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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.

PNS
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Aishwarya Shiva
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    Have you tried to estimate the effect by a back-of-an-envelope-calculation? – Qmechanic 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. https://en.wikipedia.org/wiki/Yuga – PM 2Ring May 24 '20 at 13:42

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Actually the opposite is true.

Quoted from Gizmodo - Did You Know That Earth Is Getting Lighter Every Day?:

  • 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).

Thomas Fritsch
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    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. – PM 2Ring May 23 '20 at 15:39
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    (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 https://physics.stackexchange.com/a/154514/123208 for details. – PM 2Ring May 23 '20 at 15:40
  • @PM2Ring wouldn't the heavy radioactive metals also sink into the core (being even heavier than iron and nickel) and decay there? – Paŭlo Ebermann May 23 '20 at 23:49
  • @PaŭloEbermann That sounds reasonable, but if it were true then we wouldn't have such a large quantity of uranium in the crust. As David said in the answer I linked, "Most geochemists and geophysicists are of the opinion that there are but negligible amounts of radioactive elements [...] Uranium, thorium, and potassium are strongly lithophilic elements." That means they're chemically attracted to rock. David gives more details on the chemistry (with references) here: https://physics.stackexchange.com/a/144775/123208 – PM 2Ring May 24 '20 at 05:25
  • But does the big loss of hydrogen and helium really effect the gravity? And they are very light. So, if that's the case then it's gaining mass. Isn't it? – Aishwarya Shiva May 24 '20 at 19:22
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    @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. – Thomas Fritsch May 24 '20 at 19:39
  • @ThomasFritsch But what I mean is does that effect surface gravitational pull and what about radius of the earth? – Aishwarya Shiva May 26 '20 at 10:30
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    @AishwaryaShiva The mass of the atmosphere has no effect on the gravitational pull at the surface, that's because of the shell theorem. – PM 2Ring May 26 '20 at 11:52
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    @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. – PM 2Ring May 26 '20 at 11:56
  • @PM2Ring Ok got it. Last question: what about radius variation at different places on earth? Since Earth is not a perfect sphere and also how much change in gravity we will notice if all oceans are removed? Does deepest surface of oceans have less gravity when all water is removed? – Aishwarya Shiva May 26 '20 at 20:11
  • @AishwaryaShiva If the Earth were a uniform homogeneous ball, then yes, the gravity would be slightly lower on the ocean floor. But in reality, it's complicated. ;) See https://physics.stackexchange.com/q/18446/123208 for some info about how gravity varies with depth. And see https://en.wikipedia.org/wiki/Geoid for some info & nice diagrams of how gravity varies around the Earth. – PM 2Ring May 26 '20 at 21:01