Unraveling the Mystery of Hyperbolic Trajectories

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In summary, the conversation discusses the lack of material discovered from other star systems despite the existence of true hyperbolic trajectories. It suggests that the objects making solar drive-by's in hyperbolic orbits most likely originate from the Kuiper Belt or Oort Cloud. It also mentions the observations of Oort in the 1950s regarding long period comets and their aphelion distance of 50,000 AU. The conversation then shifts to the possibility of Alpha Centauri having an Oort Cloud and the potential differences between material from the Solar and Alpha Centauri Oort Clouds. It concludes by calculating the average escaping velocity for a Solar hyperbolic trajectory to be 0.281 m*s^{-1}.
  • #1
Orion1
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If true hyperbolic trajectories really exist, then why has there not been any material discovered as originating from another star system?

 
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lack of close-up study of long-period comets
 
  • #3
A possibility, however, the probability is very high that objects making solar drive-by's in hyberbolic orbits originate in the Kuiper Belt or Oort Cloud. Around 1950, Oort noticed that no comet had been observed with an orbit suggesting it had came from interstellar space. He also noticed a strong tendency for long period comet orbits to have an aphelion distance of about 50,000 AU. There is nothing particularly special about a hyperbolic orbit, it is merely a matter of velocity.
 
  • #4
Orion1 said:


If true hyperbolic orbits really exist, then why has there not been any material discovered as originating from another star system?

1. If it is truly hyperbolic then it is a one-time pass, which would not actually be an "orbit".

2. Time, just time.
 
  • #5
Solar Centaurus...


If true hyperbolic trajectories all originate from the 'Oort Clouds' of any given star system, and given that interstellar material from another star system must also originate from a hyberbolic trajectory from the 'Oort Cloud' of that star system, then what are the possibilites that the nearest star system, Alpha Centauri, also has an 'Oort cloud'?

What would be the distinguishing characteristics between Solar and Alpha Centauri Oort cloud material?

Threshold velocity for hyperbolic trajectory reaching Sol from Alpha Centauri:
[tex]dD = 4.124*10^{16} m[/tex] - Alpha Centauri range
[tex]dt = 1.466*10^{17} s[/tex] - Sol star system age
[tex]dv = \frac{dD}{dt}[/tex]
[tex]dv = \frac{4.124*10^{16} m}{1.466*10^{17} s}[/tex]
[tex]\boxed{dv = .281 m*s^{-1}}[/tex]

What is the value for an average escaping velocity for a Solar hyperbolic trajectory?

 
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1. What is a hyperbolic trajectory?

A hyperbolic trajectory is the path that an object takes in space when it is affected by the gravitational pull of a celestial body, such as a planet or star. It is characterized by a curved path that approaches but never intersects the gravitational body.

2. How is a hyperbolic trajectory different from an elliptical trajectory?

A hyperbolic trajectory is different from an elliptical trajectory in that it is an open path, while an elliptical trajectory is a closed path. This means that an object on a hyperbolic trajectory will eventually escape the gravitational pull of the celestial body, while an object on an elliptical trajectory will continue to orbit around it.

3. What factors influence the shape of a hyperbolic trajectory?

The shape of a hyperbolic trajectory is influenced by the mass and velocity of the object, as well as the mass and distance of the celestial body it is orbiting. The greater the mass and velocity of the object, and the smaller the mass and distance of the celestial body, the more elongated the hyperbolic trajectory will be.

4. How is the hyperbolic trajectory useful in space exploration?

The hyperbolic trajectory is useful in space exploration because it allows for efficient and rapid travel between celestial bodies. By using the gravitational pull of a celestial body, spacecraft can achieve high speeds and save on fuel, making it a cost-effective and time-efficient method of space travel.

5. Can hyperbolic trajectories occur naturally?

Yes, hyperbolic trajectories can occur naturally in the universe. For example, comets and asteroids often have hyperbolic trajectories as they enter and exit the solar system. Additionally, some stars and galaxies have been observed to have hyperbolic trajectories as they move through the universe.

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