Despite being known to humans for many thousands of years, the planets in the Solar System are still active areas of study for astronomers. Each of the planets is unique in some way, allowing us to see how different conditions can produce very different results just within our own astronomical back yard. When you add in things like asteroids and comets, the Solar System is a very dynamic place!

In addition to our own Solar System, astronomers now study planets around other stars, which are called exoplanets. These planets are so small and far away that it is very difficult to learn anything about them, or if they are even there at all. However, astronomers have developed some complex techniques for studying them, allowing us to learn more about what our Solar System could have been like if things had been slightly different.


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Solar System

What planet is closest to Earth? (Beginner)
This is actually a very interesting question and the answer depends on how you ask it.
If you want to know the planet that gets the closest to Earth, the answer is Venus. Venus’s average orbital radius is about 108 million km compared to Earth’s 150 million km, meaning that when the planets are exactly lined up, they are around 42 million km from each other, which is closer than Earth ever gets to its other neighbor Mars, which has an average orbital radius of about 227 million km.
If we want to know what planet is closest to the Earth at any given time, then the answer gets more complicated and depends on the specific positions of the inner planets. Over time, this shifts between Mercury, Venus, and Mars (currently it’s Venus), but Mercury is actually the planet that is closest on average to Earth. Here are some very cool and informative YouTube videos giving the reasons why, but the summary is that since Mercury orbits so close to the Sun, it just can’t ever get that far away from Earth. Venus and Mars are very far away when they are on the opposite side of the Sun, but Mercury is on a tight leash with its small orbit so it spends more time closer to the Earth. This is a cool and unexpected result that was only really discovered in the past year or so.
How did the discovery of the phases of Venus prove that the Solar System is heliocentric? (Beginner)
The observation of the phases of Venus were a key moment in the history of astronomy, but it’s not just that Venus has phases, it’s also the size and location of Venus during each phase. The results are best summarized in the diagram below that show pictures of the phase, size, and position of Venus over time:
As you can see, unlike the Moon, Venus changes in size drastically in different phases, looking very small while close to full and very large while close to new. In addition, a full Venus can never be observed because it passes too close to the Sun (off the right edge of the diagram). So the phases of Venus are totally different from the phases of the Moon, showing that something must be different about their orbits.
The Moon’s phases make sense because it orbits around the Earth (so it stays at the same distance regardless of the phase) and can be illuminated by the Sun at any angle (so all phases are visible). However, for Venus, the only way the phases make sense is if Venus is closer to us while it is a crescent (so it is orbiting around something else), and the fact that it is hidden by the Sun when it is full means that it must be orbiting around the Sun.
We can observe the same type of phases for Mercury, so it must be orbiting around the Sun as well, and the slight phases of the outer planets plus the way their sizes change over the course of the year also only make sense if they orbit around the Sun as well. All of these data points combine to make irrefutable evidence for a heliocentric model, which is why Galileo’s discovery of the phases of Venus was so important.
Do solar storms affect the orbits of asteroids like Apophis? (Beginner)
It’s unlikely that solar storms like the ones that have happened over the past few months have any substantial effect on the orbits of bodies in the solar system. While it is necessary to account for the solar wind (the constant stream of high energy particles emitted by the Sun) when calculating the orbits of satellites, even for something as small as an individual satellite, the effect is very small. For something much heavier like a Moon or an asteroid (like Apophis), the change in the orbit would be minuscule, far below the level of precision we have for measuring the orbits in the first place.
Is Planet 9 real? Is its proposed orbit weirdly shaped because it ran into Pluto? (Intermediate)
The existence of Planet 9 is currently a large and unanswered question in solar system astronomy. The evidence for it boils down to weirdness we have observed in the orbits of comets and other bodies orbiting past Pluto in a region called the Kuiper Belt. Essentially, the orbits of these Kuiper Belt Objects seem to have all been tugged in the same direction by a single object, leading to the theories on the position and size of the planet. The current best guess is that it is larger than the Earth and on a elliptical (ie elongated) orbit that is inclined (ie slanted) relative to the orbits of all of the other planets. However, the distance and size of Planet 9 mean that it is almost impossible to find. We would have to point one of the biggest telescopes on Earth in exactly the right spot multiple times in order to see its movement against the stars in the background, which would require us being incredibly lucky since it could be almost anywhere in the sky. It is possible that an upcoming telescope survey by the Vera Rubin Telescope (formerly the Large Synoptic Survey Telescope) would find it as it scans the entire sky every few days, but we don’t know for sure.
Your question about planetary collisions is also complicated. In the early solar system, things ran into each other all the time, resulting in large piles of materials that became the planets we have today. You can think of planets as snowballs rolling through the snow gathering up more debris and becoming larger and larger. Over time, planets attract all of the material near them, absorbing it all to make the main planet larger. Planet-size things don’t bounce off each other like pool balls, they merge together like clay. Given that this process has been happening for over 4 billion years, it seems surprising then that Neptune and Pluto haven’t run in into each other yet since their orbits cross. However, Neptune and Pluto are in something called an orbital resonance, meaning that their orbits are in sync with each other. For every two times Neptune goes around the Sun, Pluto goes around three times, and this perfect synchronization means that they always end up missing each other. These kinds of orbital resonances are common in places where different objects are close enough together to interact gravitationally, like the moons of Jupiter. Pluto likely ended up in its current position because it’s a stable orbit, so it’s unlikely that it would have been knocked there by accident.
Planet 9 (if it exists) is definitely not so close that it would risk running into Pluto. If it was, its size (which we expect to be pretty large) would mean that we would be able to see it better than Pluto, and its gravity would have a noticeable impact on Pluto’s orbit as well. Currently, the only evidence we see if it is some possible disturbances of Kuiper Belt Objects, and since scientists are required to be skeptical of any bold new claims until they are proven conclusively, we must wait to see some more evidence. Hopefully this answers your questions.
If a new comet passes Earth (like Neowise), does that mean a new meteor shower will occur? (Beginner)

