# How would an earth-like planet with a habitable moon work and how to get there?

I have a planet approximately 3.5 times the mass of the Earth. I have a moon orbiting that planet that has to be habitable as well, because my story will take place on the first expedition to this moon. What size would my moon have to be it sustain life? The reason I ask is because a body the size of our current moon doesn't have enough gravity. If I end up having to move the size of my planet up I can go up to max of 5.5 times the mass of the Earth. What tech level would be required for these 'people' to escape the gravitational pull of their exceedingly large planet?

Yes, I am aware there are a couple of general habitability questions, however I think this does deserve its own question.

• I think you might be conflating mass and volume. Something can be several times the mass of the Earth and still be the size of the Moon. – Frostfyre May 4 '15 at 16:13
• @Frostfyre I want a planet at least 3.5 times the mass (and also size) of the Earth with a seperate moon that is also habitable. – JDSweetBeat May 4 '15 at 16:16
• So you want your world to be 3.5 x Earth's mass with an equal density, which (inherently) requires a volume of 3.5 x Earth's. My point was that you seemed to be combining/mixing definitions. – Frostfyre May 4 '15 at 16:19
• @DJMethaneMan When you say "size" do you mean volume, radius, or mass? Also, how fast does the planet spin? – Samuel May 4 '15 at 16:28
• @Samuel Volume. I had this question in the sandbox for a few weeks. I would have thought it would have been addressed in the comments section. – JDSweetBeat May 4 '15 at 17:05

For a planet with 3.5 times the Earth's volume and 3.5 times its mass, the surface gravity will be 1.52g.

I've previously discussed the equation for surface gravity. Just note for your own calculation that 3.5 times the volume is about 1.52 times the radius. So, if you want to work in terms of volumes you can multiply the radius term by the cube root of the volume scalar you want.

Basic surface gravity equation: $$g= {G_{(gravitational\ constant)} M_{(mass\ of\ planet)}\over {r_{(radius\ of\ planet)}}^2}$$

For a planet with 3.5x the mass and 3.5x the volume: $${G\ 3.5_{(mass\ scalar)}M_{⊕(mass\ of\ Earth)} \over { ({3.5_{(volume\ scalar)}}^{1/3}a_{⊕(equatorial\ radius\ of\ Earth)}})^2} \approx 1.52g$$

Moon's habitability-

As you've already linked, the moon's habitability is taken care of in other questions. Also Jim2B's answer describes some basic characteristics.

Getting from your massive planet to the habitable moon-

As for getting there, they can use chemical rockets, just like us.

I'm assuming what you want to know is if the higher gravity of the home planet will deter launching from it. There is a somewhat related question on the Physics SE. It relates to what I assume the core of your question is, at least. Getting to space from the surface of a planet with 1.52 to 1.76 times the gravity of Earth is not impossible, but it is more difficult. They will need very efficient rockets to overcome the rocket equation. Or, as Jim2B again pointed out, an alternative to rocket propulsion.

• Rocket Equation: There's nothing that can't be solved with more fuel, except getting that fuel into orbit with you. – Bobson May 5 '15 at 14:09
• Please take another look at your math. The factor 4 pi/3 should drop out, giving a surface gravity of ~1.5. – WhatRoughBeast May 6 '15 at 2:23
• @WhatRoughBeast You're right, I left the term in from the density calculation. – Samuel May 6 '15 at 3:35

What is the minimum size for a inhabitable body (moon)?
Let me make the following assumptions:

1. Temperature ~ Earth
2. Moon density ~ Earth
3. To be inhabitable, the satellite must retain water as an atmospheric gas
4. The primary atmospheric loss mechanism is Jean's Escape (this requires a moderately strong magnetic field).

Based upon these assumptions, the satellite must have a mass about 3x Mars ~ 33% of the Earth's ~ 10% of your planet's mass AND still have at least a partial liquid iron core.

The density and magnetic field assumptions reinforce each other as the satellite probably has an outsized iron core which increases density and odds of some of that core remaining liquid.

You probably want a separation between planet and moon greater than that between Earth and Moon or you'll get huge tides and tidal locking which would decrease the strength of the magnetic field.

I'll supply math details later as time permits.

How hard would it be to launch rockets from the planet?
The rocketry required to escape your planet would be fiendishly difficult. I consider the Earth to be borderline on the everyday practicality of chemical rocketry. We can do it, but it's so difficult/expensive we reserve it for only highly valuable/rare missions.

Chemical rocketry could be used in your case too it just increases the difficulty and reduces the payload even more.

