Option 1: Ellipse - An ellipse is a curved shape with two focal points. In this case, if another Sun-like star is brought near the Earth, it is possible that the trajectory of the Earth`s movement around the Sun could change and become an ellipse. However, this option is not the correct answer because the trajectory being undeterministic means that it cannot be predicted or determined with certainty.

Option 2: Parabola - A parabola is a U-shaped curve typically formed by the path of a projectile. In this scenario, it is unlikely that the trajectory of the Earth`s movement around the Sun would take the shape of a parabola. Therefore, this option is also not the correct answer.

Option 3: Circle - A circle is a perfectly round shape. However, if another Sun-like star is brought near the Earth, it is highly unlikely that the trajectory of the Earth`s movement around the Sun would become a circle. Therefore, this option is also not the correct answer.

Option 4: It will be undeterministic - This is the correct answer. It suggests that if another Sun-like star is brought near the Earth, the shape of the trajectory of the Earth`s movement around the Sun cannot be determined or predicted. The gravitational