Know your enemy.
Earth Data
- Names: Earth, Terra, "the world"
- Age: 4,550,000,000 years
- Mass: 5,974,200,000,000,000,000,000 metric tonnes; this increases by 10,000 to 100,000 tonnes daily due to the accumulation of meteorites and interplanetary dust
- Radius: 6,378.1 km
- Surface gravity: 9.798 m s-2
- Escape velocity: 11,186 m s-1
Simplified physical structure
| Crust | 0 to 35km | Rock, hard and soft sediments, ice, miscellaneous | 0 to 1000°C |
| Mantle | 35 to 2900km | Oxides of silicon, magnesium, iron and aluminium | 1000 to 3700°C |
| Core | 2900 to 6371km | Iron (liquid, turning to solid at 5150km) | 3700 to ~5000°C |
Chemical composition by mass
| Iron | 34.6% |
| Oxygen | 29.5% |
| Silicon | 15.2% |
| Magnesium | 12.7% |
| Nickel | 2.4% |
| miscellaneous | 5.6% |
The rest are all in the standard SI kilogram-metre-second system since it makes the working infinitely easier. You can most likely convert to kilometres and tonnes in your head, and converting to tons and miles is a simple job for the Google Calculator.
Orbit characteristics
- Mass: 5.9742 × 1024 kg
- Distance from Sun: 149,595,000,000 m
- Orbital period: 31,556,926 s (365 days, 5 hours, 48 minutes, 46 seconds)
- Orbital velocity: 29,780 m s-1
- Orbital momentum: 1.7789 × 1029 kg m s-1
- Orbital kinetic energy: 2.6488 × 1033 kg m2 s-2
Rotation characteristics
- Radius: 6,378,100 m
- Sidereal rotation period: 86164.1 seconds (23 hours, 56 minutes, 4.1 seconds - this is not to be confused with the length of a day, which is precisely 24 hours)
- Angular velocity: 0.0000729211 rad s-1
- Moment of inertia: 9.6987 × 1037 kg m2
- Angular momentum: 7.07236 × 1033 kg m2 s-1
- Rotational kinetic energy: 2.5786 × 1029 kg m2 s-2
Earth-Destruction Data
The energy required to destroy the Earth varies by method. It also varies depending on what existing "free" energy you are using. For example, burning the Earth up in the heart of the Sun takes a lot of energy, but since all that energy is freely given out by the Sun, we don't need to figure out how to generate it - just the energy needed to get it there in the first place.
Cooked in a solar oven
These calculations are all exceedingly approximate.
- Surface area of Earth: 5.112 × 1014 m2
- Black-body temperature of Earth: ~287 K
- Power radiated by Earth: ~1.966 × 1017 kg m2 s-3
- Black-body temperature of Earth after being completely boiled: ~3134K
- Power radiated by Earth at this temperature: ~2.796 × 1021 kg m2 s-3
- Ratio of these two powers: 1 to ~14,000
So if the surface area of Earth were increased by roughly 14,000 times, it would be completely reduced to a gas.
- Cross-sectional area of Earth: 1.278 × 1014 m2
- Necessary area of mirror: ~1.80 × 1018 m2
Blown up/deconstructed/smashed to pieces/overspun/etc.
The minimum amount of energy required to directly destroy the Earth in situ is equal to the Earth's gravitational binding energy:
- Gravitational binding energy of the Earth: 2.2405 × 1032 kg m2 s-2
In the case of the antimatter method all that energy will be generated from the lossless conversion of equal parts of matter and antimatter to energy.
- Mass of matter and antimatter required to blast the Earth apart: 2.4928 × 1015 kg
- Mass of antimatter: 1.2464 × 1015 kg
Hurling the Earth into the Sun
To do this we simply need to cancel out all of the Earth's current orbital kinetic energy. This is already calculated above...
- Orbital kinetic energy = 2.6488 × 1033 kg m2 s-2
- Energy output of the Sun, for reference = 3.86 × 1026 kg m2 s-3
Moving the Earth out to Jupiter
- Mass of the Sun: 1.98892 × 1030 kg
- Distance of Earth from the Sun: 149,595,000,000 m
- Gravitational potential energy of the Earth at this point: -5.3003 × 1033 kg m2 s-2
- Distance of Jupiter from the Sun: 778,570,000,000 m
- Gravitational potential energy of the Earth at Jupiter: -1.0184 × 1033 kg m2 s-2
- Potential difference: 4.2819 × 1033 kg m2 s-2
- The Earth's existing kinetic energy = 2.6488 × 1033 kg m2 s-2
- The difference which we need to make up = 1.6331 × 1033 kg m2 s-2
Practically speaking there may be ways to cut down the figures from the previous two methods by judicious use of things like gravity assists (get free energy from a passing planet e.g. Venus, Mars).
Constants and formulae I used
- The ratio of a circle's circumference to its diameter, π = 3.14159265...
- The gravitational constant, G = 6.67300 × 10-11 m3 kg-1 s-2
- The speed of light, c = 299,792,458 m s-1
- The Stefan-Boltzmann constant, σ = 5.670400 × 10-8 kg s-3 K-4
- Escape velocity = sqrt(2GM/r), where G is the gravitational constant, M is the Earth's mass and r is its radius
- Orbital velocity = 2πr/T, where r is the orbit's radius and T is the period of one orbit
- Momentum = Mv, where M is the Earth's mass and v is its velocity
- Kinetic energy = (1/2)Mv2, where M is the Earth's mass and v is its velocity
- Angular velocity = 2π/t, where t is the period of one rotation
- Moment of inertia = (2/5)Mr2, where M is the Earth's mass and r is its radius (assumes the Earth is a sphere)
- Angular momentum = Iω, where I is the Earth's moment of inertia and ω is its angular velocity
- Rotational kinetic energy = (1/2)Iω2, where I is the Earth's moment of inertia and ω is its angular velocity
- Gravitational potential energy = -GMm/r, where G is the gravitational constant, m is the mass of the object whose potential we are determining, M is the mass of the object whose gravitational field we are sitting in, and r is the distance between them
- Gravitational binding energy = (3/5)GM2/r, where G is the gravitational constant, M is the Earth's mass and r is its radius
- Einstein's mass-energy equation, E = mc2, where E is energy, m is mass and c is the speed of light
- The Stefan-Boltzmann law: P = σAT4, where P is the power radiated by a perfect black body, A is its surface area and T is its temperature