I know that gravity will turn a mass into a sphere, which is why planets and stars are that shape. But then we have asteroids and small moons which are not spherical. Such as a couple of Pluto's moons. Is there a size at which they will become spheres? Is it dependent on their composition? Does it need a certain mass? Is it only because of the heat of collisions melted the rocky planets that they became this shape while they were semi liquid?
I know that gravity will turn a mass into a sphere, which is why planets and stars are that shape. But then we have asteroids and small moons which are not spherical. Such as a couple of Pluto's moons. Is there a size at which they will become spheres? Is it dependent on their composition?
Google searches provide a wide variety of answers to this and while the other question is answered, it's only answered briefly, so I thought I'd give this a try.
Mike Brown's Planets was the best link I could find on the subject, and I can't swear by his correctness, but his numbers are in the range you find in other articles.
While we can't see most of the objects in the Kuiper belt well enough to determine whether they are round or not, we can estimate how big an object has to be before it becomes round and therefore how many objects in the Kuiper belt are likely round. In the asteroid belt Ceres, with a diameter of 900 km, is the only object large enough to be round, so somewhere around 900 km is a good cutoff for rocky bodies like asteroids. Kuiper belt objects have a lot of ice in their interiors, though. Ice is not as hard as rock, so it less easily withstands the force of gravity, and it takes less force to make an ice ball round.
The best estimate for how big an icy body needs to be to become round comes from looking at icy satellites of the giant planets. The smallest body that is generally round is Saturn's satellite Mimas, which has a diameter of about 400 km. Several satellites which have diameters around 200 km are not round. So somewhere between 200 and 400 km an icy body becomes round. Objects with more ice will become round at smaller sizes while those with less rock might be bigger. We will take 400 km as a reasonable lower limit and assume that anything larger than 400 km in the Kuiper belt is round, and thus a dwarf planet. We might be a bit off in one direction or another, but 400 km seems like a good estimate.
Other estimates I've read have 600 KM diameter for rocky bodies and Ceres is ice and rock, not really a rocky body, so I think there's some uncertainty in there.
Does it need a certain mass?
I personally don't like talking about planets by their mass cause it gets rather unwieldy in size. Take Ceres, mentioned above. It's 8.958 × 10^20 kg. A 400 KM diameter ice world would have a mass of, figure a water-ice average density, about 3 x 10^19 and 200 KM diameter, 1/8th of that, about 3.75 x 10^18. The minimum mass is somewhere in those ranges, but I think radius and composition are easier to work with.
Is it only because of the heat of collisions melted the rocky planets that they became this shape while they were semi liquid?
I can only give an intuitive answer here, but collisions that liquefy a planet are rare and, especially with smaller planets, would be more likely to blow the planet to bits as soon as melt it. Take the giant impact on Mars. Article Here and Here. The 2nd article says that the object that hit Mars was thought to be traveling at about "6 to 10 kilometers per second." and size "roughly 1,600 to 2,700 kilometers across" - so, bigger than Ceres, Smaller than the Moon and this may have melted half of Mars' surface but it didn't melt all of it cause it left a measurably difference in Mars crust one side to the other. If a collision of that enormous size didn't melt Mars all the way around - I'd wager that such melting is pretty rare.
2nd point, as a general principal, the Solar system objects orbit in the same direction and the further out you get from the sun, the slower the orbital speed (though the more likely you get eccentric orbits). The speed of collisions in space are roughly the vector addition of the 2 objects orbital speeds, which are often somewhat in line with each other, plus the escape velocity of the more massive object (or a bit more than that if both objects are massive), so once objects get to be a pretty good size, about the size where they become spheres, collisions that would melt the object grow less and less likely, and if it is large enough to do that, you should also expect a fair bit of debris from impact. My guess, based on just barely enough knowledge to think about this stuff, is that planetoids and large enough to maybe get spherical asteroids are unlikely to form into spheres due to melting from heat from collisions because due to the relatively weak gravity of smaller objects like that (Ceres has an escape velocity of 0.51 km/s, about 1140 MPH), an impact to generate enough heat to melt it would blow half the dwarf planet away, give or take.
Now, if you have a very hot planet that's very very close to the sun and at near liquid temperature anyway or if you have a coalescing and a multitude of successive impacts and lots of heat collecting in the object, then, sure. It's certainly possible but my guess is that a planetoid or asteroid forming into a sphere due to melting it's rare.
That's a layman's answer.