You are correct that many meteor showers are the result of the Earth passing through the remains of a comet tail, but the conditions have to be just right for that to actually happen. Most comets are not actually aligned with the orbits of the planets, meaning that while all of the major planets more or less orbit in one flat circle, comets can go far outside that circle. This is the case for Neowise, which, as you can see in this 3D model of the Solar System, travels completely above/below the Earth’s orbit. So it’s tail may leave some debris in the orbit of Mercury (which can’t really have meteor showers since it doesn’t have an atmosphere) but it won’t really do anything for the Earth.

What would happen to the Moon if the Earth disappeared? (Beginner)
If the Earth disappeared, the Moon would mostly just keep on orbiting around the Sun the way the Earth was before. Depending on where the Moon was in its orbit, it would get flung off in a random direction, but it wouldn’t go fast enough to change the shape of its orbit much from where the Earth orbits now (it would probably just make it a little more elliptical). So essentially, if the Earth disappeared, then the Moon would basically just take its place as a new planet. 
Is the Earth at risk of being destroyed by a rogue planet, asteroid, or black hole? (Beginner)
The good news is that you have nothing to worry about. Of course, it’s not as easy as being told, “don’t worry,” to stop worrying, so let’s look at some science.
The first thing to recognize is that an asteroid is the only sort of rogue object that has any chance of hitting Earth and causing damage to it.
Black holes are caused by the collapse of stars which are at least three times bigger than our sun. The nearest star, Proxima Centauri, is 4.24 light years away and far too small to ever become a black hole. Even if Proxima Centauri could become a black hole, it would stay right where it formed: 25,000,000,000,000 miles away.
Asteroids are a bit of a different story. We know they do move around in our solar system, because we witness rocks falling to Earth in beautiful meteor showers all of the time.
Most objects that enter Earth’s atmosphere are going to burn up before they ever reach the ground. That is what creates those bright streaking tails of meteors. However, sometimes, an object is big enough that it won’t burn up and will impact with the surface of the Earth. As I’m sure you have heard, an asteroid 6 miles across is what ended the reign of the dinosaurs and allowed mammals like us to take over the Earth. So, if a large enough asteroid were to hit Earth, it would have a pretty big effect.
That’s where the good news comes in. We, as humans, happen to be a bit smarter and more technologically savvy than dinosaurs. By using telescopes and advanced computer tracking software, we can detect and predict the movement of objects in space that are heading towards Earth. In fact, there are experts and space agencies across the world devoted to watching the skies and keeping us safe. The Guardians of the Galaxy may be the stuff of comic books, but we do have real life Guardians of Earth in the form of NASA’s Center for Near Earth Orbit Studies.
Scientists are constantly working to evaluate the best ways to deal with an asteroid if it approaches Earth. Everything from breaking it up with explosives to redirecting it. And, an asteroid large enough to cause an extinction-level event is predicted to occur only once every 100 million years. So, the chances of it occurring in our lifetime, or even the lifetime of our children, is 0.00000001%!
Do you think there could be a volcano underneath the Great Red Spot? (Intermediate)
Astronomers can be pretty sure that there is no volcano below the Great Red Spot on Jupiter. There has been a lot of study of the internal structure of Jupiter (including by the Juno space probe that is currently orbiting it) and we can be reasonably sure that if there is a solid surface anywhere below Jupiter’s clouds, it’s so far down that there is no way it could ever directly influence what is going on on the surface. The clouds we see are just a thin layer on top of thousands of miles of ultra compressed hydrogen and helium that are forced into a weird metallic fluid form by the super high pressures (see below). The Great Red Spot could be a result of some “volcano” of atmospheric gases (kind of like a thunderstorm) but it’s not anything related to the surface. Also, the storm moves around the planet at a slightly different rotation rate compared to the rest of the planet, so we know it’s not tied to anything solid.
Why does everything in the Solar System seem to orbit on a plane? Or is that’s just the way it’s portrayed due to looking at it in a 2D manner on videos? (Intermediate)
The Solar System started as a big spherical cloud of gas. The individual particles in this gas were moving around essentially randomly, but on average, the cloud was rotating slightly. You can think of this like a basketball spinning on someone’s finger: most of the air molecules in the basketball are just bouncing around randomly inside the basketball, but since the basketball as a whole is rotating, the average of all of the velocities of the air molecules will show some rotation.
