Has a heavier atmosphere and the relocation of oil around the Earth had a measurable effect on the rotation of the Earth?

Question

I am wondering if the man-made carbon emissions put in the Earth's atmosphere over the past 100+ years, and also the relocation of oil around the Earth over this same time period, has had any measurable effect on the rotation of the Earth.

By mankind extracting oil located deep in the ground and from under the ocean floor, the mass of this oil has thus been moved farther away from the center of the Earth. Its mass has also been moved farther away from the center of the Earth by it being put high into the Earth's atmosphere via the injection of carbon emissions into it from oil & gas burning sources such as electrical power plants, cars, airplanes, etc. As far as I know, this has resulted in the Earth now having a heavier atmosphere than it had 100+ years ago.

So, I am wondering if all this oil mass/weight transfer away from the Earth's center may have had a measurable effect on the Earth's rotation, due to the Law of the Conservation of Angular Momentum, perhaps causing a slight slowing or increase in its rotational speed over the past 100+ years.

Moreover, I am also wondering if by slightly changing the mass of each of the Earth's continents, due to the relocation of trillions of tons of oil between the Earth's continents by oil tankers over the past 100+ years, has somehow also had a measurable effect on the Earth's rotation.

Has a heavier atmosphere and the relocation of oil around the Earth had a measurable effect on the rotation of the Earth?

Answer 1

The effect is minuscule, because:

• Oil and gas and coal do not come from "the center of the Earth", they come from relatively close to the surface. The deepest oil wells in existence are "only" 10–12 km deep.
• The mass of the carbon emissions since 1750 has been very small compared to the mass of the Earth. One figure I found with some quick Googling is 1.5 trillion tonnes of carbon dioxide, or $1.5 \times 10^15$ kg; but the mass of the Earth is about $6 \times 10^{24}$ kg, or four billion times greater.

Overall, you would expect the fractional change in the Earth's rotation rate to be inversely related to the change in its moment of inertia; and that will be about $$ \frac{\Delta I}{I} \approx \frac{2 m_\text{oil} r_E \Delta r_\text{oil}}{\frac{2}{5} M_E r_E^2} = 5 \frac{m_\text{oil}}{M_E} \frac{\Delta r_\text{oil}}{r_E} $$
where $M_E$ and $r_E$ are the mass and radius of the Earth, respectively. Plugging in $\Delta r_\text{oil} \approx 20$ km (from 10 km below the surface to 10 km above), we get a fractional change of $4 \times 10^{-12}$, or about one part in 250 billion. And the true number is likely to be even smaller than this, because:

• Most fossil fuels were not mined from 10 km beneath the Earth, but from a much shallower depth; and
• The mass I found above was for carbon dioxide, and much of the oxygen in carbon dioxide emissions was already present in the atmosphere.