No, it is not possible for two Earth-like planets to share the exact same orbital path around the Sun without eventually colliding with each other. This scenario would be dynamically unstable due to the gravitational interactions between the two planets.
According to the laws of celestial mechanics, such as Newton's laws of motion and the law of universal gravitation, planets in a system will influence each other's orbits. Even small perturbations, such as variations in mass distribution or initial conditions, can cause significant changes in the orbital paths over time.
In the case of two planets sharing the same orbit, their gravitational interaction would lead to a phenomenon known as orbital resonance, where their gravitational pulls cause periodic changes in each other's orbits. Over time, these interactions would result in a gradual alteration of the planets' orbital paths, leading to an instability that would eventually cause them to collide or be ejected from the system.
In nature, we observe that planets in the same system tend to have distinct and non-overlapping orbits. This is because gravitational interactions among celestial bodies tend to drive them towards stable, non-colliding configurations.
It's worth noting that there are systems in the universe where planets exist in close proximity to each other, such as in multi-planet systems or binary star systems. However, even in these cases, the planets have slightly different orbital paths to avoid collisions and maintain long-term stability.