# A little peek into the world of spiders

Today we will talk about a class of animals, called Arachnids. They are easily distinguished from insects by their four pair of legs. Unlike insects, which are plenty in almost every part of the world, Arachnids are less in number. And out of many different animal species which come under the class of Arachnids, spiders are largest.

So, how these spiders find their food? As we all know, their solution to this problem is, constructing a web. Spider cannot be everywhere at the same time, but a net or a web increases its reach and can catch more insects.

Different species of spiders exist and different types of web shapes also. Some species do not build web at all, and some build circular webs, funnel shaped webs, tangled cobwebs, triangular webs etc. But let’s focus on a circular or orb web for now.

So, how does an orb-weaver spider actually make its delicate web? Surprisingly, the whole process takes about an hour or two. It has nearly seven to eight different silk producing organs (or spinnerets) underside, and there are different glands connected to it for producing silk of varying protein composition. These different types of silk are used in making different parts of the web.

The process, more or less goes something like this: first, the spider starts by flying a silk thread like a kite. The thread is very light and if there is a soft blowing wind, it clings to some surface. It spins another thread and walks along the previous thread tying it down there again. Then it travels to the middle of this second thread and due to its weight the thread takes a V like shape. There, it starts another thread, which it then ties down to some leaf or branch. So now we have a Y like shape. The three spokes of the web are ready. The next step would be to draw all remaining spokes from the center of Y in all directions, called radial threads. After completing the spokes it builds a spiral from center to outward. Then walking along that spiral again, it builds another spiral from outside which is sticky.

Now that we have a perfect orb-web, how do we know that it’s actually going to work. Let’s say a little insect flies into it, it may tear the entire web. So, to catch the insects, the web should be elastic. And it should be sticky too otherwise the insect may bounce off the web. And, the good thing is that the spiders have solution to all these problems.

We know that the spiral part of the web is sticky. When you zoom into these sticky silk thread, you will find a lot of bead like structures there, which are actually tangled threads inside a drop of liquid. The liquid is not just water but a sticky glue and hence it serves two purposes: the tangled threads of the spider silk inside the liquid gives it extra length, and it also helps in capturing the flying insects which stick to it.

In the end, let’s talk about the gossamer silk, another fine and very light silk produced by spiders. Some spiders use it to fly, which is known as spider ballooning. Spider first checks the air current using one of its legs and then shoots the silk threads. Within seconds it’s flying in the air. Although, it’s not quite obvious if spiders can actually control where the silk threads will take them, yet they cover very large distances.

This blog post is inspired by Silken Fetters, a chapter from Richard Dawkins’ awesome book, Climbing Mount Improbable

# Meeting a spiderling

While drinking tea this morning I noticed something moving on the dinner table. It was really tiny so also very cute. It was a “spiderling”, as I later found the exact word to call it by when I googled. It felt like she (or he?) is just now getting familiar with her abilities, like a superhero/girl getting out to test their superpowers. So as any superhero does, she jumped out of the table suddenly and now she was dangling down to the side of the table, the silk she was using was invisible but it was there. There was a breeze coming from the kitchen window, she started climbing towards the table again. A few moments later she jumped off again and started climbing down, I also knelt down to see her.

I find spiders quite scary but she was really small so there was not even a pinch of scariness. As I knelt down, she threw a few of her silk threads on my T shirt while she was still hovering in the middle of the air, hanging at half the table length. I could feel it because when I moved my hand she came towards me. Finally she was able to touch the floor and started moving towards the kitchen. I followed her for a few seconds and then decided to keep her somewhere safe. My tea was already finished, and I was also googling about how people feed their pet spiderlings.

It was hard to locate her because she was so tiny, I got scared that I would lose her trail, so I took out a glass from kitchen and laid it in front of her. To my surprise, she happily (not sure if she can actually feel anything like that) jumped inside. I kept a paper on top of it using tape to hold it in its place. I was a bit scared that it will be too hot for her inside the glass. But I couldn’t let her go so, kept her inside for sometime. I also started googling while watching her move around. I found that people buy special food for their spiderling pet.

I couldn’t identify her, but it felt like a tiny version of a jumping spider I had seen before, which is called Lynx spider but I’m still not sure. I also found that the best way to give water to your spiderling is by spraying it on their enclosure wall otherwise they will drown. I had a bit of water in my glass from night, and a pencil lying around. So I used the pencil to make small droplets of water and a bit of juice on the side of glass. She went towards the juice droplet and probably had a sip or two. I couldnt tell, because the droplet size was similar to her. After sometime, I decided that I wont be able to take care of her, because she would need to eat insects also. So I went out and lowered the glass on a leaf and she jumped out of the glass happily. I saw her for a bit and then she disappeared.

