# How slow would the orbital speed of the Earth need to be before it spiralled into the Sun?

The orbital speed of the Earth around the Sun is determined by the relationship between the gravitational force exerted by the Sun on the Earth and the centripetal force of the Earth’s orbital motion. As long as the centripetal force is greater than the gravitational force, the Earth will continue to orbit the Sun in a stable, elliptical orbit. If the centripetal force drops below the gravitational force, however, the Earth will start to spiral inward toward the Sun.

In order to determine the speed at which the Earth would spiral into the Sun, we must first look at the forces acting on the Earth. The gravitational force acting on the Earth is determined by Newton’s law of gravitation, which states that the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the gravitational force acting on the Earth increases as the Earth gets closer to the Sun, and decreases as it gets farther away.

The centripetal force acting on the Earth is determined by the Earth’s orbital speed. As the orbital speed increases, the centripetal force increases as well. This means that if the orbital speed is too low, the centripetal force will be smaller than the gravitational force, and the Earth will start to spiral into the Sun.

In order to determine the orbital speed at which this will occur, we must consider the distance between the Earth and the Sun. At its closest point (perihelion) the Earth is approximately 91.4 million miles from the Sun. At its farthest point (aphelion) the Earth is approximately 94.5 million miles from the Sun. Taking into account the fact that the gravitational force increases as the distance between the two objects decreases, the orbital speed at which the Earth will start to spiral inward must be less than the orbital speed required to maintain a stable orbit at perihelion.

The orbital speed at perihelion is approximately 18.8 miles per second. This means that in order for the Earth to start spiraling inward, its orbital speed must be less than 18.8 miles per second. It is important to note, however, that the exact orbital speed at which this will occur is highly dependent on the exact distance between the Earth and the Sun, and can vary slightly depending on the exact distance.

In conclusion, the orbital speed of the Earth must be less than 18.8 miles per second in order for it to start spiraling inward toward the Sun. This is the orbital speed required to maintain a stable orbit at perihelion, and is highly dependent on the exact distance between the Earth and the Sun. If the orbital speed drops below this value, the centripetal force will be smaller than the gravitational force, and the Earth will start to spiral inward toward the Sun.