h4tt3n

Nice links, it seems you are right after all. I never heard about this phenomenon before. If Triton is really a captured body, it makes a perfect circular orbit even more unlikely than if it was a "native" body like our moon - in other words this "circularizing" effect is quite big, at least in some cases.

It does seem to happen strictly to heavy sattelites orbiting close to their hosts, though. I wouldn't expect Halley's comet or Pluto to ever get circular orbits. And I'm still wondering why this effect hasn't straightened out Mercurys orbit... Any guesses?

Best regards

Michael

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I think you are correct in saying the orbits will gradually become more circular due to tidal interactions with the object it is orbiting (unless the orbits are kept out of shape by a planet or something).

 

An interesting example is Triton' date=' the largest moon of Neptune. It has a very close retrograde orbit around Neptune, and is under very large tidal forces. Its orbit is the most circular of any body in the solar system, its eccentricity is a zero to 16 decimal places. Which is pretty damn non-eccentric![/quote']

 

I'm quite sure the bit about orbits becoming circular is not true. Elliptic orbits are just as stable as circular ones. An elliptic orbit may be changed due to the gravitational pull from other planets, but so may circular orbits too. "Tidal interactions" between the planets will only affect their rotation, not the orbit itself: Earths pull on the moon has over time slowed it down to always turn the same side towards Earth, but it hasn't changed its orbit.

 

If Triton's orbit around Neptune has become circular due to gavitational pull, then what about Mercury? The Trition/Neptune mass ratio is about 4770, while the Sun/Mercury mass ratio is almost six millions, and the gravitiational force per mass is much much larger. Then why is Mercurys orbit still eccentric? Probably because elliptic orbits are stable...

 

I'm sure it can be shown mathematically too.

 

best regards,

Michael

units shouldn't matter as long as you are consistant throughout.

Hehe, except if your programming language only works with radians! I got it fixed, though. Now it automatically calculats a, b, and e for any object.

Now I only need to figure out how to calculate the orbit's angle relative to frame of reference.

Thank you very much for helping me so far!

I'll post a download-link to the program as soon as it's finished for beta-testing.

Best regards,

Michael

Thank you! This seems to solve some of my problems. Can't get it to work, though - and I think the main problem is unit confusion.

Are we using AU, km or m for distance?

Are we using degrees or radians for angles?

Are we using seconds, days or years for orbital period?

(as a european I always use SI units as much as possible... )

regards,

Michael

Ah, you're right, but it doesn't change my line of question. Of course an orbit can be parabolic and hyperbolic too, but in those cases you can't define semimajor axis, semiminor axis and eccentricity, and for the same reason I'm not interested in those specific cases. My main interest is to define any closed orbit.

Michael

Hello,

Recently I stumbled across a math problem, that I hope you can help me with. It is really about defining a planetary orbit from very little data, but since all orbits are ellipses I might as well post it here too (it has also been posted in the astronomy subforum).

I'm building a simple 2D program that simulates gravitiational attraction between celestial bodies. The program is strictly Newtonian - it calculates all movement using F = G*(M+m)/d^2 - but I'd like to calculate backwards so to speak and find the details about any orbit's eccentricity, orbital period, orbit centre and foci ect ect.

All the data I have is:

-body's velocity vector length and direction

-body's distance to sun

-mass of all bodies

-x, y coordinates of all bodies

and derived from above data

-orbit semimajor axis

The data I don't have but wish I did is:

-Orbit's semiminor axis

-Orbit's eccentricity

-Orbit's centre coordinates

-Orbit's angle relative to a pre-defined frame of reference

I just cant figure out how to isolate these values, but except for that the program works fine and is great fun to play with. The problem is solvable though, since different orbits have unique coorelation between body distance to sun and velocity depending on eccentricity. Please help!

Best regards,

Michael

Pepperchin, to your now-deleted question: I use Cartesian coordinates. I simply use the built-in screen coordinates of the computer, beeing 0,0 in the upper left corner and 1280, 800 in the lower right.

My trouble is that I don't use any of the typical formulas to calculate planetary motion. I throw in a number of bodies and simply find the resulting force vector for each of them using Newton: F=G(M+m)/r^2. Then the programs move all bodies accordingly, calculates new force vectors and so on...

It's not entirely accurate, but it allows me to play with n-body problems for n=300 or so using very simple mathematics. And you can run some pretty spectacular scenarios using relatively little computer power.

For the same reason all nice-to-know values about each body's orbit are unknown, since the program doesn't use any of them to get it's result...

Hope that was any help.

Best regards,

Michael

Sorry, won't work. The ellipse centre coordinates are unknown, and so is the ellipse angle. But thank you very much for trying to help. Only known facors are:

-Sun's mass

-Orbiting body's mass

-Orbiting body's speed

-Orbit's semimajor axis (approx. value)

and

-distance between sun and orbiting body

All I want to find is orbit's semiminor axis, eccentricity or c-value. From any one of these values, the two others can be calculated.

Can this be done, or is it impossible?

Best regards,

Michael

To Janus:

Thanks for helping, but I'm looking for the semiminor axis, not the semimajor one. Do you know how to somehow isolate this value?

To Pepperchin:

(Correction)

Sorry, but the x, y coordinates of the centre of the ellipse are unknown. If I had them, I'd be able to find b...

best regards,

Michael

Ah, yes. I know this.

I'm simply looking for an equation from which I'll be able to extract the orbits semiminor axis or eccentricity from the orbiting body's velocity - given the premise that semimajor axis and distance to sun is known but nothing else.

Well, either that or any explanation that will help me figure out the relations between those values on my own.

Best regards,

Michael

Hello,

I'm building a small, simple program that allows people to easily experiment with interactions between bodies in our solar-system and any fictive system you want to play with.

Since each body may loose its original orbit due to gravitational influence from other bodies, I need a way to determine its new orbit from its distance to the sun, mass and speed alone.

The semi-major axis of the elliptic orbit can be determined since:

v^2 = GM((2/r)-(1/a))

and therefore

a = -(1/((v^2/GM)+(2/r)))

Now, my question is: Is there a similar way to determine the orbits semi-minor axis (and eccentricity) from speed, mass and distance to sun alone?

thanks,

Michael

Hello,

I'm currently working on a small educational program that illustrates how planets orbit the sun. I'm learning the neccesary math, physics and programming on the fly, which is very interestng but also quite frustrating! I hope you might help me with some problems...

When working with orbital mechanics (or celest mechanics) You often use the gravitational constant G and the total mass of the system M, beeing very close to just the mass of the sun. This have caused me a grat deal of worry: G is 6.673e-11 N*m^2/kg^2 and Msun is 1.989e+30 kg, but when I use these values my formulas go amok.

Just yesterday I found out that the two constants are often combned in th so called "standard gravitational parameter" which for the sun has the value 132,712,440,018 Km^3*s^-2, and when I used this value my program worked perfectly.

But when I multiply the two numbers I get 1.327e+20 rather than the actual value of 1.327e+11. What am I doing wrong?

Any other general or specific advice on how to program orbital mechanis will be received with gratitude.

Best regards,

Michael

(please note that I use SI units, not U.S. ones...)