I have received some great answer here and they all mostly point to the fact that while effects on the opposite side of the planet are possible, the deformation may or may not resemble a crater but more likely an earthquake or fault zone. I have picked the answer that I think best describes this process in a way that I can build upon for use in my world.
However, my question does ask how it could happen not if it was possible (perhaps this was not clear). In my second set of bullet points I tried to express that I am open to a non-Earth like planet - or even something unlike any planet we know of so long as it could form in theory according to physical laws. I am not sure if I will get an answer satisfying this criteria but this would be the ideal answer.
In a previous question, I asked about mountains, rivers, trees, and so on forming within an impact crater surrounded by desert. I left it open about how this crater was formed.
Note: A question similar to mine has been asked here, but the answers do not help me.
Let's imagine that a large, circular or spherical object impacts a planet on one side. The desert mentioned in the previous question exists on the opposite side of the planet from the site of impact. Are there conceivable conditions under which:
- The impact would travel through the planet and cause a crater on the other side. The crater does not need to be exactly the same shape as the impact made on the surface of the planet by the object but should be similar.
- The impact would emanate outward in a cone-like fashion such that the diameter of the crater on the other side is greater than the diameter of the circle object that made the impact.
- The heat (or pressure) is intense enough for at least some of sand near the rim of the crater on the other side to turn into glass.
- Mountains of some kind could form near the edge of the crater due to the impact. If this is not possible, then hopefully there is some sort of mantle and crust that allows the gradual formation of mountains (I don't know if this is exactly how that works).
In order to achieve these specifications, let's say that:
- The impacting object may be made of any type of material, have any mass, and can impact at any velocity (though I'd like some kind of lower bound).
- The planet's internal layers can be made of any type of matter in any phase so long as its still internally consistent with the basic laws of physics and what is known or speculated about planet formation and stability.
I would like a hard-science answer if possible. However, since this is for a fantasy (with a bit of sci-fi) setting, I am okay with some hand-waving if it comes to that. This event would have happened in the far history of the world so its precise nature would not necessarily be known or understood.