# Finding the size of tides

I have a planetary system in which there is a huge planet and a moon orbiting it which has an atmosphere and water (and actually everything needed to sustain life).

Thing is that I'm sure the mass of the planet such moon is orbiting will have incredible effects on its tides. But I can't seem to find out how much the height of sea/ocean might change due to the Tide Effects.

So, how can I find out how many meters/kilometers will tide make oceans rise?

In case formulas are dependant on too many factors, let's assume the moon is like Earth, so the height is only dependant (I guess) on the mass and distance of the planet it's orbiting.

• Tide heights is also dependent on the geography of the coast line, the currents in the ocean and the shape of the continental plateau, and I'm probably forgetting a few other factors.
– Sava
Oct 29, 2018 at 22:06
• Oct 29, 2018 at 22:55

Probably very little, but not for the reason you'd think

You haven't given us much detail, but if your planet is much larger than your moon and the system has existed for some time, the moon will probably be tidally locked. This means that one side of the moon always faces the planet (this is the case with our moon and many large moons in the solar system). If this is the case, gravitational potential of the planet will not change in time on the surface of the moon, and thus there will be no tides from the planet (though the oceans will take a shape that looks bulged at the equator and squashed at the poles). There would still be tides from the local star (the sun is responsible for about 1/3 of Earth's tides), and the largest of these tides would occur at the frequency of the planet's rotational period (since the moon will be locked into the same rotational period). However, if relatively far from the local star (such as near Jupiter), this effect will be drastically smaller than the solar tides the Earth experiences.

Ok, but let's assume for your story that the moon is not tidally locked

Calculating local tides from theory only is extremely hard, maybe impossible without running models on larger supercomputers than we currently use. This is because actual tide heights vary with local bathymetry (topography of the ocean floor). So here's how scientists currently do it:

Equilibrium tide theory is essentially a guess at how tides would look if Earth were featureless and covered in a shallow ocean. This is a solvable problem, and in its solution we can see the period of various tidal "constituents." This includes subdaily, daily, fortnightly, annually, and many combinations therein. Data at some specific location from a tide gauge (measurement of local water "height") can then be analyzed to see what power exists at certain frequencies. Since we know from equilibrium tide theory what to look for, we look at those frequencies and come up with amplitudes, e.g. 50cm diurnal tide at some location means the tide varies 50cm up and down once per day there. We add all the amplitudes and frequencies at that location to get a (really) good idea of how the tides will look, to within cm or less in most places. This gives decent background and sources on the theory.

All this to essentially say we need data to predict tides well. Since your setting is contrived, the best we can do is calculate equilibrium tides there. However, this is a pretty large undertaking and to even think about doing so would require you laying out the specific orbital parameters for your planet around its star and your moon around the planet. If you want to ballpark it without a whole equilibrium tide calculation, you'll need at least the size and mass of your planet and moon, as well as the distance between the two. This would let you calculate the gravitational potential from the planet on the moon's surface, and then the difference in potential from the planet at various locations on the moon's surface. This would at least tell you what order of magnitude to expect (cm, m, km) which is probably enough for your story.

tl;dr

The moon is probably tidally locked meaning small or no tides, but if you'd like to say it isn't you'll need to specify planet and moon's sizes and masses as well as the distance between the two for a ballpark answer.

# Tidal Range is proportional to Tidal force

You can use the Tidal forces calculator. $$T=2GMmR/r^3$$ to determine (you'll need to input the mass of your moon, the planet, the distance between them and the radius of the moon) what the magnitude of the tidal force in your new system would be and compare that to the tidal range of our earth moon system to get the tidal range at any given point on your earth clone moon.

Note that tidal range is highly dependant on the size and shape of the oceans that they occur in as well as where on the surface you happen to be. So we can only really answer this by using earth as an example and extrapolating from there.