Exoplanets and measuring inclination of orbit

[B_Cary]

This question comes from reading about exoplanets. Articles explain that we can only determine the minimum mass of the planet because we don't know the inclination of its orbit. I get this in general--if you think of the sky as a flat piece of paper, the same wobble can be produced by a massive planet whose orbit almost coincides with the paper or by a smaller planet whose orbit is perpendicular to the paper.

What I don't get is the convention of measurement. Does an orbit that coincides with the flat piece of paper have an inclination of 0 degrees or 90 degrees? Or ??? Also, is the standard term "inclination" or something else?

 

[MeteorWayne]

Zero degrees inclination would be for a planet that passes exactly betwen our viewpoint and the center of the star. 90 degrees would be one that orbits around the star from our location, never passing in front of it, so would be undetectable using the radial velocity method.
MW

 

[SpaceTas]

Other way round MeteorWayne. Your angle is with respect to the line of sight and is similar to the convention used within the solar system.

An inclination of 90 deg has the planet transiting (orbit edge on) and zero planet round and round (orbit pole on). The inclination is the angle made between the plane of the orbit and the plane of the sky. When the orbit is flush with the sky the inclination is zero and we have the planet going round and round the star causing no Doppler shift for the star. When seeing orbit edge on the orbital plane is tipped 90 deg with respect to the sky; there are transits and maximum possible Doppler shift seen for the star. I believe this convention started with visual binary stars.

Here is a link to a diagram (down near bottom) http://www.cartage.org.lb/en/themes...estarsystem/VisualBinaries/VisualBinaries.htm. The handedness is wrong; the velocity arrow should be on the far side of the orbit, or pointing the other way
To find inclinations of exo-planets look up http://exoplanet.eu/catalog-transit.php

Lagniappe "a little bit extra"
An inclination greater than 90 deg indicates a retrograde orbit ie the planet (second star of a binary) appears to orbit clockwise.

To visualize this put your right hand out in front of you and curl your fingers. With your thumb pointed directly at your eye you have an inclination of 90 deg and your fingers point anti-clockwise. The inclination is the angle between your thumb and your line of sight. So When your thumb points straight up/down the orbit (the curl of your fingers is side on). Now pointing your thumb away from you (you have now turned your wrist more than 90 deg) your fingers now point in an anti-clockwise direction.

 

[MeteorWayne]

Sorry Tas, hope you'll understand if I respectfully disagree in part. In the solar system, the inclination reference is the earths orbit, which is zero degrees. An asteroid or comet with 3 degrees inclination (or all the planets, which have inclinations less than 7 degrees) are almost in the same plane. So the inner planets can transit the sun, and the outer ones can pass behind it.



However, your link does show that the inclination is the angle of the axis relative to our view. I'm just not sure that is correct. Need more research )

 

[MeteorWayne]

It does appear you are correct, unlike our solar system, the inclination of exoplanets is measured from the plane of our view to the axis of the orbit. Why that is the convention, I dont know

 

[SpaceTas]

Just had another think about the convention. They solar system and binary star (exo-planet) conventions are the same. It's a matter of perspective; we are so used to viewing things from the plane of the solar system.

Imagine changing to a position above the north pole of solar system ie perpendicular to Earths orbit on the North side.
When viewed from here the planets orbit in an anti-clockwise direction. Right hand rule: thumb along N/S axis pointing north toward observer, and fingers curling in direction of orbital motion. The top of your hand can be thought of as defining the plane of the orbit. Now an inclination of a few degrees means tilting your hand and so your thumb (axis perpendicular to plane of orbit) a little. Now take Halley's comet which is retrograde this has a > 90 deg inclination (162 deg actually). Here your thumb needs to tip 162 deg to match the -plane of the orbit and keep fingers following its motion. The orbital motion looks clockwise (backward) from our viewpoint way above the "north" of the solar system.

This convention is the same used in standard mathematics ( trigonometry, rotational dynamics etc) with angles increasing anti-clockwise when viewed from above. Note this is opposite to the geographic convention for azimuth angles.

 

[Saiph]

hmm...never thought about how the inclination conventions worked for other systems. Learn something new all the time, thanks Spacetas.

Heck, I don't think I even bothered to think about how inclination of the systems orbits would affect our measurement of the planetary mass...though I do grasp it in general terms once it was mentioned..so thanks B_Cary for bringing that tidbit to my attention.

 

[B_Cary]

Thanks, spaceTas and MeteorWayne, for the discussion. I have copied the central answer for reference until I can engrave it on my memory:

An inclination of 90 deg has the planet transiting (orbit edge on) and zero planet round and round (orbit pole on).

The links to the diagrams and the Extrasolar Planets Encyclopedia were also helpful. FYI, I wasn't ignoring the discussion: <excuse>I was in a Warm Place for a few days, watching the flights to Cold Places get cancelled. </excuse>

The link to the table of transiting planets in the E.P.E. showed some interesting stuff. Only one planet out of 69 had an inclination of less than 80 degrees, and most seemed to be in the 85-86 degree range.

I wonder--can any useful information be determined from the fact that an exoplanet does not transit its star?

 

[MeteorWayne]

Well, the closer the angle is to 90 degrees, the more likely it is that the planet will pass in front of the star, so that makes sense.

As for the second question, all we can really tell is that the stellar system is pointing pole on to us, and it is unlikely we'll be able to estimate the mass of any of the planets with great precision. We might find some info from astrometry (the path of the star wiggling back and forth at it moves across the sky) but it will be of very low precision and very low value except fro REALLY massive planets. The doppler (star moving back and forth in our line of sight) technique is far more accurate and precise.