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The size of an asteroid required to maintain its structural integrity during its orbit around the Sun depends on various factors, including its composition, internal strength, and the gravitational forces acting upon it.

Asteroids are rocky or metallic objects that can vary greatly in size, shape, and composition. Their sizes range from small boulders to bodies several hundred kilometers in diameter. The specific size required for an asteroid to avoid breaking apart depends on its structural characteristics, such as its tensile strength and ability to withstand gravitational forces.

To determine the size needed for an asteroid to remain intact during its orbit, we must consider the tidal forces exerted by the Sun. Tidal forces arise from the gravitational interaction between two objects, and they can cause deformations or stresses on a celestial body.

As a general guideline, if an asteroid is sufficiently large and dense, it would be less prone to breaking apart due to tidal forces. However, it is challenging to provide an exact size requirement without specific information about the composition, structure, and specific tensile strength of the hypothetical asteroid.

Additionally, other factors such as the asteroid's rotation, shape, and proximity to other massive celestial bodies (e.g., planets) could affect its stability.

It's worth noting that objects with sizes comparable to or larger than the Earth, such as planets or dwarf planets, are more likely to maintain their structural integrity during orbit due to their greater mass and internal cohesion. In the case of Earth, its size and internal properties allow it to withstand the gravitational forces exerted by the Sun without breaking apart.

In summary, the exact size requirement for an asteroid to avoid breaking apart during its orbit around the Sun would depend on several factors, including its composition, internal strength, and other environmental influences.

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