# The elliptical orbits and inverse-square law forces.

• d-richard
In summary, the laws of planetary motion state that objects bound by an inverse-square law move in ellipses when orbiting, rather than circles. This is due to Kepler's laws of planetary motion, which were later derived from Newton's laws of universal gravitation. Circles are also considered ellipses according to these laws.
d-richard
Greetings,
I read a chapter in the book College Physics by Vuille and Serway explaining the laws of planetary motion in terms of the universal law of gravitation. The first law stated that planets move in an elliptical orbit and the book's explanation was that all objects bound by an inverse-square law move in ellipses if orbiting, not in circles. Could anyone please explain why inverse-square law forces cause this effect? Thanks.

d-richard said:
in ellipses if orbiting, not in circles.
Circles are ellipses.

thanks for the links, and yeah I forgot that circles are ellipses. Thanks for reminding me

Hello there,

I can provide an explanation for why inverse-square law forces result in elliptical orbits. The inverse-square law is a fundamental law in physics that states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In the case of planetary motion, this means that the gravitational force between a planet and the sun decreases as the distance between them increases.

Now, when a planet is in motion around the sun, it experiences a continuous change in direction due to the gravitational force acting upon it. This force is always directed towards the sun, but as the planet moves further away from the sun, the force decreases due to the inverse-square law. As a result, the planet's velocity also decreases, causing it to move in a curved path, ultimately resulting in an elliptical orbit.

In simpler terms, the inverse-square law causes the strength of the gravitational force to decrease as the distance between the two objects increases, resulting in a curved path of motion rather than a straight line. This is why planets, and other objects bound by the inverse-square law, move in elliptical orbits.

I hope this explanation helps to clarify the relationship between inverse-square law forces and elliptical orbits. If you have any further questions, please don't hesitate to ask. Happy exploring!

## What is an elliptical orbit?

An elliptical orbit is a type of orbit in which an object, such as a planet or satellite, travels around another object in an oval-shaped path. This path is determined by the gravitational pull of the larger object.

## What is the inverse-square law?

The inverse-square law is a principle that states that the strength of a force, such as gravity, decreases in proportion to the square of the distance between two objects. This means that as the distance between two objects increases, the force between them decreases exponentially.

## How does the inverse-square law affect elliptical orbits?

The inverse-square law plays a crucial role in determining the shape and stability of elliptical orbits. This law explains why planets move faster when they are closer to the sun, and slower when they are farther away. It also influences the shape of the orbit, as the strength of the force between two objects changes with distance.

## What other factors influence elliptical orbits?

In addition to the inverse-square law, other factors that can affect elliptical orbits include the mass and velocity of the objects involved, as well as any external forces, such as other gravitational pulls or atmospheric resistance.

## Why are elliptical orbits important in space exploration?

Elliptical orbits are important for space exploration because they allow for efficient and stable travel between planets and other celestial bodies. By understanding the laws and principles that govern these orbits, scientists and engineers can plan and execute space missions more effectively.

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