# What are the requirements for an atmosphere retaining moon with a stable orbit around an Earth-like planet with non-destructive tidal forces?

For story writing purposes I would like a realistic setup where there is a planet with close to earth conditions in terms of gravity, relative position to the sun etc. However I aim to have a much larger moon with greater mass and thus a gravity sufficient to retain an atmosphere. This leads to questions of wicked harsh tidal forces on the planet.

I plan to solve the destructive tidal forces issue by moving the moon further away. This seems to be the prevailing wisdom and makes a lot of sense. However I am concerned about a sufficiently large moon breaking orbit (which my limited understanding of such things suggests would happen) and would need to work out (1) how large the moon might look from the planet's surface (2) what the tides would be like and (3) what sort of flight times between the two there might be.

I imagine that the moon would look larger, that flight times would be greater but the difference would be trivial and that the tides on the planet would be harsh on the coast while the tides on the moon would be calm (is that right?)

I am not looking for earth-like tides, they can be harsh as long as they do not make inland habitation pointless planetside.

I don't especially want to end up with a planet which is many multiples that of earth's size or gravity (up to 1.1g would be fine).

My grasp of some of the more advanced maths is limited at best so layman's terms explanations would be appreciated along with the hard science.

• Flight time to the Earth's Moon was limited not by rocketry (the Apollo spaceflights could have easily gotten to the Moon in about a day), but by the need for orbital capture. Too fast and the Apollo ships would have sailed past into interplanetary space. A larger Moon could gravitationally capture an incoming spacecraft more easily (and it can aerobrake in your scenario), so flight time could be much faster that our own Earth-Moon missions. – Thucydides Jul 26 '15 at 14:51

Ooh, fun question, or in fact, a bunch of questions bundled together

## Endowing a moon with an atmosphere.

It is still unclear what the mechanisms of atmospheric accretion and retention are exactly, since you have moons like Titan (at 1.3E+23 kg it is 0.0225 $$M_{⊕}$$ --Earth masses-- or about 1.8 times the size of our moon) with a dense atmosphere (146.7 kPa or about 140% of Earth's atmosphere), and heavier planets like Mercury (0.055 $$M_{⊕}$$ but only trace atmosphere) and Mars (0.107 $$M_{⊕}$$ with 0.636 kPa or ~1% of Earth's). Moreover, even though Earth and Venus are similar in size (Earth is slightly larger), Venus has an atmosphere ~90 times denser.

So obviously the moon's mass, distance from primary star, original gas endowment, and presence and strength of a magnetosphere play a role:

• Higher mass means higher escape velocity, helping the object retain the gases. As a rule of thumb, you generally want the object's escape velocity to be at least 6 times the particular gas's mean velocity. For example, Earth has an escape velocity of 11.2 km/s, while O2 at 20 C has an average molecular speed of 0.48 km/s, so Earth can retain molecular oxygen for billions of years. Mars has an escape velocity of 5 km/s, so molecular hydrogen --average speed at 20C being 1.9 km/s-- cannot be retained long term on either planet.

• Distance from primary star has 2 effects. The star's radiation warms the gas on the moon/planet surface (increasing molecular speed), and the star emits stelar winds, a flow of charged particles which act to strip planets of their gas (hence Mercury, closest to the sun, having only trace amounts of gas)

• Original gas endowment at the end of the planetary formation stage of the first ~200 million years of the star system's existence. This is hardest to factor in, but might account for why Venus and Earth are so different (that and the oceans on Earth). For instance, it could be that the moon-creating impact dispersed some/most of Earth's initial atmosphere.

• Magnetospheres deflect incoming solar winds, in a sense protecting the atmosphere from impacts with the highly charged particles of the solar wind and the molecular dissociation that the uppermost layers of the atmosphere would experience otherwise. These are also mysterious. For terrestrial-sized planets, they seem linked with activity in the molten iron core and speed of rotation, but we don't truly understand the mechanics well yet.

## So, what can we conclude?

Well, it depends on what kind of atmosphere you want. If you're ok with Titan (recall: its mass is 1.8 Earth moon's, ~2% of Earth) you can get 98% Nitrogen and some methane. Not breathable, but you could live with sealed scuba-like-gear if it were warm enough, not the bulky Moon-space suits of the Apollo missions. Surface gravity would be similar to the moon (more mass but less dense). You'd have lakes of gasoline-like compounds on the surface. Tides would be similar to what you see now, while the moon would be larger in the planet's sky due to its atmosphere. Of course, this might be hard to explain in terms of formation and how it is maintained, since bringing Titan to Earth-orbit would make it 10 times warmer and would probably results in full atmospheric loss in about 10 million years, but weirder things have happened.

