# World with core of changing mass, gravitational effect on tides?

I'm building a fantasy world with a planetary core that gains and loses mass in a predictable manner. I want the gravity to increase and decrease by 50% in both directions over a period lasting 2-3 generations of its inhabitants. Whether or not this is strictly possible is not very important, however, I would like to know what the effects of such a phenomenon would be on tidal forces as experienced by the planet's inhabitants.

*Edited for focus

Thank you.

• The moon will not get pulled in to a closer orbit just because the mass of the planet changes. The current momentum and velocity of the moon will still be the same and thus the moon's angular momentum will no longer be enough to keep it in the same orbit. It will require a pretty precise rate of gravity change to move the moon closer and keep it in a stable orbit without it colliding with the planet. – A. C. A. C. Jul 7 '17 at 19:41
• Welcome to Worldbuilding.SE! Please take the tour, check out how to ask a good question, and have a look around at previously asked questions. While this is an interesting idea, it's unfortunately too broad for this format (and likely to get closed as such). It looks like you're asking 8 questions; I would advise splitting this up into a series of questions and asking only one thing at a time. – Azuaron Jul 7 '17 at 19:43
• Over how long a period does this happen? And has it always happened (ie. did they evolve with it)? – Schwern Jul 7 '17 at 19:47
• As far as we know heavy mass and inertial mass are the same thing. If the planet gains mass it must slow down because of the conservation of momentum. By slowing down it will no longer remain on its original orbit and will wander on a highly eliptical orbit bringing it closer to the its primary... Then it will lose mass and alter its orbit again... Very chaotic. – AlexP Jul 7 '17 at 19:57
• Even handwaving where the hell the mass goes I am not sure this planet would have a stable orbit. I don't mean the moon around it, I mean it around the sun as a lighter planet would exhibit less gravitational attraction to the parent star (remember, its based on the mass of both objects!) and drift away. When it regained the mass it would drift closer again. – Draco18s Jul 7 '17 at 20:12

I want...

1) the gravity to increase to the point where the planet's moon is pulled close to the Roche limit

2) the planet's inhabitants experience perhaps 50-100% relative weight gain

How do these two desires interact? Let's look at some math.

Since you didn't say anything about the planet and its moon, I'm going to assume they're like the Earth and Moon. You can plug in whatever numbers you like.

If you want a 50 to 100% increase in felt weight, that means a 50 to 100% increase in mass. For the 6e24kg Earth that's 9e24kg to 1.2e24kg. You could also decrease the surface area which would be better physics, but the resulting surface upheavals would be very disastrous for the inhabitants.

The Roche Limit of two bodies depends on their relative densities. $p_M$ is the density of the planet, $p_m$ is the density of the moon, and $R_M$ is the radius of the planet. $$1.26 R_M(\frac{p_M}{p_m})^\frac{1}{3}$$

Increasing the mass of the Earth without changing the radius increases its density. This is also linear, so a 50 to 100% increase in mass means a 50 to 100% increase in density which means a 50 to 100% increase in the Roche Limit. The moon will be pulled towards the Roche Limit, but the Roche Limit will also move out toward the moon.

For the Earth/Moon system, the Roche limit is roughly 10,000 km. With its increase in mass, that will go out to 15,000 to 20,000 km. The Moon normally orbits at 385,000 km, yours is 20,000 km at its closest, probably 30,000 km at its farthest. So your planet has a very close and very large satellite regardless of where your planet is in its cycle. This means very increased tidal effects. Very bright full moons. And if its orbiting around the planet on the same plane as the planet is orbiting around its star, very long eclipses.

But if life and civilization evolved on this planet, this would all be considered normal.

How would people experience weight as the gravitational pull increases but the moon gets closer?

It would be irrelevant. The moon is too far away and its mass is too low, 1/100th of the planet's. We can do the math. $$gravity = \frac{GM}{r^2}$$

G is the gravitational constant. M is the mass of the moon. r is its distance from the surface of the planet. Your moon is roughly 7.3e22 kg. Its radius from Earth goes from about 20,000 km to 30,000 km. Plug them in and we get $0.012 m/s^2$ at its closest and $0.0054 m/s^2$ at its furthest. Compared to the $19 m/s^2$ and $9.8 m/s^2$ of the planet, the inhabitants won't notice a difference in gravity, but they will notice an enormous tidal effect.

The problem here is all this pushing and pulling will destabilize the moon's orbit. Each cycle will increase its eccentricity making its orbit increasingly elliptical. Being already so close to the Roche Limit, eventually its minor axis will cut into the Roche Limit and it will disintegrate causing many, many problems on the planet below.

So this system is unstable. There's little chance this planet could have formed with a moon nor held onto it. This moon would have to be a recently (in astronomical terms) captured body.

It might make a good story about a civilization who has just figured out the laws of gravity and planetary motion. They've predicted that in X years the moon will pass the Roche Limit where it will disintegrate and destroy the surface of the planet. The task of the civilization, and this could span generations, is to somehow avert or survive the disaster.

• @ Schwern brilliant! Thank you for taking the time to answer my questions so thoroughly. All of your assumptions were correct: increased density is what I was after. My next question would be, how would things change when the core began losing mass, to the point where it has 50% of earth's. How would the moon behave throughout an entire cycle? – Adam Halatek Jul 7 '17 at 20:45
• It's not necessarily unstable. It depends on how the period of the mass fluctuations interacts with the period of the moon's orbit. If the mass fluctuation cycle is just wrong, then yeah, you will get increasing eccentricity on each cycle. But it would also be possible to arrange the cycles such that the cumulative effects cancel out over many cycles. – Logan R. Kearsley Jul 7 '17 at 20:45
• @Logan there is unstable and unstable. System that is inherently unstable can by coincidence look as if it's stable... Until it is pushed ever so slightly. – Mołot Jul 7 '17 at 21:24