I'm building a world that orbits close in to an M-Dwarf sun. I've figured out a bunch of the physical parameters of the world, I just can't quite get a solid handle on my tides.
I know my tides will be substantial, but exactly how substantial is something I need some help on.
I have three main sub-questions:
- Am I calculating the tidal force correctly?
- Does tidal force correspond 1:1 with ocean tide height?
- All else being equal, changing the diameter of the planet should change the tide height. But hot much? How do you calculate this?
Below is the supplementary info, and a basic outline of my thinking on the matter.
- Elliptical orbit with a semi-major axis of 0.1307 AU, apoapsis of 0.1622 AU, and periapsis of 0.0991 AU.
- Planet radius 5268km.
- No moons
- Solar mass of 0.395 earth suns.
- Year of 27.44 earth days, with a rotational period of exactly half (13.72 earth days).
- The planet is in 2:1 spin/rotation resonance, so a solar day (sunrise to sunrise) equals one 27.44 earth-day year (visual). So the tides should ebb/flow based on this number, not the actual planet rotation rate of 13.72.
The relative tidal force on the planet is easy to compute. It should be:
T = M/(d^3)
Where M = mass of sun & d = distance.
So that would give us T = 0.395/(0.1307^3). Which comes out to a tidal force of 177.1 times sol's force on the Earth. Likewise the tidal force for apoapsis is 92.6 and for periapsis 405.9.
Now, the tricky parts come in: Changing planet diameter
First, this is the tidal force as measured from the center of the planet. But based on my understanding of tides, its the differential in tidal force between sides of the planet that causes the tides, not the absolute tidal force. The number I computed above would be an accurate number for relative tidal force on an exactly Earth size planet in that location, but not a smaller or larger planet. And since my planet is smaller, the tidal force must logically be smaller than this calculation.
(Example: If you get a theoretical planet of zero diameter the tidal force exerted would be...zero. So the force MUST necessarily scale by some formula from zero upward).
I don't know how to calculate that force for my smaller world and can't find any direct calculations online.
Now the second wrench into the works: Does Tidal Force = Ocean Tide Height
Does a mean tidal force 177 greater than that of sol's on Earth necessarily imply tide heights 177x greater? My intuition says no, but I don't know exactly why. I suspect the tide heights would be ameliorated to an extent by the friction between water and ocean bottom, and perhaps other factors. But...I don't know. It's far too much of a guess for me to be comfortable with. I want to have more concrete numbers based on a more concrete understanding.
Why I care
On of the reasons this is necessary to figure out to a reasonable accuracy is that tides of this size will have a MASSIVE impact on the ecology of my world. And the difference between tides of 40x sols, 100x sols, and 400x sols is huge. At the upper end of my current calculations (405.9x sols) I get max tide heights of about 101.5 meters (based on a solar theoretical tide height of 0.25meters) or maybe 72.7meters (based on the solar semi-diurnal tidal constituent of 0.179meters listed here: https://en.wikipedia.org/wiki/Earth_tide). Those numbers just seem...catastrophic to work with. Even the smaller calculation of 72.7 meters would mean that the tide rises and falls that height every 13.72 earth-days, or 5.3meters per 24 hours. Constantly. So the coasts & coastal plains of my world would be zones of perpetual flooding and draining, potentially moving many kilometers inland over just a dozen or two dozen hours. Heck, if Earth had tides of 72.7 meters a good portion of Florida would be covered/uncovered by seawater regularly. That's some interesting fodder to work with, but perhaps too much of a good thing.