What is the significance of the foci in gravitational orbits?

In summary, the conversation discusses the relationship between the trajectory of an orbiting body and the eccentricity of its orbit. The speaker shares their findings on the foci of different types of orbits and expresses their curiosity about the physical meaning of these foci in terms of forces. The conversation also clarifies that the sum of distances from a point on the orbit's circumference to each focus is only constant for an ellipse, not a parabola or hyperbola, and that only one focus is relevant in these cases. The speaker also mentions a data sheet that may provide more information on this topic.
  • #1
MattWakes
15
0
hey everyone, this is a qualitative question on gravitational orbits:

I was going through questions in which the trajectory of the orbiting body is determined based upon the eccentricity of the orbit, e.g. 0<Ecc<1, ellipses, Ecc=1, parabola, Ecc>1, hyperbola. I did the math and found out what the foci where for each case. But I would very much like to know, what is the physical meaning of these foci? Yes, they are points such that the sum of distances from a point on the circumference of trajectory to each focus is a constant. But what do they really mean, in terms of forces or whatever?

Okay, thanks!
 
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  • #2
MattWakes said:
Yes, they are points such that the sum of distances from a point on the circumference of trajectory to each focus is a constant.
As a side point, this is true only for the ellipse, not the parabola or the hyperbola.
 
  • #3
Only one focus counts.
Here is the basic data sheet, you might get something from it.
 

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Related to What is the significance of the foci in gravitational orbits?

1. What is an elliptical orbit?

An elliptical orbit is a type of orbit in which an object, such as a planet or satellite, follows an oval-shaped path around another object, such as a star or planet. This shape is called an ellipse, and the object being orbited is located at one of the two foci of the ellipse.

2. Who was Johannes Kepler and what did he contribute to our understanding of elliptical orbits?

Johannes Kepler was a German mathematician and astronomer who lived in the late 16th and early 17th centuries. He was the first person to accurately describe the motion of planets in our solar system by using three laws of planetary motion, which are now known as Kepler's laws. These laws helped us understand that planets move in elliptical orbits around the sun, rather than in perfect circles as previously thought.

3. What are Kepler's three laws of planetary motion?

Kepler's first law states that planets move in elliptical orbits with the sun at one focus. Kepler's second law, also known as the law of equal areas, states that a line connecting a planet to the sun will sweep out equal areas in equal time intervals. Kepler's third law, also known as the harmonic law, relates the orbital period and distance of a planet from the sun.

4. What factors affect the shape of an elliptical orbit?

The shape of an elliptical orbit is affected by two main factors: the mass of the object being orbited and the velocity of the orbiting object. A heavier object will have a larger influence on the shape of the orbit, while a faster orbiting object will have a more elongated orbit.

5. Are all orbits in the universe elliptical?

No, not all orbits in the universe are elliptical. While many objects, such as planets, moons, and comets, have elliptical orbits, some objects, such as artificial satellites, have more circular orbits. Additionally, objects in the far reaches of our solar system, beyond the influence of the larger planets, may have highly elongated orbits known as parabolic or hyperbolic orbits.

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