The particles in this rotating spherical cloud of gas also had gravity though, so over time, they pulled themselves towards each other, making the gas cloud shrink. As these particles were attracted to each other, they would sometimes hit each other and stick together, forming the beginnings of what would become the planets and asteroids. When these particles stuck together, the velocity of the new particle would be the average of the velocities of the two particles that made it up:
This means that if you had a particle that was going up collide with a particle that was going down, their velocities would average out when they stuck together and the new particle wouldn’t be going up or down. This process happens countless times as small particles combine into entire planets, and at every step, the velocities get averaged out more and more. We said that on average, all of the particles were rotating slightly in one direction, so after we have averaged out all of the randomness, all we are left with is this rotation.
So all of the planets are orbiting in the direction of the original rotation of the cloud of gas that created the Solar System. The various rocks and particles that combined to make them all had their randomness averaged out, leaving a set of flat orbits that only deviate from each other by a few degrees.
Could we move Pluto into orbit around the Earth? What would happen if we did? (Intermediate)
Relocating Pluto to orbit the Earth would take a lot of energy. It’s not only that you would have to move it across the Solar System (which would require changing its orbit substantially), but you would also have to speed it up considerably once it got to Earth. Pluto orbits the Sun at about 12000 mph, and you would have to reduce that to almost 0 before it would fall into the Earth’s neighborhood. However, as I told one of your children, the Earth orbits at about 66000 mph, so you would have to speed Pluto up again to match speed with the Earth. In all, just changing the speed of Pluto would require a few quadrillion times the total energy consumption of the entire world. You might be able to save some energy using some fancy rocket science tricks (spacecrafts often use gravitational slingshots from other planets to move them around the Solar System without having to use their rocket fuel), but it would still be a lot. There’s no reason it couldn’t happen, it’s just far far beyond our current technological abilities as a species.
But what would happen if it got here? Pluto is actually only about 1/6 the mass of the Moon, so if you just parked Pluto far outside of the Moon’s orbit, things would probably be fine for a bit. It would take Pluto months to complete one orbit, and it would likely cause some problems down the line because small systems of 3 or more bodies in close proximity have a tendency to turn chaotic, but if you placed Pluto just right it could stay stable for a while. The real problem would be that as soon as you got Pluto into the inner Solar System, it would start to melt. Ice can exist in the outer Solar System (beyond the asteroid belt), but the sunlight is too strong here in the inner Solar System, meaning that all of the ice (water ice as well as frozen nitrogen, carbon monoxide, and other things) would immediately start turning into gas. This is what happens to comets as they enter the inner Solar System, so you can think of Pluto developing a gigantic and permanent comet tail that stretched (probably) far across the Solar System.
I don’t know how long it would take for Pluto to melt (probably at least a few dozen million years but who knows), but for that whole time, the Earth would not be a very good place to be. Pluto isn’t all ice, it’s more of a dirty snowball with bits of rock scattered throughout, so as this ice melted, it would rain dust and rocks on the rest of the Earth system, likely causing massive harm to the surface of the Earth. The huge amounts of nitrogen gas would also likely make its way to the Earth’s atmosphere, increasing its thickness by a lot and making the atmospheric pressure at the surface crushing. All of the energy from the melting ice’s gas and dust falling to the surface of the Earth would (ironically) heat the Earth up a great deal, making it pretty inhospitable. I wouldn’t guess that life would last too long in this situation, but it’s hard to know for sure.
So the short answer is that it would be almost impossibly hard to move Pluto to orbit around the Earth, and if you managed to do it, you would probably kill everybody in the process (but produce a nice giant comet!).
Now that the DART mission has shown that we can redirect asteroids, what would it take to redirect the Earth's orbit? (Intermediate)
This is an interesting question, but things don’t really work that way because the Earth is really really big. The DART spaceprobe (the thing that we crashed into the asteroid Dimorphos) weighed about 500 kg, while Dimorphos weighs about 5 billion kg. This means that the asteroid was about 10 million times heavier than the space probe that redirected it, so it’s impressive that it was even able to make it move at all! But since it was going really fast (6.6 km/s) then it was able to transfer a ton of energy to the asteroid and change its orbit.
