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# Calculating Mercurys orbit with transit-data

3 replies to this topic

### #1 chris.catchingphotons

chris.catchingphotons

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Posted 06 January 2020 - 12:03 PM

Hey folks!
Using one hour of data from the Mercury transit last year (11.11.) I tried to figure out the orbit of Mercury by myself to follow the footsteps of earlier astronomers.

https://youtu.be/5n24QLYNjV8

I used some simplifications such as a circular orbit, the fact, that earth and Mercury were straight in line...

Did anyone use a similar method to figure out orbits of observed asteroids? I still haven't figured it out how I would do that: Elliptical orbits, shifting viewing angles..

I'd like to hear some cool stories

Greetings
Chris

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### #2 catalogman

catalogman

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Posted 11 January 2020 - 12:40 PM

Elliptic orbital elements can't be derived from a solar transit;
the time interval is too short, so there's no significant deviation
from a great circle.

Therefore, your simplification to a circular orbit is the best orbit
that you can find from a solar transit. For the Gauss method applied to
circular orbits, cf. An Introductory Treatise on Dynamical Astronomy,
by H. C. Plummer, Arts. 96-7.

--catalogman

### #3 chris.catchingphotons

chris.catchingphotons

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Posted 11 January 2020 - 02:32 PM

Ah interesting, thanks!

Yea for asteroids you tend to have more time to observe, even different nights over and over again... I try to figure out the math for that

Greetings
Chris

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### #4 smithrrlyr

smithrrlyr

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Posted 11 January 2020 - 07:55 PM

A simple approach to estimating roughly an orbit for a main belt asteroid is to observe it near opposition.  Measure the angular distance it appears to move in a given time interval. Then initially assume that the apparent motion of the asteroid just reflects the earth's orbital motion.  That lets you calculate a starting distance to the asteroid. With that as a starting point, one can try to iterate to improve the orbit using Kepler's third law to estimate the asteroid's speed at the distance of the initial estimate.    With that speed, one has a first stab at the real relative speeds of the earth and the asteroid, and one recalculates the distance to the asteroid using that speed rather than just the speed of the earth. Thus, you can get an improved distance. This approach will not, of course, be good for any asteroid that has a far from circular orbit.

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