This is a bit odd, but I have an answer specifically focused on your next question: How would the 2016 human scientific community react if a massive space-faring alien "whale" entered the Solar System?
I didn't want to detour my answer there with all this, but I can't not mention it; so this seemed a beter place to put it.
Your alien will not exist. Okay I said it, I'm sorry, I try to always work within the premise of a question happening, but the evolution of this thing really doesn't work. I'm going to try to answer this question anyways, but I have to discuss the improbabilities at the very least. Some I have suggestions to 'fix', some are...well I have nothing but suspention of disbelief to offer for them. Lets go over them, I'll try not to focus too much because I don't want to bash the idea, just show why I need to make some presumptions.
First though, one of the biggest underlying issues is simply the [square/cube law][2]. I'm only going to touch on a subset of issues caused by this law, most relevant to this discussion, but there are really a number of others. it is good to think about this law in all its many forms.
I need to first touch on energy because it comes up when discussing most other things.
Photosynthesis is like powering Las Vegas with a single shock of static electricity
The power coming in from photosynthesis is trivial compared to the energy this creature would need to move or do anything. First, lets assume that it also can feed on the background radiation of the universe, a much higher concentration of power when your traveling outside of a solar system. Still even if it can 'feed' off of all forms of radiation it's not enough. Plants barely move or do anything and yet they barely collect enough energy to grow (notice how much slower they grow compared to living things). Your planet though has a much larger mass, which means its volume is drastically huge compared to its surface area. If it can only collect energy on its surface then the amount of energy collected is pathetic relative to total mass (most relevant for movement, where the energy needed to move is directly proportional to its mass). As your creature gets larger photosynthesis grows increasingly useless as a power source, but moon size is already pathetic power source.
There are other potential power sources. For instance if it had an appropriately radioactive core (not nuclear, no suns here, just radioactive) it could gain power from that core...until the core decays enough to no longer provide sufficent energy to keep the creature alive. There are some other options but frankly none of them provide much energy per KG here. Your creature is going to have very very little energy to work with, at least relative to mass.
For the cerature to work at moon or larger sizes with the sort of energy it can intake there are a few things that must be assumed.
- It has very limited movement, and I mean very limited. Its movement is less like swimming through water and more like floating on a raft with a tiny sail you can minutely move every few months (or in his case every few hundreds of years). The tiniest twists of motion to try to change the angle of drift would be required, finding some way to 'sail' on gravity or solar winds perhaps, though I don't know how. Because ultimately his mass is just way too large relative to energy intake that he can't move by directly propelling himself.
- Either he barely does anything, lying 100% dormant most of this lifetime with brief moments of activity to allow him to store up and save energy for those brief periods or
- Most of him isn't really alive, only a small subset of the creature body is involved in actual process required to support life, and 99% of him is the equivalent of a gigantic rock outershell or
- both 2 & 3. frankly I think 3 is almost obligatory, but 2 is probable as well
Which brings us to the size issue...
You can't double size at a static rate
First example of the square cube law. Every time your alien doubles its size it needs to take in exponentially more resources. The first doubling requires he consume 4 times the resources it took to grow to moon size, the second doubling requires he take in an additional 16 times the resource it took to reach moon size, next doubling requires 64 times, then 256 etc. After a few thousand years he's consuming hundreds more planets to double. It's just not possible to keep doubling size, as his size goes the slower future growth must be.
lava belly isn't fun
The larger a creature grows the larger its gravity, including its gravity on itself. I know some will say that's not the case because gravity will even itself out, which is true in a perfectly spherical uniform mass, which your creature can't be. In reality you get all of the effects that warm the earth, the biggest being gravity working on [inconsistent densities within the body][3]. Radioactive decay also applies here (ignore the first heat souce, that's my next point).
Now a 'lava belly' is not by itself that bad. Arguably a creature might even find some way to gain energy from this process, using its lava core as a heat engine, slowly draining the heat produced by radioactive decay & gravitational differences into some useful form. I don't see this being a very efficent energy source, and both are temporary at best since they require continual growth to fuel them while giving decreased benefit as one grows.
However, it would mean that no useful structures are going to be residing in your core, and the closer to your core the harder it is to keep an orginized structure, the sort of thing needed to support whatever organ-equivalent is used to provide you the ability to do things like think, move, and eat. As you increase your mass, and thus energy production and thus size of your 'lava center' you keep having to move these quasi-organs away from your lava center so they don't melt, which is an issue since that movement would require energy, quite a bit of energy, which you just don't have to waste. Though...this is the issue I could most handwave potentially.
My food runs too fast
To continue growing you need to 'eat' more, asteroids, moons, whatever, to gain mass. However, that means you need to reach an asteroid, moon, whatever in order to eat it. As per my earlier discussion on energy as your size increases the amount of energy you can take in relative to your mass decreases exponentially, and since movement ability is proportional to mass that means it's quickly becoming difficult to produce enough energy to have any noticeable delta V. Thus your alien is going to find it nearly impossible to find new things to eat.
Did that pea just give you a black eye?
Even assuming that you could reach something that you can 'eat' the odds are that it will be going at a much different velocity then you; there is no way the alien can afford the energy required to match the velocity of his 'food'. That means a very viscious collision with your food, the sort that leaves craters on the moon; only worse because the alien has to hunt down things larger then the tiny meteors that hit the moon.
This is going to start doing some serious damage to its outer shell, no 'organs' or other important things can be kept close to your crust with the kind of bombardmants your going to receive. This could be limited if the creature meanuvered near its 'food' and let its own gravity suck the food in slowly perhaps, given astrological time scales, but not entirely fixed.