What type of space launch could you use to launch from the planet?
You'll want to use something like Nuclear Pulse Propulsion with high impulse and thrust or possibly one of the non-rocketry techniques of space launch like Light Gas Gun or Ram Accelerator that does not force you to haul your fuel up with you.

• Nice answer. I would add that in this case a space elevator would be immensely helpful as a launching point from the 'Earth', although it would require a lot of effort to begin with. – Mikey May 5 '15 at 17:00
• I agree but it would be much more difficult too. I'd have to go through the math to determine whether it'd be feasible even with something as strong as carbon nanotubes. It'd be helpful if the planet had very high rotation speed - something like 10 hours would help tremendously. – Jim2B May 5 '15 at 19:06

The conditions could be very different between the two bodies, and the life very different as well. At an early time after formation the minor body was more earth-like, similar to the case of our own Mars. The two bodies exchange material so life started on both. But as the moon changed, the early life evolved to cope with very different conditions. After starting with the same abiogenesis stock, life on the two bodies went their separate ways long before photosynthesis and endosymbiosis occurred on the Earth-like body, and cells took different routes on (warmed)Mars-like moon as it lost its surface water and atmosphere.

I imagine that instead of green leaves, beds of black goo filling maria that harvests energy chemically from harsh radiation, in the top layers of cell-less protoplasm that turns over, to circulate the activated chemicals to the “living” parts below.

More complex life include algae (giant cells) and a massive level, of endosymbiosis instead of just eucaryotes. Semi-autonomous organelles share an enclosed bag and can swap out functional parts, including various tamed procaryotes (like mitochondria) that have found different tricks for processing different minerals and other resources. Feeding off the goo above, these thread through the rock of the crust mining materials and water to form the ecosystem.

So the “conventional” aliens from the major body find, upon arriving on their moon, that the rocks are alive, and quickly find ways to eat them.

When I was a child I wondered why Superman didn't have to wear a spacesuit on Earth, since one explanation for his super strength was the much lesser gravity on Earth and humans would have to wear spacesuits to survive on the Moon despite the gravity difference not being enough to make them as strong as Superman.

And I was quite skeptical about science fiction stories where the Moon had a breathable atmosphere.

When I was 12 I read "He Who Shrank" (Amazing Stories, August 1936) by Henry Hasse" and was doubtful about the subplot involving a species who migrated from their home planet to its moon. I was very skeptical about both the planet and the moon being naturally habitable for a single species. "He Who Shrank"is otherwise a memorable story — I had a dream with a variation of its plot recently.

LEKA: The people on our moons have been in discord ever since they migrated from our planet five centuries ago. To us on the planet They're like two squabbling children. We try to help settle their arguments by not taking sides, but this time we are at a loss.

So fifty five years later writers were still not worried about smart children laughing at them for suggesting that a species that originated on a planet could survive on naturally habitable moons of that planet. See also the habitable for Bajorans moons of Bajor in Deep Space Nine.

Of course by then the idea of terraforming planets and moons to make them habitable was well known. See Project Genesis in Wrath of Khan and "Home Soil". So maybe the writers of "The Host" assumed that the people of Peliar Zel had to terraform their moons before settling them.

Thus I suggest that you might face a problem in nomenclature. Calling the larger body a planet and the smaller body a moon may make some readers think that it should be impossible for both worlds to be naturally habitable for the natives of the larger world — or for humans if humans are involved in the story.

One alternative is to describe the two worlds as a double planet instead of a planet and a moon. But not twin planets, of course.

The Earth and the Moon have sometimes been described as a double planet, and after Charon was discovered Pluto and Charon were often described as a double planet instead of a planet and its moon. So you might do well to have some of your characters discuss or argue whether the smaller world is a moon or the smaller part of a double planet.

And maybe include some ironic counterpart to the way that in our solar system the first asteroids to be discovered, and later Pluto, were considered planets and then demoted in status.

Another method would be to have the explorers from the planet talk about how their people have dreamed and argued and studied about the possibility of life on their moon and the probability that it might be habitable for them. Point out that for the people of that world a dream that died over a century ago for Earth people is a reality and how wonderful that is for them. Make it in part a wish fulfillment story for us Earthlings.

A third method — and I think you should use all three — is to show your work. Or, considering your question, the work of whoever you get to do the calculations for you.

Have calculations done to show that the smallest sized and the largest sized habitable worlds can differ in size enough to be described as a planet and its moon, or alternately as sister worlds (but not twin worlds) in a double planet.

