# Planet half the size of earth with two moons. Livable? Climate Range?

This planet I am proposing is approximately half the size and mass of earth and has two moons. The moons are respectively 1/8th and 1/10th of the size of the planet.The moons orbit the planet at distances of 150,000 miles and 200,000 miles respectively. The planet orbits its sun-like star at a distance of 85 million miles.

What kind of climates would this planet experience? Could this planet be liveable and if not then what factors would need to change to make it liveable?

• Are the moon orbits synchronized? A major effect will be to do with tides. Climate will be impacted by eg atmospheric composition, solar output, planetary tilt, solar system tilt, ocean currents, ability of rocks to weather, etc. Oct 18, 2017 at 0:52
• The moon orbits are not synchronized. Atmospheric composition is 68% Nitrogen, 31%oxygen, rest same as earth. It 0 axial tilt. Other factors are comparable to Earth Oct 18, 2017 at 1:00
• While this doesn't address your question, I want to point out that orbitally, your system wouldn't be stable. For the planet with half the mass, the Hill Sphere would be 80% the size - that much is fine, but two very large moons is a problem. It would effectively be a chaotic 3 body system leading to a giant collision or an ejection of one of the two moons into a dangerous near Earth orbit. Oct 18, 2017 at 2:49
• A planet half of Earth's mass won't retain much of an atmosphere for long, you need more gravity. It also seems unlikely that such a small planet would generate a sufficient magnetic field to protect from solar radiation. Oct 18, 2017 at 2:57
• @MatthewGauthier It would be closer to the Water/Ammonia/Methane line, but not necessarily over it. Earth's escape velocity is 11.2 km/s. Venus, 10.3. We don't know the density of this planet but if we estimate 5 g/cc, it's escape velocity would be 8.7 km/s. That might be enough to retain the lighter elements. It's close to being to small but it might be OK. upload.wikimedia.org/wikipedia/commons/4/4a/… Oct 18, 2017 at 3:24

## 3 Answers

I do not think such a system of moons would be stable.

A rough calculations :

$F_0$ = Force between inner moon and planet

$F_1$ = Force between moons at closest approach

$M_0$ = Mass of planet

$r$ = 50,000 miles

$$F_0 = \frac {GM_0^2}{8(3r)^2}=\frac {GM_0^2}{72r^2}$$

$$F_1 = \frac {GM_0^2}{(8)(10)r^2}=\frac {GM_0^2}{80r^2}$$

So the force from the planet is only slightly more than the force from the other moon.

The two moons would therefore distort each other's orbits significantly. They'd almost certainly either end up in radically different orbits (highly eccentric ) or (more likely) collide with each other or even the planet.

It's hard to see how they could form in the first place.

So this system is not likely to exist in a stable way for long enough to develop and support life of any kind, IMO.

To fix this :

One small moon (say 1/200th the mass or less of the planet).

Probably even with this you'd need to remove that moon to a more distant position or have it at the stable Lagrangian points (see Trojans) to avoid an unstable small moon ending up colliding with the large moon or planet. But that's not an option for large moons of similar size - they'd be unstable (not to mention the problem of how they'd end up there in the first place).

Earth had 31% oxygen in its past, and the animals were different. There is speculation that 31% oxygen requires different body plans.

Carbon in the atmosphere, and solar output, is a bigger driver of climate per se. Earth has had a range of carbon from ~100 to (IIRC) ~2000 ppm and we are now at 400 ppm. Solar output of our sun was 30% lower 4 billion years ago. It's a fine balance.

You can hand wave climatic effects to where you want them, by adjusting carbon and solar output. the moons will affect tides, you have huge tides when they both pull from the same direction, and small tides when they oppose each other.

Ignoring the orbital problems, Moons don't affect climate all that much. With no axial tilt (so no seasons), the Moons would frequently eclipse the sun, but that would only have a small effect on total solar insolation, maybe 1%-2%. At 85 million miles vs 93 million, that would be a 20% increase in solar energy, which is a lot. That close to a sun like star, your planet would be in danger of being too not, moons or no moons. You'd want some cooling elements. Reflective plants with perhaps some white colored leaves for shading in peak temperatures, or perhaps, massive forestation (lower gravity you could have very tall trees) and low CO2. You could also play with where your continents are, how much volcanic particulates there are in the atmosphere to reflect sunlight away. There are lots of planetary factors to control temperatures. The Moon's effect would be minimal.

Your planet would have large tides however, especially when the Moons lined up either same side or opposite sides of the planet. At peak, you're looking at tides about 10-15 times higher than on Earth. Oceans rising and falling some 40 feet vertical twice a day.

Plate tectonics is another problem. Your planet is a little small for that. As to your question, the effect the Moon have on weather is more subtle. You'd first need to determine other more direct factors, like how much land, how much surface water, planet's albedo, placement of the continents, atmospheric content, ocean currents and prevailing winds on the planet. The lunar effect on weather is secondary to all of those, even with large moons.