Death grapefruit inbound, waddle away!
also make sure you don't get too close to anything large and fast enough to break through your outer crust to your internal 'organs', you don't have the Delta V to get away at that size ;)
I know I should go have kids of my own, but I can't get over my attraction to my mother
...that is a horrible segway title, sorry.
However, this is a real issue. For a child of this creature to live it will need to one day leave the nest so to speak, and in this case the nest has a gravity well the size of a moon. Think how much energy we have to put into a tiny rocket to have it escape earth's gravity well, every child needs to do that too, and it seems likely these children will be larger then a rocket if their mother is moon sized. That's a pretty large expense to having a child, in addition to the regular 'pregnancy' expense. growing larger makes it far more costly to have children, since you can't get them to leave the nest
Why are we eating ourselves to death again?
The final question being, why grow so large? Size doesn't provide an evolutionary advantage unless it is to protect against enviroment and predators, both mostly non-issues here. When species are large enough to defend themselves they stop growing and instead focus the energy & mass they gain from their food to another use...reproduction. Simply put it makes far more sense to break off into new 'children' then to keep growing.
The point of all that being..a much smaller creature makes more sense (it can still be pretty huge mind you, say asteroid sized rather then moon sized, but the larger the harder to justify).
You don't deserve to be sapient
To be blunt, this creature has no evolutionary advantage to being sapient. Sapience costs energy to fuel your brain and takes millenia of evolutionary pressure to produce, and your creature has nothing. The biggest drivers for sapience is the need to out think predators or prey, need to construct technology to defend against the enviroment & elements, need to communicate with others of your species; specifically the complex communication that comes from large tribes with mating individuals where navigating political aliances and social complexity is the only way to manage to acheive mating rights.
Your creature has none of these elements. The closest is the ability to communicate with other's of its kind; but even then if it's asexual it's likely not expecting to run into many, or any, of its kind (which makes sense, space is huge); so no needs for social complexities, and more obviously no need to navigate social complexities to acheive mating rights when you don't mate.
And along with that, sex is sort of required to drive rapid evolution, asexual species have a much much harder time adapting or changing, so such a massive evolutionary leap is hard to have with any asexual species.
There really is no way I can see to fix this issue. The only possible justifications, all pretty pathetic, I can come up with are.
1) this species is an artificial construct by some other sentient creature, skipping over normal evolution
2) This species is a hermaphrodite equivalent, capable but not limited to asexual reproduction, and has in the past evolved in an environment where a huge number were close enough together to have a social culture and evolutionary pressures towards intellect to compete for mate choice (so many reasons this doesn't work...)
3) much like 2, but the sapience evolved from a very different, and smaller, creature in a world with other space faring predators, and only after sapience was achieved did an asexual variant get produced and spread out on its own; with its sapience effectively being vestigial, limited evolutionary advantage with its new life but since it's already evolved might as well keep it.
yeah...best to not mention this and hope most people pay no attention to the suspiciously intelligent alien behind the curtain. Though a much much smaller varient of space fairing creature, with a hibernating ability used when crossing solar systems, is the best outcome I can think of.
Shouting away your energy
sending radio waves out to 'shout' at others seems kind of detrimental. First because this species shouldn't have much of a language. Partially because it shouldn't really be sapient, but I'm ignoring that point now. Even if sapient it's asexual for a reason, it does not plan or anticipate running into others of it's species to mate with. Why should it have anything like a language to communicate with something it will never interact with?
it can't even be a language for communicating with it's own young, since they don't achieve sapience until well after they would have left their 'mother'.
However, language isn't required for radio signals, at least not the sort we know. A more basic sort of 'language' similar to body language could exist, limited signals with predefined and instinctual understood messages like "this is my solar system, don't come here or I'll eat you"
However, radio signals require energy. Not much energy admittedly, but your species is very energy inefficient, and it needs to invest enough energy to 'shout' long enough range to be heard by another of it's kind (which is going to still be very far away, space is big...) requires some resources. If the creature uses radio wave based communication at all it would make sense to be a very focused beam of communication which is done only in response to some external stimuli. It doesn't bother 'talking' unless it expects someone to listen.
when spiders accuse you of having too many kids you know you have a problem
While you didn't specify this creatures lifecycle since you referred to it doubling in size in 1000 years you imply it's going to live at least 1,000 years and likely much longer.
However, you also said that it produces two offspring a year, That's a minimum of 2,000 offspring in it's lifetime, likely more.
I've already addressed the energy expense angle many times, but in short there is no way this species has the energy to produce children that rapidly.
There is also the question of food, where are they getting the food to grow so big? 2,000 moon-sized aliens would use a decent amount non-sun mass in the solar system.
You could try sending your children to other solar systems, but then you need to get up the energy required to break your solar system's gravity well and all the gravity wells between here and whatever system your sending the child too, and after 1,000 solar systems have children your going to have to send your child very very far to reach a new one.
It could be that you expect most of your children to 'die', so your using an R mating strategy, but that begs the question what is killing these children in a world without predators? They wouldn't even be competing with themselves, without sexual reproduction there is no reason to encourage your children to compete in a survival-of-the-fittest situation the way some R species do; since each is exactly equally as fit as the last.
evolution would encourage producing fewer children with a lower mortality rate when your expense for having a 'child' is so high. Frankly the difference in size between child and parent would have to be so drastic for the 2,000 children scenario to work out that the child couldn't live because the square/cube law says anything that much smaller then a parent will find its body size too small to be viable for the physical structure their parent had.
It's best to scale this species birthrate to its lifespan, whatever its lifespan is, and its size. The longer the lifespan and the greater the size the slower the rate of birth. If it lives longer than, and is larger than, an elephant it shouldn't have a birth rate faster then the elephant. The only exception to this is if you have predator species for it to worry about.