Things look worse when we start comparing rockets to the Earth though. The heaviest rocket ever launched, the Saturn V rocket that carried astronauts to the Moon, weighed about 3 million kg, while the Earth weighs about 6 trillion trillion kg (6 x 10^24 kg). This means that even our biggest rocket was a million trillion (10^18) times smaller than the Earth, so the weight comparison is tiny compared to DART and Dimorphos. So even though parts of the Saturn V accelerated up to a similar speeds as DART, its impact on the Earth’s orbit was imperceptible.
What evidence is there for nebular theory, the idea that the Solar System formed from a cloud of gas? (Intermediate)
Nebular theory is the model of star formation where solar systems collapse out of a cloud of interstellar gas, resulting in a central star and a disc of debris that forms itself into planets. This theory is so dominant in modern astronomy that I have never heard any theory besides it, so it’s kind of hard to talk about what “evidence” would be in this case (since it’s not really an argument) but I’ll tell you a few things about our solar system and others that let us know that this is what happened.
The most conspicuous and convincing piece of supporting evidence is that all of the planets orbit in basically the same plane. Out of the 8 major planets, the largest angle that one deviates from the same plane is around 7 degrees for Mercury. This is because as the cloud of gas condensed to create the solar system, it had some dominant direction of rotation that was passed on to all of the things that it formed. If the planets were just assembled randomly by some other process, we would not expect this, so nebular theory makes much more sense. In addition, random orbits would likely be much more elliptical rather than circular.
Another supporting piece of evidence along the same lines is that the rotations of most bodies in the solar system go in the same direction as well. This is not as overwhelmingly true as their orbital directions because there are exceptions (Uranus rotates sideways and Venus rotates backwards) and these are open questions in solar system dynamics, but it is still much better than random chance.
One more piece of evidence that is a bit less obvious is the composition of the solar system. We have seen that the planets in the solar system tend to be made of similar mixtures of elements, which wouldn’t necessarily be true if they weren’t all formed out of the same cloud. Furthermore, every piece of material we have found in the solar system can be radiologically dated to basically the same time, meaning everything in the solar system must have formed concurrently, pointing to a single collapse of a gas cloud rather than separate formation.
Why is the Oort cloud round when the Kuiper Belt is flat? (Intermediate)
I think the best way to answer your question is to instead ask the opposite: Why are the orbits of the planets and the Kuiper Belt flat? The Solar System formed out of a large spherical cloud of gas and dust around 5 billion years ago. This cloud slowly collapsed under its own gravity, pulling itself inwards and becoming denser and denser until the central lump of gas got dense and hot enough to turn into the Sun. The rest of the stuff in the Solar System (the planets, the Kuiper Belt, the Oort Cloud, and us) are just the leftover stuff that didn’t make it into the star at the center of the cloud and was instead left to drift around it aimlessly.
If we started as a spherical cloud, how did most things end up flat? As the gas cloud collapsed further and further, the rocks and dust in the cloud started crashing into each other, assembling themselves into larger and larger balls of material. When two rocks collide and stick together, the momentum of the final object is the average of the things that went into it. This means that over time as things get smaller and denser, the wild motions of the gas cloud get averaged out to be in the same direction: the average direction of everything in the Solar System. So all of the planets, asteroids, and Kuiper Belt objects have undergone enough collisions and gravitational interactions with other things in the Solar System that they’ve lost all of their non-circular motion, and once things start orbiting in circles, they’ll use their gravity to pull other surrounding objects into circular orbits as well.
So why didn’t this happen to the Oort Cloud? There are a few reasons. First, the typical Oort Cloud object just isn’t very big, so it hasn’t been assembled from as many different particles and hasn’t been averaged out as much. The second reason is time. Oort Cloud objects move extremely slowly since they’re so far from the Sun, so they haven’t completed nearly as many orbits in their lifetimes (each orbit can take millions of years). This means that they haven’t had as many opportunities to cross paths with other objects and crash into them, and they haven’t felt the gravity of nearby objects as much, so they just haven’t had time to collapse down into a disk yet. The third reason is that the Oort Cloud represents the outer boundary of our Solar System, which means that from time to time, it is affected by the gravity of passing stars. Other stars pass through the Oort Cloud relatively frequently (astronomically speaking), and when that happens, all of the orbits are jumbled up again, leading to a randomized cloud of debris.
So the Oort Cloud just doesn’t have the time, density, or isolation to settle down into a disk.
