Could we Shoot our Trash Into Space, or Would Losing all that Mass affect the Earth’s orbit?
Nah — for a couple of reasons. One, we wouldn’t possibly find enough fuel. Let’s take a look at how much energy it takes to send things into “outer space”.
The escape velocity of Earth is roughly 12 km/s. You need to get something moving to the equivalent of 12,000 meters per second to escape the gravity well of the Earth in order to get it to fly away from our planet for good (it would tend to take much more energy than this to slow it down enough to fall into the sun — the Earth is orbiting around the sun at about 30 km/s).
The formula we’ll use to find this is the Newtonian formula for kinetic energy (it’s accurate for things travelling much much slower than the speed of light):
F = 1/2 * mv²
Let’s see how much it would be for a kg (2.2 lbs on Earth):
F = 0.5 * 1 * 12,000²
F = 0.5 * x * 144,000,000
F = 72,000,000 joules
There are about 6,000,000,000 joules in a barrel of oil, so, more than enough, right? Since there is about 160 liters of oil in a barrel, that means you’d only need about 2 liters of oil to get a kg of garbage up high enough to escape Earth’s orbit.
But wait… that 2 liters of oil has a mass of about 2 kg, and the space ship to get the trash and fuel up there is made of metal. So you need even more fuel to get that fuel up high enough so it can be burned to provide the energy necessary to push your payload out further.
We do have fuels which are a little more energy-dense than crude oil, but this is still a fundamental problem — the weight of the fuel needed to send things into space, must also be accelerated into space. When we send things into space — even low Earth orbit, most of that weight is fuel, and most of that fuel is used to get the rest of the fuel up toward orbit as well.
Let’s take a look at NASA’s space shuttle for an example:
The Space shuttle itself weighed 165,000 pounds empty. Its large reddish-orange external tank weighed 78,100 pounds empty, and its two solid rocket boosters weighed 185,000 pounds empty each.
Each solid rocket booster held 1.1 million pounds of fuel, though, and the primary external tank held a quarter million pounds of hydrogen, and 1.4 million pounds of liquid oxygen, for a combined fuel weight of 4.4 million pounds. The fuel was about 20 x heavier than the shuttle, and the maximum payload of the shuttle was 65,000 pounds. A typical garbage truck can hold about 50,000 pounds of trash, so that’s more than 2,000 tons of fuel, to send each garbage truck worth of garbage into space.
The USA alone produced 167 million tons of garbage that it did not recycle, in 2013. So just the USA would need to send 1 NASA shuttle into space, every 10 seconds, to using 19 million tons of fuel per day, to carry away all of its garbage.
Now, to looking at your original question, the world as a total produces a little more than 2 billion tons of garbage per year. That would take around 65 million NASA shuttles, using 137 billion tons of fuel each year to toss off of our planet. Let’s round up to an even 150 billion tons to include the shuttles or fuel tanks if we don’t get them back, or drop them back to burn up into the atmosphere.
How does that compare to the world? 5,972,000,000,000,000,000,000 tons. So, after a year, we’ll only weigh 5,971,999,999,850,000,000,000 tons, after a million years, we’ll weigh 5,971,850,000,000,000,000,000 tons, only 0.0025% lighter!
We would lose 1% of the mass of the Earth after about 400 million years (assuming we had unlimited fuel and resources to even be making all this garbage)… So, what would happen to our orbit after hundreds of millions, or billions of years? Well… nothing! Why? Because, although the Sun would be “pulling” on the Earth less, due to the Earth having less mass, the lower-mass Earth would be affected by the gravitational pull of the sun, by the same difference, causing no change in its orbit around the Sun! This is a similar principle to what Galileo showed us, how objects fall the same speed, regardless of their mass.
