Season 1 Weekly

Discovering Gravity from scratch

Had the apple not fallen that day Newton might still have formulated the laws of gravitation. But for today’s article we’ll presume that either gravity wasn’t discovered until the ripe old age of twenty first century or that you’re reading reading this article in the seventeenth century. Either way, gravity isn’t discovered yet. And the responsibility to discover it rests solely upon our shoulders.

Now, we’re not physicists. We’re just some common 17th century human with a curiosity. We like to perform thought experiments in lonely solitude and scribble down some stuff when the information overflows our memory. From now onwards, I’ll swiftly change the first person plural to a second person singular pronoun, I hope you won’t mind!

Everyday you walk from your home to your farm. You have to first walk for 5 kms straight then take a right and walk 5 more kms west. One fine day you injure your ankle a little and wish your farm was closer. Now technically your farm can be closer if you can take a shorter path! That’s to say trod over your neighbour’s farm and follow a hypotenuse.

In a momentary spirit of evil intentions, you enter their farm and step upon a few crops. As the stalks crush beneath your sole, you proceed unhindered. Half an hour later you reach your farm! It did indeed come closer. From 5 + 5 = 10 kms it is now sqrt(5^2+5^2) kms or about 7 kms. You just saved yourself 3 kms of walking with an injured ankle (and 3 more considering the return).

All this leaves a strong impression upon your mind. A week later you go for a vacation. It’s a hilly area with a threat of wildlife venturing arbitrarily intown to feast on human flesh. You learn that natives here have devised a method to throw a rock at these wildlifes to scare them away. But sadly, they miss the target most of the times.

You decide to give them an advice. You ask them to build a wooden wedge and tie heavy rocks on top and the bottom near the forest road. So that when the animals pass the spot the rocks can be released and then the will hit the animal at the earliest. It sounded like a better idea than having humans throw the rocks.

It did work for a few times but this plan too mostly missed. On the last day of your vacation you learn that the wooden plank had broken under the weight of the rocks and has been deformed into a curved shape. Yet surprisingly, this curved wedge worked every time hence and knocked out ten animals in a row!

You return home confused why the rocks descend quicker down a curved a path than the obviously shorter hypotenuse. It seems the path of shortest time and shortest length don’t coincide in the vertical direction. This somewhat baffles you but you soon forget about it.

Then the next week your naughty nephew arrives. Being an absolute package of ungodly mischief as he is, he starts kicking around one of your nice and round earthen pots. Something tells you you’ll soon learn the definition of karma.

Next morning someone tells you that your nephew is in your farm. Now given that you’re a thoughtful person, you had carefully designed your farm. When the winter arrived and yield was low, that is, now, your farm would have a gradient of grasses from heavy growth to light. At one end the farm was as green as jealousy. The other end was as brown as the soil (because it was literally the colour of the soil).

Your nephew was standing on the green side and kicking your earthen pots which graciously rolled its way upto the other end. Yep, that’s karma. In the process it simply ruined the beautiful lush green grasses that grew in its track. As soon as you enter the farm, you stand dumbstruck. Not because of your nephew’s deeds but rather due to the shape of the tracks.

These immediately remind you of the curved plank you had observed in your vacation. You rush home and start to think. In your farm as the density of grasses got rarer, the quicker the round pot rolled. Therefore it could cover equal longitudinal distance even if it’s angle got a bit obtuse, thanks to its higher speed. And this, resulted in the curved path as the reduction in the resistive forces of the grasses caused continuous increase in the velocity of rolling pot.

It was almost as if someone pulled the pot harder as it proceeded. This effect seems to be absent when such forces in the direction of motion are absent. Since such gradients of grasses are a rarity, horizontal motion mostly yields straight line travel at an angle.

Now air seems to have no such gradient right upfront! That means, and wait for it my friend, every falling object must have some invisible force pulling on it because the similar curved trajectory is observed when an object travels in a vertical plane! That is why it is so difficult to jump and keep going up forever. This force, whatever it is, reduces your speed till it’s zero and then starts pulling you down faster.

You try to draw this trajectory from your memory of the bend wooden plank and curved grass trails. Your nephew reaches home meanwhile. Dude sees your drawing. He says, “Haha…that’s just what my tyre valve does!”. You jump up, “Your tyre valve?”.

He shows you a tyre that he often rolls in his free time down the road with a stick and this tyre has an inlet valve. As the tyre translates and rotates, aka rolls, this valve traces out a weird semicircle like path. Apparently your nephew had seen this pattern from afar and had identified this pattern with your drawing.

You roll some tyres, draw some diagrams and come up with the conclusion that any fixed point on the circumference of a rolling circle traces out this curvy shape, which is exactly the path of shortest travel between two points when there is a pull or push in one of the dimensions.

Centuries pass and today your name is associated with the first proof that Earth exerts a force on every object and the discovery of brachistochrones and cycloids! Lucky you. Now you’re immortal in the story of science.

The reason I wrote this was to emphasize on the fact that discoveries in sciences rarely follow a molded path. New discoveries can happen from daily observations and may come from ordinary people. Had Newton not discovered gravity somebody else would have done it. How that would have happened is just as unknown as gravity was before its discovery.

This is to say that, never stop asking questions as there is no blueprint of scientific success that lies ahead. Although with the present scientific sophistication simple ideas turning into blockbusters have become less probable, the fact that the same discoveries can be made in multiple ways still remains true. And that sounds awesome as this portrays science as a field full of possibilities rather than the strict discipline which it is often portrayed as in our schools. Cheers!

Arkadeep Mukhopadhyay