# Kepler's Law of Areas: Radially Directed Force

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• DM107
In summary, Kepler's Law of Areas is a mathematical relationship that describes the motion of planets around the sun. It states that the line connecting a planet to the sun sweeps out equal areas in equal amounts of time. This law is significant because it helped to establish that planets move in elliptical orbits around the sun, and it is related to Newton's Law of Universal Gravitation in describing the effects of gravitational force. It can also be applied to other objects that orbit around a central body, but there are limitations as it assumes a constant force and only applies to nearly circular orbits.
DM107
Hi,

Just wanted to know how can we attribute the kepler's law of areas to a radially directed force?

DM107 said:
Just wanted to know how can we attribute the kepler's law of areas to a radially directed force?
The law of areas amounts to a statement that the angular momentum of a satellite about a central point is conserved. If there were an off-center force, that would amount to a torque and angular momentum would not be conserved.

I think you may need to elaborate on the question.

## 1. What is Kepler's Law of Areas?

Kepler's Law of Areas is a mathematical relationship that describes the motion of planets around the sun. It states that the line connecting a planet to the sun sweeps out equal areas in equal amounts of time.

## 2. What is the significance of Kepler's Law of Areas?

Kepler's Law of Areas is significant because it helped to establish that planets move in elliptical orbits around the sun, rather than in perfect circles as was previously believed. It also provided a mathematical basis for understanding the motion of planets, laying the foundation for future advancements in celestial mechanics.

## 3. How is Kepler's Law of Areas related to Newton's Law of Universal Gravitation?

Kepler's Law of Areas is related to Newton's Law of Universal Gravitation in that it describes the effects of a radially directed force, which is the gravitational force exerted by the sun on a planet. Newton's law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

## 4. Can Kepler's Law of Areas be applied to objects other than planets?

Yes, Kepler's Law of Areas can be applied to any object that orbits around a central body, as long as there is a radially directed force acting on it. This includes satellites, comets, and even artificial satellites launched by humans.

## 5. Are there any limitations to Kepler's Law of Areas?

Kepler's Law of Areas is based on the assumption that the central body exerts a constant force on the orbiting object. In reality, this may not always be the case, as other forces such as perturbations from other objects can affect the orbit. Additionally, the law only applies to objects with nearly circular orbits, and may not accurately predict the motion of objects with highly elliptical orbits.

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