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The Superlunar Cycle

Back home, Earth's moon is 2159 miles wide, orbits the planet from a distance of 238,900 miles and has 1/81 the planet's mass. It usually takes the moon 27.3 days to complete one orbit around Earth, but one lunar cycle--the transition from new moon to new moon--lasts 29.5 days.

In an alternate Earth, the moon is 3743 miles wide, orbits the planet from a distance of 426,000 miles and has 1/18 the planet's mass. How would this change in dimension affect the overall lunar cycle?
 

Viorp

Minstrel
If the moon was this big it would not be considered a moon anymore.

Earth and the moon would be probably considered a double-planetary system.
I'm sadly unable to provide you exact math, but the time of cyrcling would change a lot.

I propose watching artifexians videos on this.
 

elemtilas

Inkling
A moon is a moon if it is smaller than the parent it orbits.

From what I've read, there are not a few astronomy folks who do consider Earth-Moon to be a double planet already. And also a planet-satelite system at the same time. Depends on what behaviour you're looking at, I guess!
 

Vaporo

Inkling
*Starts shaking rapidly. Spontaneously sprouts a pocket protector and large overbite.*

Well, it's kind of arbitrary what defines a double planet vs a planet-moon system. Physically, both work the same. The most common definition I've heard is that a double planet system is one in which the barycenter (The central point about which both bodies orbit) is above both planets' surface, a requirement which the earth-moon system does not satisfy.

Calculating the new orbital characteristics of your new moon is pretty easy. The formula for gravitational attraction is G*(m1*m2)/(r^2). Put your values in and you get 2.81E+20 N of gravitational force. There must be an equal centrifugal force to balance it if the two are in orbit. The formula for centrifugal force is F= mv^2/r. r depends on the location of the barycenter, the formula for which is r= a*m2/(m1+m2), which puts the barycenter at 36083187 meters from earth. So, 2.81E+20 = 5.972E+24 *v^2/36083187. Solve for v and get 41.2 m/s (174.8 m/s for the moon). The circumference of the earth's orbit in our case is 226717159 m, which gives an orbital period of 5502844 seconds, or 63.7 days.

The length of the lunar cycle is actually a bit tricky. I believe that the equation is sin(pi*x/63.7)=-sin(pi*x/365). This is actually rather annoying to solve by hand. However, through the power of computerized solvers, I can tell you that your lunar cycle will last about 77.16 days.

Also, the earth's radius is 6,371,000 meters. Our barycenter is 36,083,187 meters from the center, so by the definition I've heard this would be considered a double planet.

*Starts shaking rapidly again. Teeth return to normal. Pocket protector retracts into skin.*

Where are you getting these numbers from? Are you just making them up as you go along, or is there a specific reason that you want these particular numbers?
 
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Where are you getting these numbers from? Are you just making them up as you go along, or is there a specific reason that you want these particular numbers?

The distance, kind of. I was just looking for the right distance to make sure that the larger moon does not result in tides being another major natural disaster. As for the diameter, I take advantage of record-breakers. For example, I was muddling on a brainstorm involving Earth being orbited by someone like Ganymede.
 

SMAndy85

Minstrel
The other pocket-protector inducing thought is that with a moon that large, and the barycenter being above the surface of both (such a large moon suggests that would be the case), then you'd end up with another common phenomenon... Tide Locking.

So, with your numbers, you're looking at the moon being roughly half the diameter of Earth. That's not enough for it to become instantly tide locked. The moon would still be tidally locked to the Earth, because of the huge mass difference, but it would probably cause the rotation of Earth to be closer to locked than it is now. Consider that Pluto and Charon are both tidally locked to each other, and most of Jupiter's moons are tide locked to Jupiter. It's a common thing which happens to all planetary bodies given enough time. Currently, the calculation of this means our sun will expand to destroy us before we become tide locked to it.

The length of our day is increasing very slowly as time goes on. Charon is 1/8th the mass of Pluto, and half the diameter, and they are both tide locked to each other. It's something you need to consider! Chances are, it would just mean the day lengthens faster than it does currently. We gain 2 milliseconds of day per century, roughly.

The moon is currently 1.2% the mass of Earth, or 1/83rd, ish. Increasing this mass to 1/18th is a significant difference!

But for your actual question, a larger body, further out, would have a longer orbital period. That would mean the oceans would be pulled for a longer time in one direction, before changing. I don't know how the calculations work, or how to calculate that in relation to the spin of Earth, but consider that Earth has a longer year than Venus. (Venusian year is 225 days) purely because it's further away. It's a good comparison, since Venus and Earth are very similar mass and diameter.
 
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