Double planet system

[76561199036238808]

Is there a way to make a stable double planet orbiting around its star? I'm trying to make it so that two planets revolve around a common center of mass, and together around a star. But so far they are only breaking each other's orbits. Creating a pair and balancing the momentum does not help, since they immediately change the overall orbit, and it is impossible to restore it through the barycenter.

[76561198025051992]

I wrote up instructions to make binaries with exact orbits work, both for orbiting larger bodies, and for smaller bodies orbiting the pair. It's long and in-depth, but quite specific. I'll paste it here, in case you want to take the time. It was written for an older version, so there might be some shortcuts that could be taken now that barycenters can be chosen as orbital parents. In ether case, binaries are kinda the final boss of this game.

Originally posted by Aledore:

I know people have struggled to construct systems with binary planets (or stars, or moons) in the past, and while I could do it myself, it was a lot of trial and error and not something I could explain well. I have since stumbled upon a method that is reliable and can be put into a step by step procedure. In this example, I’ll put Earth and Venus in a tight binary orbit with Luna in a one-month orbit around them with them in a one-year orbit around Sol. I’ll be very specific to assure repeatable results, but often the specifics aren’t necessary. I’m doing this in version 32.1.0, but hopefully it will work in future versions (and probably past, if that’s relevant).

This should also include the tools necessary to build systems around binary stars, and planets with binary moons. While this doesn’t include specifics to build trinary, quaternary, and greater systems (systems with more than two bodies with significant effect on the barycenter location), the same methodology should work.

I start by opening the existing sim of the “Solar System - Just Planets” with the “start all simulations paused” checkbox checked. In this simulation, the earth’s orbital parameters are already set, and they’ll became the orbital parameters for the binary system. If using a different system, just enter the desired orbital parameters for the pair into the more massive of the two bodies.

With the simulation still paused, I set the simulation speed to 1ms/s. This will allow the starting of the simulation to allow orbital parents to be determined without any significant movement or acceleration to occur.

I select Venus and write down its orbital parameters: eccentricity, 0.00647; inclination, 3.40°; argument of pericenter, 57.1°; longitude of the ascending node, 76.6°; and true anomaly, -39.7°. These values will determine Venus’s and Earth’s orbit around each other. They could be whatever, but I have to pick something.

I also write down Venus’s rotational parameters relative to its orbital plane: obliquity, 179°; argument of obliquity, 30.2°; and yaw, 180°. This will determine the rotation and tilt of Venus while in a binary orbit with Earth. These values aren’t realistic, but it that’s okay for this example.

Next, I’ll move Venus in the simulation to be near as possible to Earth. There are many ways to do this. The most direct is to select the “relative to” dropdown in “motion”, select object, and select Earth. Keep in mind the selecting Earth from all the other objects may just enter it in the list and it then must be selected from the list. Then enter 10000km into distance.

The next step isn’t obvious. I’m going to lock the mass of Venus and reduce its radius by 90%. To do this, expand “radius” in “overview,” and change the “radius from” to “density,” click the padlock in front of “mass,” and click the x0.1 button under “radius.” This is necessary to allow Universe sandbox to select Earth as Venus’s orbital parent while Venus is so close to the barycenter between the two (just ask the devs).

At this point the simulation will need to be started and immediately stopped again to set Earth the orbital parent. This will be more visually obvious in the view is set to “orbits.” The Earth should still have the sun as its orbital parent.

Now the radius of Venus can be returned by clicking on the x10 under “radius.”

It’s time to reenter Venus’s orbital parameters that we wrote down earlier. This will define the two planets’ orbits around each other. If you want to base the orbit’s parameters off Earth’s equator instead of the solar system’s plane, you need to do some heavy spherical trigonometry to determine Venus’s new inclination and longitude of the ascending node. I have this entered this math into two excel formulas in another thread. This will be long enough already, so I won’t include that here. The results of those formulas are an inclination of 22.84° and a longitude of the ascending node of 171.45°.

Also enter Venus’s obliquity, argument of obliquity, and yaw relative to its orbital plane.

Finally, enter an orbital period of 12 hours. This is an arbitrary value that’s close enough to allow the moon to orbit in a one-month period, but far enough to keep the tides from ripping the planets apart. If you have a difficult time entering the time, use the fine tune slider to make the change.

Earth and Venus are now in a proper orbit, but if the simulation was now run, their orbit around the sun could be highly elliptical, with a period of much longer or shorter than a year. This is because right now their orbit around the sun is based on Earth’s position and velocity. For the orbit of the pair of planets to be as it’s currently described in Earth’s orbital parameters, the barycenter of the two needs to have the position and velocity that Earth currently has.

