I agree that the plan in the science fiction is not practicable due to radiation, over-heat, and other stuff, but to accelerate Earth to escape velocity does not need 97% of the Earth mass.
The following is a combination of my idea and revise of another guy’s calculations in english to prove this:
Use the following equation to solve the escape velocity of the Sun: 42.2km/s
The linear velocity of Earth Revolution: 29.9km/s
Therefore, the Earth needs to increase 42.2-29.9=12.3km/s to reach the sun escape speed. (Note that here is the algorithm for accelerating the Earth, not for launching rockets from the Earth, the calculation method is different from the third cosmic speed)
Ejecting speed of the earth engine:
It is estimated that the specific fusion of deuterium fusion is 1.500000 seconds and the exhaust velocity is 15000 km/s. (From “Introduction to Star Trek”, Chapter 7, Section 6)
Assume that the heavy element fusion engine and the ejecting speed is the same.
The amount of energy that is converted into energy in a nuclear reaction is very small, usually only a few thousandth of the total mass. The main consumption of the earth engine is to spray the particle stream generated by the reaction into space, so the mass lost in the nuclear reaction is ignored here, and only the mass of the sprayed working medium is calculated.
Principle: The rocket’s jet acceleration process obeys momentum conservation
M1/M2=0.00018 is the ratio of Earth mass after and before the acceleration:
In other words, when the earth accelerates to the speed of the sun’s escape, it loses about eight ten thousandths of its mass. Assuming that the Earth is a homogeneous sphere with a radius of 6400km, the entire surface of the Earth will be scraped off 1.728 kilometers. This is unbearable for the earth.
If you want to accelerate to the speed of light that is five times the number of light in the film, that is, 1,500 kilometers per second, you need to spray a dozen of the earth. This is equivalent to scraping off the surface of the earth more than 200 kilometers deep, and all known ecosystems, underground cities, and planetary engines will disappear.
If we consider the decelerating process in the story in order to enter the Centauri-Alpha system, another great mass must be consumed.
Although it is practically impossible, the sci-fi story of the Wandering Earth derived from the theoretical possibilities, built a magnificent engineering plan for us, describing a magnificent history of the struggle between man and nature and warm praise. The spirit of human beings will never admit defeat. From the grandeur of imagination, the deep description of human nature and society, and the inspiration of the novel itself, this novel and film are masterpieces in the history of science fiction.
P.S. The calculations are not precise. I will do another english version with better format when I have spare time latter.
As @YangYe said,
The rocks in Earth have great varieties of composition and most of them are composed of silicate I expect, which are composed of Silicon, oxygen, and some light metals. Though they may cannot be used efficiently but theoretically they make the production. As we can see in the specific binding energy curve @dnk1234567 has referenced, before Fe there is still many elements doable for fusion, though not at a very steep slope. (which means they are not as efficient as H to He)
I am looking forward to see how Gregtech can incorporate these futuristic ideas. They are fantastic, and we should be more open-minded and innovative when receiving suggestions like this one. Thank you, @YangYe .
At last, I really recommend you to read The Wandering Earth novel. It farbics a much broader, deeper meaning of its universe, with humanities values.