Introduction:

The motion of planets around the sun is often considered as a two-dimensional motion due to certain characteristics and factors that influence their trajectories. Although the motion is influenced by various forces and factors, such as gravity, the conservation of angular momentum, and the absence of significant external forces, these can be simplified and analyzed in a two-dimensional plane.

Gravity:

1. The primary force governing the motion of planets around the sun is gravity. Every planet is attracted towards the sun due to its gravitational pull.
2. Gravity acts in a radial direction towards the sun, and the planets move in response to this force.
3. The gravitational force can be broken down into two components: one along the radial direction and another perpendicular to it. The component perpendicular to the radial direction does not affect the motion of the planets in the plane of their orbits.

Conservation of Angular Momentum:

1. The conservation of angular momentum plays a crucial role in the two-dimensional motion of planets.
2. Angular momentum is the product of the moment of inertia and the angular velocity of an object.
3. In the absence of significant external torques, the total angular momentum of a planet remains constant.
4. The conservation of angular momentum restricts the motion of the planet to a two-dimensional plane, as any motion out of this plane would require an external torque.

Absence of Significant External Forces:

1. The absence of significant external forces acting on planets also contributes to their two-dimensional motion.
2. Unlike other celestial bodies like comets or asteroids, planets have relatively stable orbits due to their large mass and distance from other objects.
3. The absence of significant external forces allows the planets to maintain their motion within a plane.

Conclusion:

The motion of planets around the sun is considered two-dimensional due to the combined effects of gravity, the conservation of angular momentum, and the absence of significant external forces. Although the actual motion is influenced by factors in three-dimensional space, the simplification to a two-dimensional plane allows for easier analysis and understanding of the orbits and trajectories of planets.