To do this, start by selecting the two planets at the same time using the control key. In the multiple objects screen, click the “make barycenter” button. Select the barycenter and in “actions,” replace it with a random object. I will use the moon, only because we’ll need to add it later.

Then select Earth and select the “relative to” dropdown in “motion”, select object, and select the barycenter. Again, check if the barycenter is truly selected. Then expand “distance” and “speed” and write down the X, Y, and Z values for each. Change the speed’s units to m/s from km/s for better resolution. These are the “position vectors:” X, -14280; Y, -1683; Z, -1895. These are the “velocity vectors:” X, 360; Y, -788; Z, -1946.

Once these are written down, double all these values. This will move the earth away from the barycenter, pulling the barycenter towards where Earth was. It will do a similar thing to the barycenter’s velocity. You find that the orbit with Venus will fall apart during this, but that’s to be expected.

Next, select Venus and choose the moon for its “relative to.” Again, just because the moon is in the list, doesn’t mean it’s selected so select it again to be sure. Like with Earth, expand “distance” and “speed” and write down the X, Y, and Z values for each. Don’t forget to change the speed’s units to m/s from km/s if you did that for Earth. These are the “position vectors” for Venus: X, 17520; Y, 2065; Z, 2325. These are the “velocity vectors:” X, -442; Y, 967; Z, 2388.

Add the earth’s values to Venus’s and enter those. This will change Venus’s speed and position the same amount Earth’s speed and position was changed to maintain the orbit of the two. It will also move the barycenter’s speed and position the rest of the way two where Earth was. As this is done, the orbit of Venus around Earth will be corrected.

The moon has no further use and can be deleted. Now we have a binary planet in the same orbit around the sun as Earth used to have. I’m going to save this as “Earth Venus Binary” and test it. The orbits dance around every 12 hours, but with the view set to “trails,” it’s pretty clear that the pair is in proper orbit around the sun.

Let’s add the moon in. I’m going to open up the Solar System simulation with moons in it to get the orbital and rotational information for the moon. The moon’s orbital parameters: eccentricity, 0.061; inclination, 5.16°; argument of pericenter, 260°; longitude of the ascending node, 42.4°; true anomaly, -170°, and orbital period; 650 hours. The Moon’s rotational parameters relative to its orbital plane: obliquity, 5.15°; argument of obliquity, 9.84°; and yaw, 43.0°.

Then we open the Earth Venus Binary saved simulation, but we can’t place the moon in orbit around either of them because the other exists. The simulation was saved and reopened, but in no way is that necessary, but it is important to create the barycenter a second time after the speeds and positions are changed.

Again, select the two planets, create a barycenter, and replace it with another object. This time I’m going to select Titan to prevent confusion when the moon is added. We’re going to use Titan as the orbital parent for the moon to orbit, so its mass will need to be raised to the sum of the masses of Earth and Venus. Venus’s mass is 0.815 earth masses and Earth is of course 1. If you increase the mass of Titan to 1.815 earth masses, is will grow to touch Earth, so like we did with Venus, expand “radius” in “overview,” and change the “radius from” to “density,” click the padlock in front of “mass,” and click the x0.1 button under “radius.”

Now we have a body for the moon to orbit, but the Earth’s and Venus’s gravity are still in effect. Go the “overview” of each and turn off “pull others.” This will make the Moon’s orbit based entirely on the barycenter.

Select the add object and place the moon in orbit around Titan. Anywhere around 0.003 AU away from Titan should work. Then enter the moon’s orbital parameters and rotation parameters we wrote down before, including the orbital period.

The final step is to remove Titan and turn on “pull others” for Earth and Venus. Then we can save the simulation and test it. The trails don’t really tell the story about where the moon is going, and the orbit is even less useful, but if you go into “visuals” of Earth and set it as the “trail center,” you’ll see the moon is making a spiral path around the Earth, which is actually an elliptical path around the barycenter of Earth and Venus.

Keep in mind that this makes the assumption that the moon isn’t massive enough to significantly alter the orbit of the binary pair around the sun. If it were massive enough to cause a significant error, a barycenter would need to be created between it and Titan, a random object placed there, and the position and velocity of Titan relative to this new object would need to be added to Earth, Venus, and Luna, before Titan and the new object were deleted.

I knew that was going to be long, but that's even more than I expected. If someone knows a streamlined way of doing this, I'd love to hear it.