If a rogue planet entered the Solar System now, would its orbit eventually flatten to the rest of the planets' orbits? (Intermediate)
At this point in the evolution of the Solar System, the answer is probably no. It would face some pressure from the other planets’ gravity to align, but there’s not enough free floating mass in the Solar System now to get it totally in the plane. You can see this with Mercury (which has an orbit that is inclined by about 7 degrees relative to the other planets) or the comets and asteroids, which frequently have much larger inclinations. Without the large volume of random collisions, planet would likely just keep doing what it was doing.
Are infrared telescopes sophisticated enough to peer through the thick atmospheres of gas giants like Jupiter and Saturn since infrared light can pass through gas and dust better? (Advanced)
This is a very interesting connection to make. One of the appeals of IR telescopes is that IR light is not blocked by gas and dust as much, enabling observations of things that would otherwise be hidden (this is one of the main motivations of the James Webb Space Telescope and many other infrared telescopes). And you’re also correct that the thick cloud layers in gas giants prevent us from knowing very much about their internal structures. So one might think that this would be helpful for studying Jupiter’s interior, but these two ideas don’t really fit together in the way you might hope.
You may have seen a picture like the one above before. This is a dense gas cloud called a Bok globule (specifically Barnard 68), a very dense cloud of gas and dust that are thought to be in the process of collapsing down to form a star, observed at wavelengths ranging from blue to mid infrared. Visible light (shown in the 0.44 and 0.55 micron images) is almost entirely blocked by the center of the gas cloud, but the cool thing about this collage of pictures is that the cloud gets so much more transparent at the longer infrared wavelengths because infrared light can pass through more easily, allowing us to see the stars that are behind it. However, I want to point out that this process is not magic. There is still a noticeable amount of dimming from the gas and dust even in the longest wavelength image in the bottom left, so even infrared imaging has its limits.
The other thing to point out is that this cloud of gas, which is extremely dense by galactic standards, is still essentially a vacuum. The average density of this cloud is about 500 quintillion times smaller than the average density of Jupiter, despite Jupiter only being about 100 million times smaller. So a beam of light travelling through Jupiter would have to get through significantly more gas and dust if it wanted to escape the planet, meaning that even with the benefits of IR observations, we still wouldn’t be able to see that far. This isn’t really a question of “sophistication” of the telescopes, it’s just that there isn’t anything to look at.
This is compounded by the fact that Jupiter is not all just gas clouds. Eventually the pressure of the hydrogen atmosphere gets so high that it condenses the hydrogen down into a liquid metal, which would reflect basically all light. So any core would be below thousands of miles of dense gas followed by thousands of miles of even denser liquid metal. Realistically, no light is going to be able to make it through that.
So although astronomers are excited about upcoming IR instruments for a number of reasons, looking at Jupiter’s interior is not really one of them. Currently, the best information about Jupiter’s interior we have is from the very precise gravity readings from the JUNO probe which can give us a rough idea of how lumpy it is.
Why is Mercury's solar day so much longer than its orbital period? (Advanced)
You’re not the first person to get confused about the rotational period of Mercury! When NASA originally sent space probes to it decades ago, they flew past it in 3 year (264 day) intervals and saw that the planet was in the exact same orientation every time, From these observations, they concluded that it must not be rotating with respect to the Sun and that it must actually be tidally locked, but this is not the case. In fact, it completes exactly 1.5 rotations on its axis per year, which leads to some weird problems when calculating the solar day. See the diagram below:
If you were standing directly under the Sun at the start of a Mercury year (position 1), then 1.5 rotations per year would mean that you would point the same way again 2/3 of the way around the circle (position 5). And this is indeed true! But the problem is that even though you’re facing the same direction, you’re not looking at the Sun anymore. Mercury’s orbit around the Sun kept you looking at the Sun for far longer than you would if it were not orbiting, so now you have to wait through a long night (positions 5-10) before seeing the Sun again. The movement of Mercury around the Sun messed with your concept of daytime, meaning that the day is extended to two full years.
I know that this is very confusing, so I recommend acting out the above diagram using a lamp in a dark room. If you follow the positions you’re supposed to be pointing as you “orbit” the lamp, you should see that even though you complete a rotation in 2/3 of an orbit, you don’t return to your starting orientation until 2 orbits later