The life cycle of all spiders starts with eggs, then after hatching, the spiderlings mold many times to become full adult spider. So she still has to mold many times and grow.

# Dark Matter

One evening, out of curiosity I started watching a video lecture “Dark Matter and Galaxy Rotation” by Dr. Bob Eagle. After watching it, I got motivated to learn about this topic in a little more detail. I found a series of videos by theoretical physicist Sabine Hossenfelder on dark matter (Part 1, 2, 3) which are also really awesome. Another video showing a debate between scientists on similar topics was quite interesting to watch.

From classical mechanics, we know that the balance between sun’s gravitational force and centripetal force keeps the planets from flying away from their orbits. Assuming that all planets move in circular orbits we can equate these two factors, the gravitational force on the left and centripetal force on the right:

$\frac{G M_s m_p}{r^2} = \frac{m_p v^2}{r}$

$v^2 = \frac{G M_s}{r}$

According to this relation, the speed $v$ of planets decreases as their distance $r$ from sun increases. This inverse relation is visible in the graph below. Its also known as the rotation curve.

Now, if we see the rotation curve for a galaxy we would expect it to be similar. But that’s not what was observed. The rotation curve of different galaxies show this similar property that the velocity of stars does not decrease as we move away from the galactic center.

As per the relation, if the distance from the center increases, the velocity of stars should decrease but it doesn’t. If the velocity of stars is as high as it has been measured then they should just fly off. Because the gravitational force from the stars is not enough to balance the centripetal force. We can assume that the mass keeps increasing as we move farther from the center so that the term $\frac{M}{r}$ remains constant. But if it is true then where is all the extra mass?

Surprisingly, when the mass of the different galaxies was calculated using gravitational lensing it was found to be greater than what was calculated from the total mass of the stars. This extra mass is now thought to spread evenly throughout the galaxy in halos and is called dark matter.

A very famous theory called MOND or Modified Newtonian Dynamics was used to explain this observation. It modifies Newtonian Gravity by assuming that at low accelerations, the relation $F \propto \frac{1}{r}$ should be used instead of $\frac{1}{r^2}$ but this theory has long been ruled out because of many reasons, one of them is that Newtonian gravity already works for planets and stars very well.

In the end, I would love to quote Sabine Hossenfelder:

Dark matter is a model which fits the data and observations to some extent and that’s how science works.

# Apparent size

Sitting at the dining table, once I was calculating how planets appear to the human eye from our planet. I was trying to calculate the angular diameter or apparent size of planets using trigonometry. I have no idea where that notebook is, but today, I found an awesome blog which gave me enough background to start doing some calculations again.

This time I am going to calculate the apparent size of ISS. I have seen it floating across the sky a few times.

Angular diameter, $\delta = 2 sin^{-1} \frac{D}{2d}$
$d$: Distance of ISS from Earth = $400 km$
$D$: Length of ISS = $109 m$
$\delta$: angular diameter of ISS = ?
$\delta = 2 sin^{-1} \frac{109}{2 \times 400 \times 10^3}$
$= 2 sin^{-1} (0.000136)$
$= 2 \times 0.0079 = 0.0156 \deg$
$0.0156 \deg = 0.9 arcminute$
Its almost equal to the apparent diameter given on Wikipedia, which is 1 arcminute.

Close your eyes and imagine yourself flying above the ground, up above the clouds, passing the satellites you see the blueness of the Earth.

Another blink and you are out of the solar system. You see millions and millions of rocks circling around and dancing under the force of Sun’s gravity.

Blink again and you are out of the galaxy. You see the shimmering stars spiraling around a singularity, which can only be seen if you somehow found a way to step into the fourth dimension. The so called black hole.

All the mysteries of the universe live either in the quantum world or inside a singularity. Let’s get out of here. Close your eyes, you have seen enough suns.

What you see now are the biggest structures discovered by humans so far. These are dancing and swirling threads, threads of light and matter. Cluster and superclusters of galaxies, forming filaments.

Blink again, and you will be in empty space, which ofcourse is only empty to your eyes. You wonder what’s beyond the universe. No matter how many times you squeeze your eyes you are still in the blackness of space.