A few questions regarding the transit of planets

Question

Here we will be concerning ourselves with the transit of a planet with it's parent sun.

I have a few questions that I am not sure about:

1) Do all planets transit their parent sun? It would seem to me that if all planets "cross" their parent star in some form, then depending on our point of view, we should be able to see the transits. For example, we never see a Mars transit, but if we alter our point of view to be farther then mars, then we would.

2) If all the planets are in the same orbital plane, would the transit of one, imply the transit of all the others? For example, our solar system is relevatily in the same plane, and it seems like Mercury/Venus transit, would also imply earth and beyond transits. We just have to be in right perspective.

3) If a planet transits its star, does the probability of a transit increase/decrease/same if planet semi major axis changes? I am not sure about this one. I still think that it would be 100% the fact that a transit will occur, but its more unlikely that we would ever see it, because we need our angle to be just right.

4) If a planetary system has multiple planets, would we detect transits from several planets if they are all in the same orbital plane, or if they have different orbital planes? This kind of builds off of #2, and I think the answer is the same orbital plane, because the "different" orbital planes could be such that are 90 degrees from our point of view, meaning we would never see the transit.

I want to know if my understanding of transits is correct by these questions. Thanks!

Answer 1

You need to draw yourself a diagram. A right angle triangle with one side equal to the radius of the star $r$ and another, the distance from the planet to the star $a$.

Unless your line of sight is in the angle defined by $\theta = \pm \tan^{-1} (r/a)$ then you won't see a transit.

If $a \gg r$ then we can say the probability of a transit given a random orbital orientation is about $r/a$.

See http://ay20class.blogspot.com/2011/11/transit-probability.html for the details.

For multiple transits then all planetary orbits would have to be confined within a range of angles defined by $\pm \tan^{-1} (r/a)$, using the $a$ appropriate for each planet. Thus more distant planets are less likely to transit and there are tighter constrains on their orbital inclinations if they are to be one of multiple transiting planets

Answer 2

When we talk about a transit, we are normally talking about one that is visible from Earth, or at least from some planet in the solar system.

But if you are willing to go to a point is space, it is always the case that every planet is transiting the sun from somewhere. So the Earth is right now transiting the sun from any position that is directly opposite the sun and more than about 1600000km from Earth (otherwise the sun won't be transited, it will be eclipsed.

The transits of all the planets can be seen from exterior planets, though the transits of (say) Saturn from Neptune are exceedingly rare

If you are in the orbital plane of the planet, you will eventually see a transit. But you may be waiting a long time. The semi major axis doesn't have any effect.

If the planet in a planetary system are in the same plane, then you may see more than one transit. But you are less likely to see the outer planets as they are further from the star.