Consider it doesn't collide with any other objects. Would it be preserved perfectly in the vacuum or would its surface be damaged by anything like UV rays, radiation, gas, space dust, etc?
1$\begingroup$ Anything from nothing to falls into a gravity well of a star or planet. A million years is an awfully long time scale. I think the question is simply too broad and opinion based. $\endgroup$– StephenG - Help UkraineApr 2, 2018 at 7:04
5$\begingroup$ @StephenG There are very good estimates, what happens to them in billion years... I don't think it would be too broad an opinionated. $\endgroup$– peterhApr 2, 2018 at 8:23
$\begingroup$ @peterh I think you miss my point. Exactly where it is and how it is moving to start with is going to determine what happens as much as anything else. "In space" is too broad. $\endgroup$– StephenG - Help UkraineApr 2, 2018 at 8:32
$\begingroup$ @peterh If you have a reference on what happens to material like marble over these timescales would you provide such a link (and perhaps make an answer) ? $\endgroup$– StephenG - Help UkraineApr 2, 2018 at 16:03
4$\begingroup$ "...doesn't collide with any other objects...damaged by anything like...gas, space dust, etc" that would be colliding with other objects unfortunately $\endgroup$– user1886419Apr 3, 2018 at 1:03
There are three main space weathering processes that will affect the surface of the marble.
Cosmic rays, high energy particle from the sun and beyond, will hit the surface. This can change the chemistry of the surface.
Solar wind particles, hydrogen and helium, can become implanted in the surface
Micrometeoroids will impact the surface, causing small craters, melting, and the inclusion of other elements such as iron.
These processes will tend to change the surface, developing a patina on a timescale of a hundred thousand years. The surface will darken (though as marble is not a typical rock in asteroids, there isn't any direct evidence of what happens with marble.
Marble is largely CaCO3, and this is in a equilibrium with CaO and CO2. At standard temperatures and even the very low partial pressure of CO2 in the atmosphere, this equilibium favours CaCO3. In our atmosphere one needs a temperature of 550⁰C to decompose Calcite. However in space there is no CO2, and so the Calcite would very slowly decompose to CaO. Calcium in meteorites is mostly in the form of CaO.
1$\begingroup$ Downvoting because this answer is assuming the object is in near-solar orbit. I don't think that qualifies as the most general case of "in space", most of which is fantastically free of solar-sourced particles, micrometeoids, etc. $\endgroup$ Apr 2, 2018 at 17:20
17$\begingroup$ Upvoting because cosmic radiation is everywhere, and the reactions that are described -- low CO2 partial pressure -- remains the same even outside the heliosheath, etc. $\endgroup$ Apr 2, 2018 at 18:32
$\begingroup$ The presumption is being made that $CaO$ in meteorites comes from the decomposition of $CaCO_3$. Is there evidence of this ? Have we detected and $CaCO_3$ at all or evidence of this decomposition in conditions like those is what we're loosely calling space ? This is a major issue I have with all these $CaCO_3$ based answers. $\endgroup$ Apr 3, 2018 at 2:07
Cosmic rays may impinge pressure on the statue, which will deteriorate its surface. Various electromagnetic rays (X-ray, Gamma rays and Infrared) can interact with the chemical elements of the statue.
2$\begingroup$ Apologies if this is a translation problem - cosmic rays transfer their kinetic energy to the statue, not pressure. $\endgroup$ Apr 2, 2018 at 17:21
Piggy backing on James K's answer above, there is a fourth process depending on the proximity to any star, which is thermal stress.
As the statue rotates with respect to any "near" star, thermal stress will lead to surface weathering over time: https://en.wikipedia.org/wiki/Weathering#Thermal_stress
Thermal stress weathering (sometimes called insolation weathering) results from the expansion and contraction of rock, caused by temperature changes. For example, heating of rocks by sunlight or fires can cause expansion of their constituent minerals. As some minerals expand more than others, temperature changes set up differential stresses that eventually cause the rock to crack apart. Because the outer surface of a rock is often warmer or colder than the more protected inner portions, some rocks may weather by exfoliation – the peeling away of outer layers. This process may be sharply accelerated if ice forms in the surface cracks. When water freezes, it expands with a force of about 1465 Mg/m^2, disintegrating huge rock masses and dislodging mineral grains from smaller fragments.