On a tidally-locked planet, what sort of conditions would have to be in place for both sides of the planet to be inhabitable? (Beginner)

The short answer is essentially that it is very unlikely that a tidally locked planet could ever be habitable all the way around without some weather condition being unfavorable. Usually, astronomers don’t consider tidally locked planets to be inhabitable at all.

For a more detailed explanation, tidally locked planets have a number of problems, mainly due to the fact that one side is very hot all the time. The temperatures would be extreme, with temperatures far too hot for life under the sun and far too cold on the dark half of the planet. Favorable temperatures would only be found somewhere in the “sunset zone” around the edge of the planet where the sun is low on the horizon. If you imagine an ocean facing the sun all the time, it would eventually evaporate and have its moisture carried off elsewhere, likely to the other side of the planet where the temperatures are hundreds of degrees colder and the moisture would freeze out, depositing a large amount of water on the other side. Beyond this, heating up rock continuously leads to it expelling gas, leading to a Venus-like runaway greenhouse effect, further messing with the planet’s weather.

The only way I could see the temperature being somewhat consistent would be if there were extremely strong winds going in bands around the planet. These types of winds exist in some form on the Earth (I’m not a meteorologist so I don’t know the details), but if you had winds that distributed the sun’s energy more equally around the planet, it might extend the habitable zone a bit. Of course, this would cause lots of other habitability issues and extreme weather, so this probably wouldn’t be nice.

