# Question of the Week

B R Sitaram

Here are the answers to questions that appeared in the April 2019 issue.

Q 1. Why will 2100 not be a leap year? After all, 2100 is divisible by 4!
A. When Julius Caesar introduced the idea of the leap year, it was thought that the earth took 364.25 days to complete one orbit. Hence the addition of one day every 4 years to compensate. However, in the 17th century, it was realized that this was not correct: actually the earth takes 364.2422 days to complete an orbit. By adding a leap year every four years, we get 3 extra days every 400 years. To compensate, 3 years which would otherwise have been leap years are converted into ordinary years. Thus for example, in the 400 year period between 2001-2400, the three century years 2100, 2200 and 2300 will not be leap years, while 2400 will be. In general a century year is a leap year only if the year is divisible by 400.

Q 2. Newton’s law of gravitation says that the apple falls to the ground because of the force of gravity. The law is supposed to be universal, so should apply to the moon too. How come the moon does not fall to the ground?
A. It does apply and the moon does fall towards the ground. However, the moon is also moving in a perpendicular direction. The combination of these two motions, falling towards the earth and moving in the perpendicular direction is what leads to a circular orbit!

Q 3. Some of you might remember from your school days that a calorie is the amount of heat required to heat 1 g (or 1 ml) of water by 1 degree Celsius. A typical cup of coffee would be made with 200 ml of water and you would have heated it by at least 50 degrees Celsius, so you would have used 50 x 200 = 10,000 calories. Weight watchers will remember that an adult is supposed to consume about 2000 calories a day. How come our body can do so much of work with just 1/5th the energy required to make a cup of coffee? Or is it really that we hardly do any work?
A. Actually, dieticians cheat! They use a much larger unit of energy, called the kilo calorie, which is 1000 calories. Kilo calories are supposed to be written with a capital C, but no one bothers, leading to this misconception! So, our body would typically consume 1,800,000 to 2,000,000 calories, not 1800 to 2000. I wish they would use the longer form, with all the 0s. Would you eat a samosa if you knew it gave you 308,000 calories?

Q 4. Many Indian books claim that Aryabhatta was the first scientist to state that the earth was round. What historical fact, taught in most curricula and found in most Indian textbooks on science or geography, shows that this claim is absurd?
A. The simple fact is that Eratosthenes, a Greek scientist, actually measured the circumference of the earth in 240 BCE. Aryabhatta lived in the 5th century CE, so this was 700 years before Aryabhatta! And, thanks to Alexander’s invasion of India, Indian mathematicians were fully aware of Greek ideas (and vice versa!) In fact, Greeks were convinced about the sphericity of the earth.

### Questions for this month

1. Isaac Newton was born on Christmas day 1642 and Galileo Galilee died on Christmas day 1642. But the two events actually took place on different days. How come?
2. I have three photos taken of the night sky on three consecutive nights. One of the objects in the photos is a planet. How do I make out which one?
3. Most diets are based on the idea of the calorie and talk about consuming a certain number of calories (actually kilo calories) per day. What is fundamentally wrong with this approach?
4. Everyone knows that Christopher Columbus was not given funds by many kings and queens till he got funds from Spain. If everyone at that time believed the earth was round, why was he denied funds?