A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (Ms≳0.1M⊕; Tachinami et al., 2011); to sustain a substantial, long-lived atmosphere (Ms≳0.12M⊕; Williams et al., 1997; Kaltenegger, 2000); and to drive tectonic activity (Ms≳0.23M⊕; Williams et al., 1997), which is necessary to maintain plate tectonics and to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Gurnett et al., 1996; Kivelson et al., 1996), suggesting that satellite masses>0.25M⊕ will be adequate for considerations of exomoon habitability. This lower limit, however, is not a fixed number. Further sources of energy—such as radiogenic and tidal heating, and the effect of a moon's composition and structure—can alter the limit in either direction. An upper mass limit is given by the fact that increasing mass leads to high pressures in the planet's interior, which will increase the mantle viscosity and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed around 2M⊕ (Gaidos et al., 2010; Noack and Breuer, 2011; Stamenković et al., 2011). Summing up these conditions, we expect approximately Earth-mass moons to be habitable, and these objects could be detectable with the newly started Hunt for Exomoons with Kepler (HEK) project (Kipping et al., 2012).

This indicates a minimum mass for the smaller world of at least 0.25 Earth masses and a maximum mass for the larger world of no more than 2.0 Earth masses, thus indicating the difference in mass can be almost 8 times the mass of the smaller world.

Since the sister planets — or planet and moon — would almost certainly be tidally locked both will rotate with the same period as their obit around their center of mass. The days of both will be equal to their month.

But the faster a world spins the more likely it is to generate a strong magnetic field that protects the outer atmosphere from charged particles. So the orbits of the two worlds need to be designed to give them short enough months and thus fast enough spin.

Some studies suggest that even extremely slow rotation would allow for substantial magnetic shielding, provided convection in the planet's or moon's mantle is strong enough (Olson and Christensen, 2006). In this case, tidal locking would not be an issue for magnetic shielding.

If correct that may greatly lessen the necessity to make the orbits as short as possible.

Note that the article discusses the habitability of exomoons orbiting gas giant exoplanets in the habitable zones of their stars (orbiting "Hot Jupiters") instead of exomoons orbiting Earthlike planets, which may modify some of the calculations a bit.

you will need to calculate both the surface gravity and the escape velocity of both the worlds. It is a well known fact that long term exposure to the microgravity or weightlessness of Earth orbit causes health problems for human astronauts. It is not known if long term exposure to the lower gravity of Mars, for example, would have the same effect on human health.

Thus you can choose to:

1. Ignore health effects of lower gravity on your natives of the planet.

2. Have their scientists use centrifuges set to simulate the gravity of their moon in their orbiting space station and discover that the natives of the planet don't suffer any bad effects from long term exposure to it.

3. Have the characters from the planet make only short stays on their moon.

4. Have the space ship include centrifuges to simulate the gravity of their planet.

5. Have the characters take other precautions against the long term effects of lower gravity, much as Earth astronauts do during long stays on space stations.

6. Have the characters discover the problem during a long stay on their moon, and find out they need to return home immediately, preferably when for other reasons it is least possible or desirable.

7. Have the planet and the moon have very similar surface gravity despite the differences in their sizes and masses, so that it isn't very surprising that the natives of the planet are not harmed by the minor difference in surface gravity.

Or some combination of two or more of the above.

If you make two very dissimilar worlds have similar surfaces gravity despite having very different masses and diameters, they will have to have different densities, despite there being both upper and lower limits of density for Earthlike worlds. The smaller world will have to be denser and the larger world will have to be less dense.

Both the worlds will have to have high enough escape velocities to retain their atmospheres for geological time spans. The escape velocity of the larger world should be as low as is possible, since Earth's is certainly high enough to make reaching orbit and leaving orbit very difficult. Making the larger world less dense (within practical limits) will keep its escape velocity as low as possible.

The Youtuber Artifexian has some good information on the topic, in which he explores star system and planetry building using equations (which I am currently compiling into spreadsheets for ease of use).

According to Artifexian's videos, The mass you gave is great (3.5 Earth Masses is the absolute maximum size I'd use to make a habitable world), and your moon should be less than the mass of your planet, but greater than 0.25 earth masses. This may turn your planet and moon into a binary planet system (like Pluto and Charon) so when calculating things such as orbit you may need to find the Baricentre of the two bodies first.

• Can you go over how you came to those numbers? – JDługosz Apr 8 '17 at 8:59
• Artifexian's youtube channel. – Hannah Apr 8 '17 at 9:24
• So say, at least, “based on the linked presentation,” if you don’t want to summarize how those numbers are found. Note that the comments are review notes, not a discussion! Don't answer via another comment; edit the paragraph. – JDługosz Apr 8 '17 at 9:28