How do astronomers determine the rotations of celestial-bodies outside of our solar system? (Beginner)

It is very difficult to measure rotation for planets outside the solar system (exoplanets) and stars, but mostly astronomers rely on looking for regular fluctuations in brightness. If an exoplanet or star has a dark cloud or surface feature on it, then you can expect that once per rotation, that dark cloud would reduce the overall amount of light that you see from that object. If astronomers see regular dips in brightness like this, then you can guess that the time in between the dips is one day for that thing.

Do other solar systems have Oort clouds? (Beginner)

We can’t even make any direct observations of our own Oort cloud, let alone any clouds around other stars! The furthest object we have ever seen (the imaginatively named FarFarOut) is only 132 AU away from the Sun, which is not even 10% of the distance to the inner edge of the Oort cloud. So how do we even know that the Oort cloud is there if we can’t see it? The comets we see streaking through the inner Solar System every once in a while have orbits that take them far away from the Sun and in all directions equally, implying that there must be some large spherical cloud of comets out there even if we can’t see it. There’s no reason to expect that our Sun’s debris cloud looks any different than any other similar star, so it’s probably safe to assume that there are Oort clouds around them as well, but it’s essentially impossible to see such dim, distant, and diffuse clouds of material.

Can stars between galaxies have planets? (Intermediate)
Before I answer your question, I want to talk about where extragalactic stars come from in the first place. Stars form from dense clouds of gas undergoing gravitational collapse, so it’s impossible for them to form anywhere that doesn’t have lots of gas, which usually means a galaxy. This can be a very small galaxy (there are dwarf galaxies around the Milky Way that only have a few hundred stars in them), but they’re still part of something. If there is a star that is truly on its own outside of any other structures, then it would have had to get thrown out there by some violent process (these are called hypervelocity stars). This can happen if another star or a black hole flings it in a random direction with its gravity, or it can happen if something like a supernova explosion pushes it away from its galaxy fast enough to escape.
So do these stars have planets? I’m going to say probably not. The only way a gravitational force can be strong enough to fling a star out of a galaxy is if it gets really really close to a large object, and that would probably be close enough to rip away any planets that used to be around the star. The same logic probably applies to supernovas too: any explosion big enough to send a star flying out of a galaxy is probably strong enough to separate it from its planets. The one scenario I can come up with where an extragalactic star could maintain at least some of its planets is if it got ejected from a dwarf galaxy. Then it wouldn’t have to be flung that fast to escape the gravity of the tiny galaxy, so it could maybe keep its solar system together.
How perfectly aligned to exoplanet orbits have to be in order to be observed by the transit method? (Advanced)
This is actually something I’ve been thinking about in the back of my mind for a while, and this question made me sit down and do the research and math to answer it properly. You are correct in your calculation of the angle of inclination that is necessary to see the Earth in front of the Sun, but let’s be a bit more careful about figuring out your chances to observe this. First, it is necessary to double the angle since you can observe the Earth from above or below its orbit so we actually have a window of about 0.5 degrees. Next, we have to realize that we can observe this from any angle around the Earth’s orbit, so we have to revolve this around 360 degrees and divide by the area of the sky. After all of this, we land with a probability of about 0.5% of being in the region of sky that could observe a transit of the Earth.
This is indeed a very small chance, and this is why exoplanet observers typically monitor large numbers of stars to see which ones line up. For instance, the Kepler space telescope observed approximately 150,000 stars simultaneously to look for transits, so with the chances from above, it would be able to see about 750 earths.
However, Kepler ended up observing over 2500 planets (more are still being confirmed) for a couple of reasons. First is that the vast majority of known exoplanets are closer to their star than the Earth is, meaning that the possible viewing angles are much larger (for a typical “hot Jupiter” 0.1 AU, the fraction of the sky increases to 5%, and for the first exoplanet ever discovered 51 Pegasi b which is only 0.05 AU away, the fraction is almost 10%). So these planets are much more visible than further planets, and their larger size also means their transit dips are easier to detect. The other reason Kepler detected so many planets is that many stars have multiple planets in their system, and if one planet is aligned properly, then the others have a higher probability of being aligned too. About a third of Kepler’s planets are in multiplanetary systems.
So even though astronomers can’t confirm that every star has planets using transits, they can make statistical arguments based on how many planets they see versus how many they would have expected to see probabilistically. Also, orbital planes don’t tend to align with the plane of the Milky Way (ours doesn’t, it’s about 60 degrees off) because the orbital plane is determined by the specific way the gas cloud that made the solar system collapsed.
Would it not make sense that maybe we would have more rocky planets like earth in nearby solar systems with similar elemental makeup? (Advanced)

