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I get that gravity depends on the mass of an object: more mass = higher gravity. But over time humans have been doing stuff to the total amount of stuff on the Earth due to space travel. At which point would we feel the effects over various ventures into space? We have taken metals and ore etc. out of the ground and blasted it into space in the form of probes and satellites, conversely we've also brought samples of the moon back with us (I'm not aware of any probes to mars having automated sample return modules, which is why a lot of effort is made to send probes with compact mobile labs for sample analysis on the ground as it were).

Whilst, as a percentage of the Earth's total overall mass, the amount we've sent up and brought back down equates to a minute number, there must be a point where one day we launch yet another.

Even without sending stuff off the Earth's surface, does extracting ore from the Earth's inner layers and bringing it up to the surface (i.e. mining) affect the Earth's 'mass'? Essentially, does the matter of the Earth have to be within certain distance (i.e. density) of the rest of it to affect the mass and gravity of Earth?

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    $\begingroup$ What difficulty do you have in applying Gauß law for gravity to answer this question? $\endgroup$
    – ACuriousMind ♦
    Commented Aug 31 at 20:08
  • $\begingroup$ @ a curious mind I suppose my difficulty is wondering if materials taken out of the ground and used to build things on the surface ( building etc. still count towards the earths total mass? and so as such does external matter ( asteroids meteors etc. that have hit the earths surface count towards the mass if they just sit on the suface? $\endgroup$
    – Matt Bartlett
    Commented Aug 31 at 21:41
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    $\begingroup$ My point is that Gauß' law of gravity does not contain things like "earth's total mass" - it just contains the density of matter in a certain region. Are you asking this question because you're not familiar with any version of gravity that deals with densities rather than "objects"? $\endgroup$
    – ACuriousMind ♦
    Commented Aug 31 at 21:49
  • $\begingroup$ Mass that is transported to Mars is taken outside the sphere of mass and energy that causes the attraction of the Moon to the Earth so they will very slightly affect the orbit of the moon. Mass transported to the Moon will slightly alter the orbits of lower satellites like the ISS. See my answer to this question physics.stackexchange.com/questions/535648/… which is about how the loss of mass from the Sun as radiation and solar wind alters the orbit of the Earth, which is a similar sort of situation. $\endgroup$
    – KDP
    Commented Sep 1 at 3:21
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    $\begingroup$ Redistributing mass so as to change local densities will alter the local gravitational field, but the calculations get very complicated very quickly. $\endgroup$
    – KDP
    Commented Sep 1 at 3:23

3 Answers 3

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A great tool for answering these types of conceptual questions is an order of magnitude estimate, or a Fermi estimate.

Let's assume the Curiosity Rover has about the same mass as a car. A quick search reveals that the average car is about 1500 kg. Let's call this simply $10^3$ kg. The Earth's mass is about $10^{24}$ kg. So sending a rover to Mars decreases the Earth's mass by about

$$\frac {10^{3}}{10^{24}} = 10^{-21}$$

of the total.

So, a Mars Rover leaving the Earth affects its mass about as much as losing a single protein molecule (much smaller than a cell) would affect your mass.

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  • $\begingroup$ A lot more mass is actually lost as a propellant when getting the Rover to Mars. $\endgroup$
    – fraxinus
    Commented Sep 1 at 8:33
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    $\begingroup$ On the other hand, the Earth actually constantly grows in mass because all of the cosmic dust (and larger particles) it gets. Compared to this, the whole space exploration is negligible. $\endgroup$
    – fraxinus
    Commented Sep 1 at 8:35
  • $\begingroup$ @fraxinus Also there was the main craft body, the descent system, the chute and the lander. weebau.com/satplan/msl.htm says 3389kg. Wikipedia additionally tells us that the Centaur III weighs 2316kg and has up to 20,830kg of fuel. So the estimate is an order of magnitude low. But since that's on the order of your body losing 10 protein molecules, it's still pretty insignificant. :) $\endgroup$
    – Graham
    Commented Sep 1 at 9:11
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    $\begingroup$ @fraxinus Most of propellant mass (used by launcher's first stage) fall back to Earth. $\endgroup$
    – user13964273
    Commented Sep 1 at 12:04
  • $\begingroup$ For context, en.wikipedia.org/wiki/Atmospheric_escape suggests the Earth loses approximately 94608000 kg of hydrogen from the atmosphere each year. $\endgroup$
    – chepner
    Commented Sep 1 at 18:54
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The real answer is "if you have to ask what counts as Earth-mass, it's a poor unit for the question at hand." We only use this for approximations, giving a sense of scale to otherwise absurd units. It's not really a super-well defined concept.

Wikipedia states that the Earth's mass is $(5.9722\pm 0.0006)\times 10^{24}\text{kg}$. That means our uncertainty in the Earth's mass is on the order of 60,000,000,000kg. So until we lift something on the order of that mass, any satellites fit within the uncertainty of our measurements.

According to Orders of Magnitude (mass), this is about ten times the mass of the pyramid of Giza. So we've got a lot to go.

As for how far something has to move before it's not Earth mass, the above statement still holds: if you have to ask, then its a bad unit to use. However, Earth Mass tends not to include the moon, so I'd feel comfortable saying the line in the sand is being in orbit.

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In addition to the previous answer: the mass of the Earth is not constant. You have examples of objects leaving the Earth, but the mass can also increase when meteorites (big or small) hit the Earth. However, the relative change in mass can be neglected in all but extreme cases. Even if a Moon-sized object were to collide and fuse with Earth this would add $\sim 1.2\%$ to the mass of Earth: a non-trivial and possible detectable effect but we’d have other things to worry about.

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