# Doubt about the elliptic orbits of the planets

• LCSphysicist
In summary: It shows that for central forces, the only possible bound orbits are circular, elliptical, and parabolic. This is because the only force that can result in bound orbits is proportional to 1/r^2, and the only possible values for n in this equation are 1 and -2. Since n=1 is unlikely, the only remaining option is n=-2, which results in an elliptical orbit. This is supported by the fact that for closed orbits, the orbital speed is constant, but the speed with respect to other frames of reference varies. Therefore, the only possible option for a closed orbit is an elliptical one. In summary, the only possible bound orbits for central forces are circular, elliptical, and parabolic,
LCSphysicist
Homework Statement
I was thinking, if it were ask to me why is the orbit of planets elliptic...
Relevant Equations
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I was thinking to myself, if it were ask to me why is the orbit of planets elliptic, how to justify?:

If the person don't know the Newton's law of gravitation said:
"It is easy to show, first, that the force is central, we have the motion in a plane, we can also show the energy and angular momentum is conversed without mention to power function of the force."
"Now, we can show that the only forces that could result in bound orbits, whatever be the particle, is the f = -kr^n, n equals one or minus two"
"But, n equals one is such unlikely, the only one n possible is equals minus two"
"So, we can now integrate the orbit equation, and get the equation of conics"

if he know said:
"Here is the thing, since we could say that the orbit is closed (or, at least, approximately), the only possible path is circular or elliptic"
"It's sufficient one statement to close the discussion: Find out if the orbital speed of the planet is constant or not, because L = rxmv,for circular orbits, |r| remains constant and perpendicular to the velocity tangential, but L is constant, so V would be constant."
"But the speed with respect to the stars, or the center of mass of universe or whatever frame inertial, varies with the time"
"Only the elliptical orbit remained"
"So is elliptical"

The bould phrases i just know to justify with collected dates.

IS this a reasonable justification?

Last edited:
You might find it interesting to have a look at the justification for Bertrand's Theorem.

## 1. What is an elliptic orbit?

An elliptic orbit is a type of orbit in which the path of an object follows an oval shape, with the object moving closer to and farther away from the body it is orbiting. This shape is called an ellipse, and the body being orbited is located at one of the two foci of the ellipse.

## 2. Why do planets have elliptical orbits?

Planets have elliptical orbits because of the gravitational pull of the sun. According to Newton's law of universal gravitation, the force of gravity between two objects is inversely proportional to the square of the distance between them. This means that as a planet moves closer to the sun, the force of gravity increases and pulls the planet towards it, causing the planet to speed up. As the planet moves farther away, the force of gravity decreases and the planet slows down, resulting in an elliptical orbit.

## 3. Are all planets' orbits perfectly elliptical?

No, not all planets' orbits are perfectly elliptical. While the orbits of the planets in our solar system are very close to being elliptical, they are actually slightly irregular due to the influence of other planets and objects in the solar system. This is known as orbital perturbation.

## 4. Can an object have an elliptical orbit around more than one body?

Yes, an object can have an elliptical orbit around more than one body. This is known as a binary or trinary orbit, and it occurs when the object is influenced by the gravitational pull of two or more bodies at the same time. An example of this is the orbit of the dwarf planet Pluto, which is influenced by the gravitational pull of both the sun and its largest moon, Charon.

## 5. How do scientists study and measure the elliptical orbits of planets?

Scientists use a variety of methods to study and measure the elliptical orbits of planets. These include using telescopes to observe the position and movement of planets in the sky, analyzing data from spacecraft missions that have orbited other planets, and using mathematical models and simulations to understand the dynamics of planetary orbits. Additionally, the laws of planetary motion developed by Johannes Kepler and Isaac Newton have been instrumental in understanding and predicting the elliptical orbits of planets.

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