This is an interesting question that I had to spend a bit thinking about. There are a number of factors at play here that make the answer to your question a bit complicated. The first thing to note is that usually when astronomers talk about what a given star is made of, they talk about its “metallicity.” Conceptually, this is the amount of heavy elements (heavier than helium) present in a star, and practically this is usually defined based off of the ratio of iron to hydrogen in a star (Fe/H). You have correctly pointed out that younger stars tend to have higher metallicities than older stars because they incorporate metals from previous generations of stars. 

Typically, stars form in large clusters from a single cloud of gas that condenses down into numerous stars in close proximity. These stars stay together for a period of time (the Pleiades star cluster in the night sky is a good example of what this looks like) but after a few hundred million years, their movement through the galaxy carries them away from each other, scrambling up the stellar population throughout the galaxy. So to answer your immediate question, the Sun’s “siblings” i.e. stars that were born from the same gas cloud and thus have the same composition, are likely very far from the Sun now so there should be no local grouping of “similar planets.”

However, in a broader sense, we do expect there to be roughly similar planet trends around our Sun because there is a trend in stellar metallicity as you go radially outwards from the center of the galaxy. Since there is more stuff (i.e. stars, gas, dust, etc.) in the center of the galaxy, more stars are formed and more metals are created compared to the more sparse outskirts of the galaxy. Astronomers have also observed a correlation between the metallicity of a star and the number of planets that form around it, so at a given distance from the galactic center (i.e. for a certain metallicity), there will actually be some similarity in the number of planets in a given solar system. If you’re interested in some more technical reading, I recommend this paper from Fischer & Valenti in 2005 about the subject, specifically Figure 4 which shows that stars with more iron are more likely to have planets. 

So the Sun isn’t particularly related to the stars immediately around it, but it does fit in with an overall trend through the whole galaxy that makes it so nearby stars may be somewhat similar planet-wise.

I tried applying Kepler's third law to an exoplanet solar system and it didn't work. Why not? (Advanced)
Kepler’s third law in the format of T^2 = a^3 is really an experimental observation rather than a physical law. Kepler observed that if you worked in a very specific set of units (years and AUs) then the relation holds for all of the planets he could observe. However, if we derive it from Newton’s law of gravitation instead (which Kepler didn’t know about at the time), then we get the same relation but with an important modification:
In this formation, we still see the T^2 = a^3 basis, but there is a coefficient in front that contains some extra things to be worried about. We have pi (which comes from having to worry about the circumference of the orbit), Newton’s gravitational constant G (which comes from having to calculate the strength of the gravitational pull), and the masses of the two bodies involved M1 and M2. These mass values are the source of your problem. In our Solar System where M1 is the mass of the Sun and M2 is the mass of the Earth (or any of the other planets), all of the values work out so the equation simplifies to T^2 = a^3 in units of years and AUs, but as soon as you change M1 or have an M2 that isn’t much much less than M1, the simplification doesn’t work anymore. You have to go the long way and use the full equation.
Interestingly though, we can come up with a simplified version of Kepler’s third law in every exoplanet system, we just have to change the definition of a “year” and an “astronomical unit”. If you choose a planet in an exoplanet system to serve as the basis for these definitions (in the way we have done with the Earth) then all of the rest of the planetary orbits can be calculated in terms of these values. They just won’t match up with our Earth definitions.