This article is from the WeChat public account: Nutshell (ID: Guokr42) , author: matrix star
Just this week, the U.S. stock market suffered a major crash, all three major stock indexes fell sharply, and the fuse mechanism was triggered twice in a week. Among them, the Dow Jones Index fell more than 4,000 points, breaking multiple historical records.
When the stock market crash came, many netizens turned out a tweet allegedly sent by US President Trump during the 2015 election campaign: “If one day the Dow Jones Index plummets more than 1,000 points, the then president It should be loaded into a cannon and fired at the sun at a very fast speed. No excuses can be found! “
However, the major media quickly broke the rumor. Twitter is actually a p-map of netizens. Trump himself has not established such a flag. Nevertheless, the question mentioned in this fake Twitter is very interesting-how big cannon do we need to launch a person from the earth to the sun?
To discuss this issue, let’s assume that there is a classmate named Ogawa whose dream is to design a cannon and shoot himself towards the sun 150 million kilometers away.
Track of classmate Xiaochuan
Let’s imagine what the process of a cannon firing Ogawa into the sun is like.
The first step is to prepare the cannon and let Ogawa climb into the deepest part of the barrel. boom! Ogawa flew out of the gun barrel in an instant.
Cannon launches Ogawa | Soul Painting Hand Flute
Under normal circumstances, Ogawa will soon fall back to the ground after flying heavily. But because the cannon was powerful enough and fired fast enough, Ogawa had never landed, and was flying farther and farther, showing no sign of stopping the atmosphere.
After flying for several days, Ogawa can’t see the earth at all, and she finally got rid of the shackles of the earth’s gravity. However, because he had been attracted by the gravity of the earth before, his speed was also much slower than when he was out of the barrel.
Ogawa flew out of the earth, and finally got rid of the gravitational restraint of the earth | Soul painting hand flute
After bidding farewell to the earth, Ogawa decided to use the sun ’s gravity to fly to the sun.
When he first flew from the earth, Ogawa was more than 100 million kilometers away from the sun. According to Newton’s law of gravity, he will slowly approach the sun along the elliptical orbit under the attraction of the sun. During the flight, Ogawa may see Venus and Mercury, and sometimes several comets fly by., But he was lucky to avoid these obstacles.
Ogawa flies to the sun along an elliptical orbit | soul painting hand flute
After nearly half a year, Ogawa finally flew to the sun’s outermost corona. Facing the red fireball in front of him, Ogawa excitedly announced that he had realized his dream.
Ogawa flies to the solar corona, realizing her dream | Soul Painting Hand Flute
This is really a dream journey. However, the premise of all is that our cannon must be powerful enough to launch Ogawa fast enough to shoot him into the distant sun.
The question comes: How fast can cannon fire Ogawa to send him to the sun?
Warning, the following is the mathematical derivation!
If you are not interested, please read the last paragraph of this section directly!
We assume that Ogawa fired from the cannon at a speed of v.
In the first stage of the solar journey, because Ogawa was attracted by the earth, his flying speed will change from vSlowly decrease to v1 when finally free from the gravitational restraint of the earth.
Ogawa ’s mechanical energy is conserved while flying away from the earth. You may not know what “mechanical energy conservation” means, or you may not know why conservation, this is not important. Anyway, we can list the first equation accordingly.
Conservation of mechanical energy during Xiaochuan’s flight from the earth
Looking at the second stage of the journey, Ogawa orbits the sun in an elliptical orbit.
Ogawa was the farthest from the sun when he first flew out of the earth, with a distance of about 149.6 million kilometers; when he flew to the corona, he was closest to the sun, with a distance of about 6 million kilometers. Ogawa conserves mechanical energy and angular momentum in elliptical orbits. Based on these two “conservations”, we can list the second and third equations. In this way, we can calculate the speed v2 of Ogawa when it is farthest from the sun.
Conservation of mechanical energy and conservation of angular momentum during Ogawa’s movement around the sun
Why v2? Because the speeds v1 and v2 are related, knowing v2 can calculate v1. Both velocities are the speeds when Ogawa just broke away from the gravity of the earth, but v1 is relative to the earth reference system, and v2 is relative to the solar reference system. Earth’s orbital speed relative to the sunIt is 29.78km / s. From this, it can be found that v1 is 23.93km / s.
Find v1 using speed composition relationship
Substituting v1 into the first equation, we can find the velocity v when Ogawa was dislodged from the cannon.
Find the velocity v that Ogawa fired from the cannon is 26.42km / s
Note, the math derivation part is over!
Finally, our answer is 26.42km / s. Only at this firing speed can the cannon send Ogawa to the sun. Whisper: At this speed, it only takes about 40 seconds for Xiaochuan to fly from Beijing to Shanghai.