If you want an Earth-like atmosphere with water and all that, stable over the billions of years, you may need a molten core for magnetosphere, high enough gravity, etc. which means you probably need something about 0.4 $$M_{⊕}$$ or larger, so a moon larger than Mars. At that point, it's not really a moon, but a double planet. That comes with its own headaches. With mass that high, the two worlds would quickly become tidally locked, which is to say rotate in synchrony, and always show the same face to the other. (Your 'moon' would only ever be visible from half the planet, no tides at all and possibly very long days).

Moons do not escape their orbits They can drift outward and inward over time, but there is a limit to how far out they can drift. Our moon is currently drifting outward by a few centimeters per year due to its slowing of Earth's rotation. This slowing effect on the Earth transfers energy to the Moon pushing it away. When the Earth finally becomes tidally locked to the Moon (in about 15 Billion Years) the moon will stop drifting outward. Plus the farther out the Moon drifts the less drag on our rotation it has, slowing its outward drift and making the process take much, much longer.

Moon Atmosphere As a rule, the closer you are to the sun the more massive the planet needs to be in order to retain an atmosphere due to the sun energizing the particles more. As a safe bet for a planet at roughly earth distance I would make the moon at least half as massive as the earth to be able to retain those gasses and prevent massive escape. Depending on the density of the moon though this could lead to varying sizes of the globe.

Magnetic Field With the magnetic field, your best bet would be to have a free-spinning moon massive enough with enough internal heat to generate its own field. Tidal forces can act to further heat the interior to keep it nice and toasty. A tidally locked world in a close orbit can also generate a decent magnetic field if its orbit is not completely circular. Changes in tidal strength can act to squeeze and pull on the core to heat it up. That combined with a decent rotation rate should be all you need. Another possibility for a close orbiting moon would be that it sits inside the parent planets magnetic field. The magnetic field of the parent planet would probably have to be several times stronger than our own in order to accomplish this though.

Tides As far as tides are concerned there is a give and take. If you want a close in moon it is probably going to be tidally locked, which wouldn't mean no tides, but would mean "frozen" tides. High and low tides that would never move. High tide would always face the other moon, and on the exact opposite side. The sun would still raise tides, but this would only be about 30% as strong as the tides here on earth. This can change drastically though depending on the size of the planet, the star, and the orbit. If you wanted to keep your planet free-spinning like the earth put the moon farther out. The more massive the moon, the farther out it needs to be to avoid tidal locking. Meanwhile while standing on a less massive moon, tides are stronger due to the larger pull of the parent planet in relation to your own more meager gravity. If the moon is of the same mass as the parent planet then the tides would be equal.

First, you don't need to worry about the moon "breaking away". That only happens in bad science fiction shows.

The moon can be as large as the planet (in which case they become co-planets).

In the long run, wicked harsh tides solve themselves - the two bodies become tidally locked. The process of that locking, which is going on today with the earth slowly losing rotation speed, results in the two bodies slowly moving apart, with the separation stabilizing when both bodies are locked. At this point there are no tides on either body.

Assuming the two bodies were formed symmetrically, with identical masses and rotation rates, the tides on each body will be identical. If the smaller body is still rotating (unlike our moon), the effect of the larger body on it will be to create larger tides than are found on the larger body.

Apparent size of satellite from the primary will depend entirely on the separation, and vice versa.

You want the moon to be large enough to have geological activity, so a magnetic field is produced, and an atmosphere can be retained. With a maximum of 1.1 g, one thing I'd suggest is to decrease the density of the planet, so let's decrease it to Mars', or 3933 kg/m^3. That's 71.3% of Earth's density. That way, the planet's radius can be up to 1.54 Earth radii, as if density is kept the same, gravity increases linearly with radius. The planet's mass would be 2.62 Earth masses, and you would want to increase the mass of the moon to at least .027 Earth masses. If we kept the orbital radius of the moon, and the density, the same, the tidal heating should be 291 times stronger for the moon. That way, there should be enough magnetism to hold to at least a semblance of an atmosphere.