Maximum size of a visible planet without effects on my world

Question

I want to build a world where one planet could be visible from the sky, day and night with the naked eye periodically (like Earth's moon behavior) and not everywhere at the same time (since my world is a round-shaped planet too). My world would have a moon and a star/sun (both similar in relative size and distance of the Earth's).

The visual I want for my world is similar as the background image of this StackExchange. I want a planet as visible as the big white planet in the sky.

I'm wondering what could be the maximum size of the planet for it to have minimal impact on my planet. I'm looking for a way the planet would not have an impact on the day/night cycle or even too much impact on gravity (no apocalyptic event, minor events would be fine though) or even my world's climate.

For now, I think that for the planet to have the minimal impact would be for it not to be between my world and my sun. I don't want my planet to hide the star but I don't want either for it to reflect the sun too much by night (the planet could have a color not as reflective as white ?)

From there I want the planet to be as visible as possible for the creatures on my world.

Answer 1

Unfortunately, it is really hard to do what you ask.

The specific thing you asked for in the comments is for the planet to be "bigger in the sky." You also mention the visual from the WorldBuilding page to be an example of the kind of planet you want to see.

The trick is that those angular sizes are huge. Most planets are so small that they appear to be point sources until you look at them with a telescope. Jupiter, as large as it is physically, is only about 50 arcseconds wide visually. Now most people don't think in arc seconds, so to give you a sense of scale for that, the Moon is about 1,860 arcseconds wide. The human eye can resolve objects who size is about 60 arcseconds, meaning objects larger than that appear to be "distributed" objects rather than point sources. This suggests that if you moved Jupiter closer, you could easily cross that threshold and people would see Jupiter as a circle rather than a point.

However, if you want to move towards the scale of the moon, it gets trickier. If we pick an angular size (such as 1,860 arcseconds), then the radius of the planet scales linearly with the distance. So a planet 2x as far as the moon is from us would have to be 2x as big in radius to appear to be the same size. The mass goes up by the cube of this, so the mass of the planet would be 2x2x2 = 8 times more massive. The effects of gravity go down by the square of the distance, counteracting some of the mass. Thet net result of all of thes proportions? The gravitational impact of an object which appears to be a chosen size scales up linearly with the distance to the object.

This has profound implications. Mars is at its closest about 55 million km from us. The moon is about 0.4 million km, so a Mars orbit is about 140 times further than that of a moon. This means that an an object that appears to have the radius of the moon would be approximately 100 times larger than the mass of Jupiter, and would have a gravitational effect of 140 times that of the moon.

There's a reason that reasonably sized planets, like Jupiter, appear to be so small. For perspective for what this means, we could also look at the sun. The sun happens to be roughly the same size at the moon visually, which is why eclipses are such an exacting phenomena. This means that a planet 1AU away from your planet would literally have to be the size of the sun.

So the solution is that if you want an object to be visible, but not have a major gravitational effect, you want it to be closer. What you really want is a smaller closer moon, which appears bigger but has a smaller gravitational impact. If your object needs to be planet sized, it simply gets tricky to make that a reality.

Answer 2

Here are couple views of Jupiter from its moons, and they do look like the background image. https://www.jpl.nasa.gov/spaceimages/details.php?id=PIA17043
http://www.spacetelescope.org/products/art/frank_hettick_1/

They are simulated images, but made by space agencies, so I hope they got the scale right.

I know you wanted your planet to have its own moon, but it is apparently not very likely if your planet is a moon of a gas giant. You will have view of other moons, though.

Btw, if you really get two similarly-sized planets close together, they can get tidally locked, so the neighboring planet will be in the same spot in the sky, and you will not be able to see it from half of your planet. On the plus side, you could put in a space elevator between planets.

Two equally sized planets and a smaller moon is a three-body problem, and I remember reading that it is possible but unlikely.

Finally, the true limiting factor is Roche limit (I am too tired to explain). But apparently, Moon can be a lot closer to Earth than it currently is.

Answer 3

According to this List of Exoplanet Extremes:

https://en.wikipedia.org/wiki/List_of_exoplanet_extremes1

The planets Kepler-70b and Kepler-70c approach each other to a distance of about 240,000 kilometers, and when they are at the closest approach, Kepler-70c would appear 5 times the size of the Moon in Kepler-70b's sky.

