Astrometry and Elliptical orbits

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In summary, you can determine the orbit of an object by measuring its angular position at different times and applying the theory of conic sections. This method was devised by CFG 200 years ago and is still used in modern observation astronomy. For a more in-depth understanding, you can refer to the book "Statistical Orbit Determination" by Tapley, Schutz, and Born.
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Mu naught
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You can measure the distance to an object orbiting the sun using parallax, and you can determine its angular velocity by measuring its change in position over several hours or days.

From this you can calculate its orbit... if it were circular. However, comets and asteroids follow elliptical orbits, not circular ones. How do you determine the true orbit of an object and its eccentricity?
 
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http://www.schillerinstitute.org/fid_97-01/982_Gauss_Ceres.html

EDIT:
Just read a bit into the paper. Sorry, seems to be crap written by a philosopher. It's 85 pages, though, so maybe there's something worth reading in the rest of the paper.
However, what I wanted to say: You determine orbits not on the assumption of circles, but of conic sections. That covers everything.
 
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  • #3
Ich said:
http://www.schillerinstitute.org/fid_97-01/982_Gauss_Ceres.html

EDIT:
Just read a bit into the paper. Sorry, seems to be crap written by a philosopher. It's 85 pages, though, so maybe there's something worth reading in the rest of the paper.
However, what I wanted to say: You determine orbits not on the assumption of circles, but of conic sections. That covers everything.

thanks i don't have time to look at it now but i will tomorrow. I understand that an ellipse is a conic section, but what I don't really understand is how to apply the measurements you can make - distance and average angular velocity over some interval of time - to the equation for an ellipse.

I should mention the reason I ask is because I'm taking a course in observation astronomy and I'd like to calculate the orbit of comet Hartley for my research project.
 
  • #4
Actually, what you measure is angular position at different times, and nothing else. I hereby frankly admit that I don't know how to calculate orbits from these measurements, but CFG seems to have devised a valid method 200 years ago. Try to find it.
 
  • #5
For a fairly extensive description of the process I can recommend [1]. For an introduction I would recommend that you find an astronomy textbook suitable for your level that also describes orbital determination (like Gauss method). There is a fairly big difference between just knowing what practical observations to make in order to determine orbits, and then to derive the theory and computer code needed to make the actual calculations.

[1] Statistical Orbit Determination, Byron D. Tapley, Bob E. Schutz, George Henry Born. Elsevier Academic Press, 2004. (http://books.google.com/books?id=qePVQF9v15kC)
 

Related to Astrometry and Elliptical orbits

1. How does astrometry contribute to our understanding of elliptical orbits?

Astrometry is the branch of astronomy that deals with the precise measurement of the positions and movements of celestial objects. By accurately measuring the positions of objects in the sky, astrometry can help us track the orbital paths of planets and other objects, including those with elliptical orbits. This allows us to better understand the characteristics and dynamics of these orbits.

2. 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 elliptical or oval-shaped path around another object, typically a larger body such as a star. This type of orbit is characterized by the object being closer to the central body at some points in its orbit and farther away at others, rather than maintaining a consistent distance throughout the orbit.

3. How are elliptical orbits different from circular orbits?

Elliptical orbits differ from circular orbits in that they are not perfectly circular, but rather have an oval or elliptical shape. This means that the object in orbit will have varying distances from the central body at different points in its orbit. In contrast, a circular orbit has a constant distance from the central body throughout the entire orbit.

4. What factors contribute to the shape of an elliptical orbit?

The shape of an elliptical orbit is primarily determined by the velocity and direction of the object in orbit, as well as the gravitational pull of the central body. The closer the object is to the central body, the stronger the gravitational pull and the more circular the orbit will be. On the other hand, a higher velocity or a more tangential direction can result in a more elongated elliptical orbit.

5. Can elliptical orbits change over time?

Yes, elliptical orbits can change over time due to various factors such as gravitational interactions with other objects, tidal forces, and the effects of relativity. In some cases, these changes can lead to a transition from an elliptical orbit to a more circular one or vice versa. It is also possible for a planet or satellite to be captured into an elliptical orbit by a larger body, such as a star or planet, through a process known as orbital resonance.

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