School competence of physics and astronomy at war

On September 1 Ukraine is celebrating the Day of Knowledge. This year we are doing it just in the midst of a full-scale war. School mathematics, physics and astronomy can be really useful to the military. Today we will tell you how school subjects help bring our victory over Russia closer.

Шкільні фізика та астрономія можуть стати у нагоді на війні
Even astronomy can be useful at war. Source:

Comprehensive mathematics

Witnessing the full-scale invasion of Russia into Ukraine, we can distinctly see quality winning over quantity. That is, a smaller, but more educated and motivated army offers exemplary resistance to a huge foe’s hordes. In the modern war, the victory is the result of the ability to think logically, to analyze swiftly the situation on the battlefield, and to calculate your forces and capabilities. Mathematics teaches all of this. It permeates everything.

Basic math is needed by the tank crew to calculate how much fuel they will use for that day’s maneuver. It is necessary for the commander who orders ammunition for the next few days. A clear calculation is also needed in order to place it in such locations and in such a quantity that the losses in case of enemy’s hit would be minimal, while there is always enough ammunition for your own soldiers.

Від знання математики залежить життя саперів
Detonation using a blaster fuse. Source:

And sappers, for example, need to be able to calculate the amount of explosives to detonate an obstacle or unexploded ammunition. If, for example, a blaster fuse is used, then an error in calculating its length can cost lives.

How to determine the distance to the target?

The complex and dull science of trigonometry can also be useful on the battlefield. In particular, it allows you to determine the distance to the target using ordinary binoculars. Lines in the field of view of military models of this optical device show how many mils an enemy soldier or tank covers.

Mil (or milliradian) is an artillery measure of an angle equal to 1/1000 of a complete circle. Knowing approximately the height of a person and the height of military equipment and how many mils it covers, you can use a simple formula to determine the distance to these targets with fairly good accuracy.

Формула тисячної
The mil formula and its application (l is a length of the tank; u is the angle covered by the tank as it is visible in binoculars). 

Army also knows the method of determining distances without binoculars or another protractor. For this, their own hands and objects are enough. For example, the width of the index finger of a person at arm’s length covers 0.3 mils, of the thumb – 0.4, and the length of a matchbox – 0.9.

Artillery physics problems

Physics is generally a military science. For example, the most famous equilibrium problem describes a projectile flying out of a cannon barrel and traveling a certain distance, overcoming gravity and air resistance. In reality, these calculations are usually reduced to simpler formulas or are generally entrusted to the computer, but every artilleryman should know the general principle of the calculation.

These skills are especially relevant for mortars. After all, in this case, the range of the shot is often regulated by installing additional charges on the mine. Here, the knowledge of physics allows you to calculate what additional force the charge should create in order to hit the target at a greater distance.
A school problem in physics can be extremely relevant for artillerymen. Source:

Physics also allows us to understand the maximum distance a HIMARS rocket can fly. Here it is worth knowing not only the rules of adding forces and Newton’s three laws — the law of conservation of momentum will also come in handy. After all, all rockets fly by accelerating the products of fuel combustion in one direction, and the rest of the rocket — in the other. So, knowing the mass of one and the other, you can calculate the maximum flight range.

Military astronomy

Even a science as unworldly as astronomy can easily be applied to military needs. If only because the habit of looking at the sky and determining the positions of objects on it helps you to see enemy aircraft in time.

The most obvious application of the knowledge provided by astronomy is the prediction of the motion of the Sun and Moon. Despite the proliferation of night vision devices, ground reconnaissance mainly operates at night. Understanding that twilight and complete darkness at different latitudes and longitudes come at different times allows you not to catch the enemy’s eyes.

Also, knowledge of the phases of the Moon and even its position in the orbit can be useful for scouts. After all, if the night is clear and the Moon is full, and it is at perigee, the night can turn out to be fatally bright.

The planets of the solar system cause great problems for many people who do not know astronomy. The fact is that they are much closer to us than stars, so they have quite large disks. Atmospheric distortions of light coming from different parts of these disks are mutually compensated, due to which the planets almost do not flicker. Because of this, to many people they may seem like lanterns on unknown aircraft. Venus and Jupiter were especially unlucky in this regard: except for abovementioned absence of flickering, these heavenly bodies are also very bright. During the large-scale invasion, there were repeated attempts from both sides to shoot them down, including with the help of expensive MANPADS.

Астрономія рятує від витрачання боєприпасів на стрільбу по Юпітеру
Jupiter in the night sky. Astronomy saves you from wasting ammunition shooting at Jupiter

Space and time given by astronomy

Since 2014, Russia has been actively trying to jam GPS signals, thereby trying to deprive the Ukrainian military of the opportunity to learn about locations and exact time. They usually fail to do this, but just in case, it should be remembered that it is astronomy that makes it possible to determine both without the help of satellites.

In this regard, it is easiest to determine the cardinal directions. It must be remembered that the Sun, the Moon, all the planets and stars that appear from beyond the horizon in the east, then deviate from the zenith to the south, and set in the west (it all concerns the Northern hemisphere, where Ukraine is situated).

It is also useful to remember that, unlike moss, which actually grows on trees as it pleases, the Pole Star in the Northern Hemisphere always points in the direction of the corresponding pole. And don’t forget that the positions of the magnetic and geographic poles are markedly different.

Застосування секстанта
Navy around the world still use the sextant. Source:

A more accurate way of determining time and location requires an instrument called a sextant. In fact, it is a protractor that allows you to determine the height of a celestial body above the horizon. Most often, for this purpose, the Sun is used during the day and the Pole Star (α Ursa Minor) at night. But the presence of appropriate tables allows you to use almost any bright star as a means of navigation.

At the same time, it is worth remembering that it works both ways. That is, knowing the exact time and astronomical parameters of the celestial body, you can always determine your coordinates. And knowing the exact coordinates and position of a heavenly body, you can find out the time.

In addition to the direct practical application of knowledge, education disciplines the mind and makes it more flexible. Difficult tasks teach us to think outside the box and to look for at least two ways to solve the same problem. Liberal arts teach us not to be brutalized and to preserve ourselves in the midst of this horror. War has long ceased to be about the number of soldiers on the field. It has become a high-tech science and needs sober intelligent soldiers.