Xiaochuan takes only 40 seconds to fly from Beijing to Shanghai | Soul Painting Hand Flute
Launching the cannon needed by Ogawa
With the speed of launching Ogawa into the sun, the next step is to find a cannon based on this data.
How big is the cannon to shoot Ogawa into the sun? Considering the extreme conditions, we refer to the longest range cannon in human history-the Barbados cannon. This cannon is 36 meters long and 424 millimeters in diameter. It once hit 190 kilograms of shells at 180 kilometers in space at a muzzle velocity of 2100 meters per second.
Barbados Cannon | Sky and Telescope
The energy of the Barbados artillery to fire the shells is not enough to let Ogawa fly to the sun? We can compare the energy of Barbados projectiles and Ogawa’s movement, which is kinetic energy in physics, and it is related to the mass and speed of the object.
A simple calculation, we finally conclude that the kinetic energy needed by Ogawa to fly to the sun is 66.64 times the kinetic energy of the cannonball.
It’s far from enough!
The kinetic energy required by Ogawa is compared with the kinetic energy of the Barbados cannonball
It’s okay, let’s think about it again.
According to the principle of artillery firing shells, gunpowder will cause rapid expansion of gas after being ignited. The inflated gas did work on the shell in the barrel and finally fired the shell. The easiest way to increase the speed of the projectile is to lengthen the barrel, so that the gas can work longer in the barrel.
In other words, if we want to use the Barbados cannon to shoot Ogawa into the sun, we need to expand the barrel length at least 66 times. Barbados’s barrel is about 36 meters, its 66.64 times is … 2400 meters.
What is this concept? Stand the gun up to 7.4 Eiffel Towers.
Barbados’ barrel requires 7 Paris Towers so tall | Soul Painting Hand Flute
The length of the barrel is afraid that it will not be able to withstand the pressure when it is half-built, and it snaps off. Even if we can really make a 2,400-meter gun barrel, it would take a lot of time for Ogawa to slide to the bottom of the gun barrel, and when firing, he would be pushed by the gas all the way for two kilometers.
Considering the comfort of Ogawa ’s journey, we had better find him a cannon with a slightly shorter barrel.
After some searching, we decided to replace the Barbados artillery with one of the largest artillery ever made by humans-the Gustav Cannon. The Gustav Cannon is a super cannon manufactured by the Nazis during World War II. It can be called a giant among ground weapons. It has a total length of 42 meters, a barrel of 32 meters, an armor-piercing shell weighing 7 tons, and a gun.The initial velocity can reach 0.72km / s.
Gustav Cannon during World War II | Wikimedia Commons
Gustav Cannon Model | Wikimedia Commons
Repeat the above calculation steps, we were pleasantly surprised to find that the kinetic energy needed by Ogawa is only 15 times more than the kinetic energy of the Gustav Cannonball!
The kinetic energy required by Ogawa is compared with the kinetic energy of the Gustav cannonball
The length of the Gustav cannon is 32 meters, which is only 492 meters when multiplied by 15.39, which is about 1.6 Eiffel Towers high. Compared to the 2,400 meters of Barbados artillery, this barrel can be said to greatly reduce the suffering that Ogawa suffered while staying in the barrel.
If you fire Ogawa with a Gustav cannon, there is another benefit. The barrel diameter of the Gustav cannon is 800 mm, which is several times larger than that of a normal cannon. A little fat Ogawa does not need to worry that he will not get into the barrel of the Gustav cannon. .
Gustav’s barrel needs only one and a half towers of the Eiffel Tower | Soul Painting Hand Flute
It seems that as long as we can reconstruct a 492-meter Gustaf cannon, we can successfully realize Ogawa’s dream of being shot by the cannon towards the sun.
Someone may ask, during the firing of the cannon, the temperature of the barrel can reach hundreds of degrees Celsius, and the solar corona that Ogawa is going to go to is more than 1 million degrees Celsius. How can he withstand such high temperatures? That was of course borrowing NASA’s protective clothing with Trump next door.
Image source: Washington Post
Finally, let’sLet’s review the wonderful journey of Ogawa to the sun again:
Ogawa’s Bizarre Adventure | Soul Painting Hand Flute
[[1] https://en.wikipedia.org/wiki/Schwerer_Gustav
[2] https://en.wikipedia.org/wiki/Project_HARP
[3] https://en.wikipedia.org/wiki/Muzzle_velocity
[4] https://www.warhistoryonline.com/war-articles/schwerer-gustav-hitlers-giant- gun-worked-turned-disaster.html
This article is from the WeChat public account: fruit shell (ID: Guokr42) , author: matrix Star