What would the orbit of the Earth be like if we constantly sent our waste to the Sun?
Let's say we get a cheap technology to collect and then send (hypothetically all) our waste to the Sun by a rocket, and we choose this technology as the main (and only) method to utilize our waste.
What would the orbit of our planet be like after years of using this technology, as in the Earth-Sun kinetic-potential system, the Earth is continuously sending its mass to the Sun?
Or will that mass sent from Earth to the Sun return to the Earth in a form of irradiated energy and we (i.e. our descendants) will feel no effect?
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What Shihab Dider said. The Earth is monstrously massive compared to everything humans have ever built, and the Sun is monstrously massive compared to the Earth.
How monstrously massive are we talking about here? The mass of the Sun is about 1.99 $\times$ 1030 kilograms. The mass of the Earth is about 5.97 $\times$ 1024 kilograms. To put that in perspective . . . Well, perhaps it's best if we don't. Six orders of magnitude is quite a lot. Adding an entire extra Earth mass to Earth would barely change its orbit.
How much waste do we generate? Well, it depends on what you define as "waste." Garbage, feces, uneaten food - all could fall in this category. According to Duke University, a human (on average) generates 4.3 pounds (or 1.95 kilograms) of waste per day. I think that's only for Americans because stats from the EPA match it nicely, but we'll extrapolate it to the world, just to give a worst-case scenario (this is also interesting).
1.95 kilograms per person $\times$ about 7 billion people = 13.65 $\times$ 109 kilograms of waste per year. In other words, if we were to bring all this waste to the Sun, the Earth would lose only 1/1014th of its mass each year (not counting the spend rocket fuel). That translates to a change in orbital radius of . . . oh, something very small. You can do the exact math, if you want.
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