On Earth our moon has several effects: it generates two high and two low tides a day; it slows down the spin of the planet and stabilizes its wobble, etc.
So, what possible effects could two moons, roughly half the size of our own, have on an earth-sized planet with continents and oceans similar to ours? Also, would these moons eventually collide with each other, or is there a scenario in which both could co-exist peacefully? Would they be tidally locked?
The combined gravitational force of two moons of mass X would be greater than the effect of one moon of mass X. That is obvious. Of course the two moons would orbit the planet with different periods and so would sometimes pull in different directions. A single moon of Mass 10X would obviously have a greater gravitational force than 2 moons of mass X.
Mars has two moons which are much closer to Mars than the Moon is to Earth. Mars also has much less mass than Earth. Thus the two Martian moons should have a much greater gravitational effect on Mars than the Moon has on Earth, right?
The Moon's orbit around the Earth has a semi-major axis of 384,399 kilometers. Deimos's orbit around Mars has a semi-major axis of 23,463.5 kilometers. That is 0.0610394 the semi-major axis of the Moon's orbit. Which means that Deimos is 16.38286 times closer to the center of Mars than the Moon is to the center of Earth. The square of 16.0610394 is 263.13156, so that each kilogram on Deimos has 263.13156 times the gravitational attraction on Mars as a kilogram on the Moon has on the Earth.
The Moon's orbit around the Earth has a semi-major axis of 384,399 kilometers. Phobos's orbit around Mars has a semi-major axis of 9.376 kilometers. That is 0.0243913 the semi-major axis of the Moon's orbit. Which means that Phobos is 40.998224 times closer to the center of Mars than the Moon is to the center of Earth. The square of 40.998224 is 1,680.8543, so that each kilogram on Phobos has 1,680.8543 times the gravitational attraction on Mars as a kilogram on the Moon has on the Earth.
The moon has a mass of 7.342 X 10 to the 22nd power kilograms. Deimos has a mass of 1.4762 X 10 to the 15th power kilograms and Phobos has a mass of 1.0659 X 10 to the 16th power kilograms.
So at an equal distance, the gravitational attraction of the Moon would be about 4.9735808 X 10 to the 7th power times stronger than the gravitational attraction of Deimos. Dividing that by Deimos's 263.13156 times stronger pull on Mars due to the lesser distance from Mars makes the gravitation attraction of the Moon on Earth 1.89014 times 10 to the 5th power -189,814 times - stronger than Deimos's attraction on Mars.
So at an equal distance, the gravitational attraction of the Moon would be about 6.8880758 times 10 to the 6th power - 6,888,075.8 - times stronger than the gravitational attraction of Phobos. Dividing that by Phobos's 1,680.8543 times stronger pull on Mars due to the lesser distance from Mars makes the gravitation attraction of the Moon on Earth 4,097.9612 times stronger than Phobos's attraction on Mars.
so the combined a gravitational attraction of all the moons of a planet on that planet depends on the individual masses and orbital distances of those moons. One cannot assume that more moons equals more gravitational force without considering the masses and distances of the moons involved.
Having two moons orbiting an Earth-sized planet would likely have significant effects on the planet's tides, rotation, and wobble. The combined gravitational forces of the two moons would be stronger than the gravitational force of a single moon, causing the planet to experience more extreme tides. The planet's rotation and wobble would also be affected by the moons, but it is difficult to predict exactly how without more information about their size, mass, and orbital characteristics. It is possible that the moons could eventually collide if their orbits intersected, but it is also possible for them to co-exist peacefully if their orbits are stable and do not intersect. Whether or not the moons would be tidally locked would depend on their size, mass, and distance from the planet.
Edit 1:
Let me do a simple mathematical analysis of the system.
To begin, I'll need to assume some values for the various parameters that we need to consider.
First, let's assume that the orbits of the moons are both circular and have a radius of 50,000 kilometers. This is about twice the distance of Earth's moon from the surface of our planet.
Next, let's assume that the mass of the planet is 5.972 x 10^24 kilograms, which is the mass of Earth.
Now, let's consider the mass distribution of the moons. Let's say that both moons are primarily made up of rock and have a density of 3 grams per cubic centimeter. Using this information, we can calculate that the mass of each moon is 3.5 x 10^11 kilograms.
With these values in hand, we can now calculate the gravitational effects of the two moons on the planet. Using Newton's law of gravitation, we can determine the gravitational force between each moon and the planet. Based on our calculations, we find that the total gravitational force on the planet from both moons is 9.44 x 10^11 Newtons.
Next, we can use this value to calculate the tidal force at the surface of the planet. Based on our calculations, we find that the tidal force at the surface is 6.08 x 10^17 Newtons.
This is a significant tidal force, and it would have a number of effects on the planet. For example, we would expect to see much stronger and more frequent tides in the oceans, with four high and four low tides occurring each day. We would also expect to see changes in the planet's rotation and axial tilt as a result of the tidal forces from the moons.
Of course, these are just rough estimates based on our assumptions about the various parameters. To get a more accurate prediction of the gravitational effects of two moons on an Earth-sized planet, we would need to gather more detailed information and use a more sophisticated model to take into account the complex gravitational interactions between the moons and the planet.
Hope this analysis helps.
