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Oil underground is much denser than greenhouse gas in the atmosphere.

Does the conversion in anyway effect the gravitational force from earth.

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Comment to the question (v1): In such type of questions, OP is encouraged to perform a crude back of an envelope calculation as a sanity check, and possibly include it in the post. – Qmechanic May 15 '14 at 12:46
up vote 8 down vote accepted

As Hoytman points out, fossil fuel combustion does not change the mass of the earth, and so its gravitation with celestial bodies is unchanged. But moving mass from the subsurface to the atmosphere would slightly decrease surface gravity.

Let's see whether that decrease would be measurable. Let's suppose that, in some dystopian future, fossil fuel combustion has removed so much material from underground that the surface collapses and the radius of the entire earth $R_\oplus \approx 6\times10^6$ m shrinks by a meter. The volume beforehand was $$ V = \frac{4\pi}3 R_\oplus^3 $$ and the change in the volume is $$ dV = 4\pi R_\oplus^2 dr $$ We'll pretend that the earth was a uniformly dense sphere before and after. In that case the fractional change in local gravity $dg/g$ is equal to $dV/V = 3dr/R_\oplus \approx \frac12\times10^{-6}$. This is about ten times smaller than the uncertainties on $G$ and $M_\oplus$, so it's safe to conclude that even in this extreme case the gravitational shift you're asking about wouldn't be measureable.

A fastidious reader might note that if the earth actually shrank as the mass moved to the atmosphere, the effect would be even smaller: also changing the denominator of $g=GM_\oplus/R_\oplus^2$ reduces the size of the effect to $1\times dr/R_\oplus$.

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To be super pedantic, the mass of the Earth IS changed by an amount equal to (chemical binding energy used + excess thermal energy radiated to space)/$c^{2}$ – Jerry Schirmer May 15 '14 at 14:53
Whether the change in chemical binding energy is larger or smaller than $10^{-6}$ of earth's mass is left as an exercise to the reader :-) – rob May 15 '14 at 15:00
you could almost say his pedantry sucked, just by an infinitesimal amount – John Nicholas May 15 '14 at 15:55
@JerrySchirmer The chemical binding energy isn't destroyed, it just lingers as heat, retaining its mass, (unless of course, you are including it in the energy radiated to space, but then adding it would be redundant.) – PyRulez May 15 '14 at 22:05

Because gravity is a property of mass and mass is neither created or destroyed when fuel is burned, the only measurable difference would be caused by the change in the location of the mass. When fuel is burned, mass is taken from the surface of the planet and added to the atmosphere. this would cause a (slight) reduction in the downward gravity felt by objects on the planets surface. As you move away from the surface of the planet (both up and down) the difference would shrink.

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This is a pretty academic exercise. The calculation ignores the many side effects to the conversion. Depending on the composition of the oil, you will need to consider atmospheric pollution leading to a greenhouse effect. The atmosphere would contain more water vapour which impacts on atmospheric pressure. While total mass of earth plus atmosphere is the same, surface gravity as well as surface pressure will change. The change in surface pressure would be more noticeable than the change in surface gravity.

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