# Does Earth's Gravitational pull increase with time?

Gravitational field depends on mass ($$g = \frac{GM}{r^2}$$) and every year many outside cosmic objects like asteroids or tiny object are hitting earth. So I think may be in a very microscopic amount the mass of Earth is increasing. But does it increase the Gravitational Pull or Gravity on Earth?

And also, does it result in decrease in height of organisms in each century? Because some older people say that people in their time or in ancient times were taller and more aged. I am just curious if it is the reason or not.

• Have you tried to estimate the effect by a back-of-an-envelope-calculation? May 23 '20 at 13:33
• Some interpretations of ancient Hindu scriptures claim that people in ancient times were extraordinarily tall, and had immense life spans of many thousands of years. Such claims are not consistent with modern science. en.wikipedia.org/wiki/Yuga May 24 '20 at 13:42

Actually the opposite is true.

• Earth gains about 40,000 tonnes of dust every year, the remnants of the formation of the solar system, which are attracted by our gravity and become part of the matter in our planet. Our planet is actually made from all that starstuff.

• Earth's core loses energy over time. It's like a giant nuclear reactor that burns fuel. Less energy means less mass. 16 tonnes of that are gone every year. Not much.

• And here's the big mass loss: about 95,000 tonnes of hydrogen and 1,600 tones of helium escape Earth every year. They are too light for gravity to keep them around, so they get lost. Gone into space.

So, summing all these effects mentioned above, you get a mass loss of 57,000 tonnes per year.

But this is still much too small to have a measurable effect on gravity ($$g = GM/r^2$$) even after millions of years, because the mass of the earth is $$M = 6\cdot 10^{24} \text{ kg}$$ (i.e. 6,000,000,000,000,000,000,000 tonnes).

• I think the 2nd point in that Gizmodo quote is potentially misleading, in particular "It's like a giant nuclear reactor that burns fuel". Yes, the Earth loses some mass because the surface radiates heat which has migrated out from the interior. There's still quite a lot of residual heat from the Earth's formation, and some is from radioactive processes in (mostly alpha decay, rather than fission like in a reactor), but there's not much of that happening in the core, which is mostly iron & nickel, which aren't radioactive. May 23 '20 at 15:39
• (cont) A major heat source is from the freezing of the liquid outer core onto the solid inner core, which releases a lot of latent heat. See physics.stackexchange.com/a/154514/123208 for details. May 23 '20 at 15:40
• @AishwaryaShiva What do mean by "they are very light"? A ton of hydrogen as just as heavy as a ton of rock. The hydrogen lost from upper atmosphere will soon be replaced by hydrogen from somewhere down. May 24 '20 at 19:39
• @AishwaryaShiva The mass of the atmosphere has no effect on the gravitational pull at the surface, that's because of the shell theorem. May 26 '20 at 11:52
• @AishwaryaShiva The effect on gravity of changes to the Earth's mass over time is tiny. Even over a billion years (assuming the mass loss rate over that period was roughly constant) the difference to the surface gravitational acceleration is about 1 part in 100 million. There's some more info about the variation in the Earth's mass on Wikipedia. The variation in the Earth's radius is similarly negligible. May 26 '20 at 11:56