But from what I see they are unlikely to be habitable planets.

https://en.wikipedia.org/wiki/Kepler-702

From what I have read the potentially habitable planet with the shortest year is TRAPPIST-1d with a year 4.05 Earth Days long.

https://en.wikipedia.org/wiki/List_of_potentially_habitable_exoplanets3

TRAPPIST-1E at closest approach to TRAPPIST-1d would be about 2.731 times as far as the Moon is from Earth, and has 0.91 the radius of the Earth. The Moon has a radius of 0.273 the radius of Earth, so TRAPPIST-1E has 3.333 times the radius of the Moon. At it's closest approach TRAPPIST-1E would appear 1.220 times as wide as the Moon from TRAPPIST-1d, though at other times it would look much smaller than the Moon.

https://en.wikipedia.org/wiki/TRAPPIST-1#/media/File:PIA22094-TRAPPIST-1-PlanetLineup-20180205.jpg4

So this example shows that it is possible for a potentially habitable planet to sometimes get close enough to another planet in its solar system to see that other planet at least as large as the moon looks from Earth.

But if you want a situation where the other planet looks much larger than the moon from the surface of the habitable planet you will have to get someone else to construct your solar system and do the calculations.

Another possibility is a habitable planet in a Trojan orbit with a gas giant planet and a star. If the star is a really dim red dwarf the habitable planet would have to orbit very close to the star. Thus the orbit of the habitable planet would be a relatively small one and the 60 degrees of separation between the gas giant planet and the habitable planet would be a relatively small distance.

If the habitable planet and the gas giant planet orbit at 10,000,000 kilometers from the star, the two planets in a Trojan relationship would be about that far from each other. At that distance a gas giant the size of Jupiter would have an angular size of about 0.75 degrees or 45 arc seconds, about 1.5 times the angular diameter of the moon as seen from Earth.

The smaller, habitable planet would actually move a lot around the exact L4 or L5 position, and would get significantly farther and closer to the gas giant planet, making it appear sometimes smaller and sometimes larger than calculated.

Since TRAPPIST-1d is in the stellar habitable zone and orbits TRAPPIST-1 at only 3,330,000 kilometers, a habitable planet could be a third as far from its star as in the Trojan system above. Thus if the gas giant is as large as Jupiter it could appear 4.5 times as wide as the moon from the habitable planet in the Trojan position.

Unfortunately Jupiter is almost as large as the largest possible gas giant. Gas giant planets much more massive than Jupiter are believed to have smaller diameters as their intense gravity compresses their atmospheres.

Another possibility for a planet appearing very large as seen from a habitable planet would be a hot Jupiter. Hot Jupiters are gas giant planets orbiting very close to their stars and having very high temperatures, hundreds or thousands of degrees hotter than Earth. Some hot Jupiters are called "puffy planets" or "hot Saturns" because they are very large and have very low density. They are so hot that their atmospheres swell up and their diameters increase.

WASP-17b, the puffiest known planet, has about twice the diameter of Jupiter and half of it's mass.

Unfortunately, a habitable planet would have to orbit their star several times the distance of the hot Jupiter in order to have habitable temperatures. Thus their star would have to be a very dim one for their orbital separation to be only a few million kilometers. And the hot Jupiter would look the largest when it was between the habitable planet and the star and thus would look like a very thin crescent during the day.

Also you might want to check out this:

https://planetplanet.net/2017/05/03/the-ultimate-engineered-solar-system/5

And ask about calculating to make the distances between planets as small as possible.

Thus my calculations indicate that it would be difficult to get another planet to appear more than a few times the apparent diameter of the Moon in the sky of a habitable planet. Possibly someone else can suggest a plausible orbital arrangement to make another planet look much larger.

But if the habitable world is not a planet but a hypothetical Earth-sized moon of a gas giant planet orbiting in the habitable zone of their star, the gas giant can appear quite large in the sky of the habitable moon. And other large moons would appear to get larger and smaller as they orbited the planet.

There are, of course, some limitations on the maximum and minimum apparent diameters of gas giant planets as seen from any habitable moons they may have.

If the planet has a diameter between those of Neptune and Jupiter, for example, the planet's apparent diameter as seen from a moon at a specified distance would be between those of Neptune and Jupiter at that distance. And depending on the mass of the planet and the mass and distance of the star, there are inner and outer limits for the orbit of habitable moons.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/36

Can a gas giant have its own habitable zone?7