be incorporated into one plastic container to create what is called a "multi-well plate". As well as making agar plates, empty Petri dishes may be used to observe plant germination or small animal behaviour, or for other day-to-day laboratory practices such as drying fluids in an oven and carrying and storing samples. 5. A volcanic eruption requires a tremendous amount of energy. Where does this energy come from? The answer to this question will appear in the next issue of JM. --Ed.