I've heard of stars gaining weight but planets... If you want this to happen to a habitable planet, you have problems, because any mass gained would mean something crashing to the surface. Make it a very localized phenomenon, for instance on the poles of the planet, leaving the remaining surface intact. Make the incoming matter magnetic and the magnetic poles can drag it in from the planet's outer magnetosphere out in space.
If the Earth gains 20% of mass, you would have to redo the third Kepler's law. Meaning you would have to move the Earth farther away from the Sun and the year would become longer. So you would definitely have a colder climate because the Sun is farther now (not too much, I think. I'll do the math and report back.)
Edit: reducing mass of the planet could be done by a large pocket of anti-matter deep in the core of the planet, slowly annihilating with the matter. It could cause the same heat as the radioactive decay that is happening inside Earth. Of course this would mean that you are getting a gradually larger void inside the planet, which could mean collapse of the matter above.
Edit: here's the third Kepler's Law:
GM/4pi^2 = a^3 / P^2, where G is the gravitational constant, M are the combined mass of the Sun and Earth, a is the distance between Sun and Earth and P is the period of the Earth's path around the sun (1 year). If the Earth gains 20% of its mass, the combined mass of both bodies would be virtually the same due to the large mass of the Sun. Therefore, the change in a or P would most likely be non-detectable.
In cold brute math, this means: dM/M = 3 da/a = -2 dP/P
The Mass of the Sun is 2*10^30 kg. The mass of the Earth is 6*10^24 kg. a of the Earth is 150*10^9 m. P of the Earth is 365 days.
M means both masses combined but since the Sun has a million times more mass than the Earth, you can skip the Earth.
dM is 20% of Earth's mass, which means 1.2*10^24 kg.
This would mean that the distance between the Earth and the Sun would increase by 30 km or almost 19 miles.
The year would be longer for almost 10 seconds.
[This message has been edited by MartinV (edited December 12, 2010).]
Planets do gain mass, although very slowly. This is usually through accumulation of meteorites.
The nature of the weight gain in your story will change things somewhat. Is it constant, such as a means of absorbing WIMPS may do? Or is it stochastic (i.e. variable with time) such as meteorite accumulation? Or perhaps it is periodic, such as accumulating the solar wind (the closer to the sun, the more it accumulates)?
Also, adding weight reduces the velocity (due to the conservation of momentum). This could destabilise the orbit, depending on the rate of weight addition and the cause behind it (remember an assumption behind Keplers's Law, though he didn't know it at the time, was that the orbits were stable). On the other hand, solar wind, for example, may add an outward momentum that offsets the reduction in velocity. This method may push the body outward, as Martin above suggested, to a new stable orbit. I'm not entirely sure which will have predominance, though, and we are talking very long time periods.
Bigger than Jupiter sized planets found around other stars have shown the Kepler's law is just an observation, not an actual law. There might be changes in orbit and rotational speeds due to the changes in mass, but it not Newtonian and Einsteinian rather than Kepler
Planetary size change over a period of more than a thousand years would not be "noticeable" by the life. Succeeding generations would adapt to the increased gravity.
Man made structures would suffer. What was sufficient engineering for one level of gravity would collapse or be unable to handle normal loads at another.
Thrust calculations to get into space would become wrong. It would cost more to get into space.
As for the cause, Stars go around the Galaxy on different routes and rates compared to each other. Nebula do the same thing. All one needs is for the solar system to pass through a light nebula and acquire a lot of mass as it passes through.
AS for the size, I remember reading a piece by Isaac Asimov where he said that there are no planets in our solar system between 10? and 100 times the mass of our moon. The idea is that when a planet reaches a certain mass, it develops the gravity to hold volatiles, and then develops atmospheric mass rapidly.
An off the top of my head thought; Solid matter is not the only thing with mass. Earth is not considered a cosmic 'big guy'. Maybe the sun could draw mass into the solar system from a passing, anomolous cloud of 'space gas' (just rambling this out). Each planet would capture a portion into it's own gravitational pull... etc. It would be a slow enough process to give your characters time to react, but fast enough to produce a threat.
Hey, just letting the imagination wander a bit.
Martin, very cool stuff Mon...
edit; read a 'Register' article about the moon shrinking, beginning to crumble in on itself.
Mass is constant...weight goes up and down...
I remember a Larry Niven gimmick involving dropping iron fillings in a vacuum set up between two teleportation gates. As their speed approached that of light, their mass increased, eventually enough to affect Earth (or whatever planet the gates were set up on). The mathematics of it eludes me, though...
This is a really interesting thread, although I'll admit that the math eludes me. I have been considering the opposite problem for a story - what happens when a planet's mass decreases? (In my story, the planet is being agressively mined.) This thread has given me some things to think about.
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The math is 3rd Kepler's Law and the differential version of it.
If you want to see the effect of reducing the planet's mass, just input a negative dM in the above equation. You get negative da - the distance gets smaller - and positive dP - the period grows larger.