# Change in earth mass since the time of the dinosaurs

Is there a significant difference in the mass of the Earth between now and the time of the dinosaurs (250 - 75 million years ago)? I was just wondering if the force of gravity on dinosaurs would have been significantly less when they were around.

I gather, but may be wrong, that the mass of earth at present increases by around 108kg/day. All else being equal, one would expect the earth to have gained a mass, since 75 million years ago, of:

$$75^6 \times 365 \times 10^8 kg = 6.496 \times 10^{21} kg$$

The current mass of Earth according to Wikipedia is 5.97224kg, so if my math is correct, the change since the time the dinosaurs went extinct would be less than 0.1%.

Is my math correct here? If it is, would the change in the mass of the Earth over this period of time have had any noticeable effect on weight from its gravity?

• Where did you get the information about the mass increase? – user889 Mar 3 '15 at 19:50
• Meteorites, perhaps? – Gimelist Mar 3 '15 at 20:00
• @SabreTooth - Google, but I lost the original link. In looking for it again though I did find this topical page: universetoday.com/94392/… – Brian M. Hunt Mar 3 '15 at 21:48
• @BrianM.Hunt very interesting article! Quite a compelling question - the article has hints to an answer as well. – user889 Mar 3 '15 at 21:54
• Your mass-increase calculation is given incorrectly. The number on the left shouldn't be $75^6$, it should be $75 \times 10^6$. And please cite a source for your daily increase of $10^8$ kg – 410 gone Mar 4 '15 at 11:32

I gather, but may be wrong, that the mass of earth at present increases by around 108kg/day. All else being equal, one would expect the earth to have gained a mass, since 75 million years ago, of:

$$75^6 \times 365 \times 10^8 kg = 6.496 \times 10^{21} kg$$

First off, that should be $$75\times10^6$$, not $$75^6$$. That alone makes your estimate high by a factor of 2373. Correcting this error, the mass gain is only $$2.7\times10^{18}$$ kg, rather than $$6.5\times10^{21}$$ kg.

Secondly, I've never seen anywhere close to that magnitude of mass gain. The article you cited in a comment gives a range of 5 to 300 metric tons per day. Your value of $$10^8$$ kilograms per day is 100000 metric tons per day, which is high by at least a factor of 333 (and up to 20000). With this, the mass gain is between $$1.5\times10^{14}$$ and $$8.2\times10^{15}$$ kg. This seems big, but it's tiny compared to the mass of the Earth.

Thirdly, you are ignoring atmospheric losses. Almost all of the atmospheric losses are in the form of hydrogen and helium. Most of the lost hydrogen results from water vapor that makes its way from the surface of the Earth into the stratosphere and is dissociated. Most of the lost helium results from radioactive decay in the Earth. Both forms of atmospheric loss represent a decrease in the mass of the Earth. Estimates on this mass loss also vary widely, from 100 to 300 metric tons per day.

Putting these widely varying estimates together means the mass of the Earth is increasing by as much as 200 metric tons per day (+300 mass gain, -100 mass loss), or decreasing by as much as 300 metric tons per day (+5 mass gain, -300 mass loss, and since the numbers vary so widely, that's just -300). Either way, it's small potatoes, even over the course of 75 million years. This means g was between $$13\times10^{-9}\,\text{m/s}^2$$ smaller than it is now and $$9\times10^{-9}\,\text{m/s}^2$$ larger than it is now. Both of those numbers are very small.

• I have marked this as correct, but it would improve this answer to include citations for atmospheric loss (noting though those by @stall below). Cheers – Brian M. Hunt Mar 4 '15 at 15:06
• The estimated mass for Earth is $5.972 \times 10^{24} \text{ kg}$ (after quick check). The mass gain (or loss) gets even proportionally smaller. – carnendil Feb 8 '16 at 21:10

Earth loses more mass as gases (especially Hydrogen and Helium) escape the atmosphere. Also, the numbers you mention as well as the mass of the air that is lost likely has large error bars associated with them.

Edit: For example see here or here.

• Thanks for the response Stali. Great points. Before marking an answer like this correct, I would like to see the numbers for weight loss and gained over time and our sources for this. Cheers – Brian M. Hunt Mar 3 '15 at 23:55
• I have added some links. But again, without error bars the numbers don't mean much. – stali Mar 4 '15 at 2:14