Discover the Fascinating Reason Behind Our Solar System’s Flat Shape

The Flat Solar System: A Tale of Gravity and Fake Forces

The Elevator Analogy

Imagine you’re in a stationary elevator. Two forces act on you: the downward gravitational force and the upward-pushing “normal” force from the floor. According to Newton’s second law, the net force on an object equals its mass times acceleration (Fnet = ma). If the elevator is stationary, the acceleration is zero, and the floor pushes up with a force equal to the gravitational force, resulting in a net force of zero.

Now, if the elevator starts moving upward, the floor must push up more than gravity pulls down to have a non-zero net force. However, we can also describe the motion using the elevator’s reference frame. Since the elevator is accelerating, Newton’s second law doesn’t work unless everything is measured with respect to a non-accelerating reference frame (an inertial frame). To make things work in the non-inertial frame, we add a fake force in the opposite direction, equal to your mass multiplied by the elevator’s acceleration.

This fake force is not due to an interaction between two things, but it’s a simple way to explain why you feel heavier in an accelerating elevator.

The Centrifugal Force

Consider a ball attached to a string moving in a circle. Using the ball’s reference frame, there are two equal forces: the string pulling toward the center and an outward-pushing fake force called the “centrifugal force,” which means “center fleeing.” This is the force you experience when taking a fast turn in a car. Increasing the angular velocity or making the circle smaller (like a hairpin turn) increases the centrifugal force.

Creating a Solar System from a Rotating Cloud of Dust

Let’s create a solar system from a slightly rotating giant cloud of dust. Consider two particles: one on the equator and another near the top, close to the axis of rotation. Both experience the same magnitude of gravitational force but in different directions, and they have the same angular velocity. In the rotating cloud’s reference frame, the particles also experience a fake centrifugal force.

For the particle on the equator, if the gravitational force (FG) and the centrifugal force (FC) balance out, the dust will move in a circular orbit. However, for the particle near the axis of rotation, the centrifugal force points away from the axis, not the center of the cloud. Additionally, the centrifugal force has a smaller magnitude due to the particle’s proximity to the axis. These forces cannot balance, causing the particle to accelerate toward the equatorial plane.

Modeling the Flattening Process

To model this, we start with 100 dust particles randomly distributed in a spherical shape, all with the same mass and velocity consistent with the cloud’s angular velocity. By calculating the gravitational force on each particle due to the others and using a numerical calculation method, we can determine how the velocity and position change over short time intervals.

The model shows that the cloud flattens out as predicted. Masses closer to the axis of rotation accelerate toward the equatorial plane, forming a giant disk. However, they oscillate through the disk until the net gravitational force slows them down.

The Role of Collisions

To prevent the up-down oscillation, we introduce collisions. When two masses from opposite poles collide and stick together, their vertical momentum essentially cancels out, resulting in a larger mass. Including these collisions in the numerical model yields a flatter solar system.

In summary, the solar system started from a slightly rotating cloud of dust. Particles near the equator found stable circular orbits, while those near the poles were pulled toward the middle, forming a flat disk. Particles at the pole had no centrifugal force and were pulled into the center, where the sun would eventually form. Although the centrifugal force is a fake force, it helps us tell the true story of our flat solar system.