Central Meridians Revisited

[Bob Hegwood]

Brain-Dead again...

I'm in a quandry when trying to understand how a particular planet's
Central Meridian is located and/or defined.

If I have just downloaded a texture for Mercury, for example, how do I
know if the Central Meridian is located correctly? I understand how to
revise a texture to MOVE the meridian, but how do I know if it needs to
be moved?

Sorry, but I'm simply at a loss as to how to determine what is correct
and what is not. The only way I know that a meridian is incorrect so far
is by comparing an image with one which has already been defined as
being correct by one of you more knowledgeable people.

Is there a better way?

Thanks, Bob

[selden]

Bob,

The prime meridia of planetary coordinate systems are assigned rather arbitrarily by the IAU. For example, Mercury's 20° meridian is defined by the crater Hun Kal.

As a result, you have to compare the map with a known good one

A relevant document is the "Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2000," by P. K. Seidelmann, et al. It's avaiable in several formats at http://astrogeology.usgs.gov/Projects/ISPRS/PREPRINTS/index_preprints.html

A history of the mapping of Mercury is available at http://history.nasa.gov/SP-423/surface.htm

You also might want to take a look at http://cps.earth.northwestern.edu/merc.html
which documents Mark S. Robinson's project to recalibrate the Mariner 10 images of Mercury.

[Bob Hegwood]

Selden,

As always, thanks very much for your help. I'll have a look at the
sites you pointed me to, and I'll see what I can learn.

A point though... If I have an image which is not aligned correctly
to begin with, how on Earth will I ever locate the crater Hun Kal?

Just kidding... I'll get it sooner or later.

Thanks again, Bob

[selden]

Bob,

The NASA document "SP-423 Atlas of Mercury" may help. I referenced one of its chapters above. Its table of contents is at http://history.nasa.gov/SP-423/contents.htm

In particular, Figure 17, at http://history.nasa.gov/SP-423/p21.htm, is a map that shows the regions of the planet that were photographed. Note that they put 0 degrees of longitude at the edge.

The approximate location of 0 degrees was determined long ago using low resolution Earthbound observations. The choice of Hun Kal made it more precise.

[Bob Hegwood]

In particular, Figure 17, at http://history.nasa.gov/SP-423/p21.htm, is a map that shows the regions of the planet that were photographed. Note that they put 0 degrees of longitude at the edge.

Well that url certainly makes the process easier.

Thanks again Selden. Don't you ever get tired of answering stupid
questions from jerks like me?

Take care, Bob

[Evil Dr Ganymede]

This may not be particularly relevant to Celestia, but for tidelocked bodies like the satellites of the giant planets (or any planets that are tidelocked to stars), the 0 meridian is defined by the IAU (or at least the USGS, that maps those bodies) as the longitude line that faces the primary. In other words, the sub-primary point - the point directly underneath the primary on the satellite's surface is at lat/lon 0N/0E. The "anti-primary point" is 180 degrees around the planet, at 0N/180E - this faces directly away from the primary.

The centres of the leading and trailing hemispheres are 90 degrees from these points - the leading hemisphere is the one that faces the planet's direction of motion in its orbit (it's not rotating relative to the primary, remember), and the trailing hemisphere is the one that faces away from the direction of motion. The centres of those hemispheres are at 0N/90E and 0N/270E , but I can never remember which one's which.

[granthutchison]

This may not be particularly relevant to Celestia ...

Gasp.
That was a week of my spare time, that was, making sure that all central meridians of synchronous satellites were correctly orientated.

Grant

[Bob Hegwood]

Gasp.
That was a week of my spare time, that was, making sure that all central meridians of synchronous satellites were correctly orientated.

And that week of your spare time made it possible for us non-scientists
to find out where all those neat craters, mountains, volcanoes and a wealth
of other interesting features were located! Thanks very much for
the effort. It's sooo much nicer being able to know what you're looking
at during a tour.

By the way, can you tell me what Dr. Ganymede just said above? I thought
I understood English, but I have no idea what he just said.

Take care, Bob

[Evil Dr Ganymede]

(sorry Grant. I wasn't slighting your efforts there, I just couldn't remember if that was how it worked in Celestia )

By the way, can you tell me what Dr. Ganymede just said above? I thought
I understood English, but I have no idea what he just said.

Sigh. I thought I was pretty clear about it. Let's try again.

Right. You know what tidelocked bodies are, yes? If not, they're objects like the moon, which has one side permanently facing the body it orbits (which I refer to as the primary).

So this being the case, they don't rotate relative to the primary. So imagine a latitude/longitude grid overlaid on the satellite's surface. This grid also isn't going to rotate relative to the primary. So imagine that in your head (or better still, look at something like Europa or Ganymede in Celestia).

Now, if you're on a tidelocked world, there's going to be a point on the surface that is always directly beneath the primary (so if you stood there, the primary would be directly overhead throughout the whole orbit). That's the sub-primary point. If you go 180 degrees around the planet to that point, you'll be facing directly away from the primary - that's the "anti-primary point.

The leading and trailing hemispheres are those that face the direction of the satellite's motion in its orbit around the primary. If you like, the centres of those hemispheres are where the orbit line drawn in Celestia enters and leaves the body of the planet. They're 90 degrees around the planet from the sub- and anti- primary points.

The Zero Meridian for these worlds is simply defined as the longitude line connecting the north and south poles of the satellite that passes through the sub-primary point. So if you walk directly north or south from the sub-primary point, you're walking along the Zero Meridian. And that's how the maps in Celestia are set up too.

Is that clearer?

[granthutchison]

Bob:
You've got my grid overlays add-on, don't you? Try turning on the grids while you watch a tidally locked body like Io revolve around its parent planet.

Grant

[granthutchison]

sorry Grant. I wasn't slighting your efforts there, I just couldn't remember if that was how it worked in Celestia

No worries. I wasn't upset. I've got used to the fact that all this orbit and orientation stuff is effectively invisible if I'm doing it correctly. Sigh. The texture jockeys always get the glory ...

But wait'll you see what I've done with the Nearby Stars add-on now that star orbits are implemented - I've got stuff lolloping around barycentres all over local space!

Grant

[Bob Hegwood]

Right. You know what tidelocked bodies are, yes? If not, they're objects like the moon, which has one side permanently facing the body it orbits (which I refer to as the primary).

Sorry, did not know what a tide-locked body was. Now I do, so
thanks for that explanation. If I understand you correctly now, any
tide-locked body orbiting a planet will always maintain the same face to
the planet in question. Yes?

So this being the case, they don't rotate relative to the primary.

Ah, but they do rotate in an exact synchronous state, or the same face
would not remain locked to the planet's surface. Yes?

So imagine a latitude/longitude grid overlaid on the satellite's surface. This grid also isn't going to rotate relative to the primary. So imagine that in your head (or better still, look at something like Europa or Ganymede in Celestia).

Okay so far...

Now, if you're on a tidelocked world, there's going to be a point on the surface that is always directly beneath the primary (so if you stood there, the primary would be directly overhead throughout the whole orbit). That's the sub-primary point. If you go 180 degrees around the planet to that point, you'll be facing directly away from the primary - that's the "anti-primary point.

Okay again... Now that I understand the underlying basics.

The leading and trailing hemispheres are those that face the direction of the satellite's motion in its orbit around the primary. If you like, the centres of those hemispheres are where the orbit line drawn in Celestia enters and leaves the body of the planet. They're 90 degrees around the planet from the sub- and anti- primary points.

I'm getting there. I understand the sub-primary and anti-primary points now.

The Zero Meridian for these worlds is simply defined as the longitude line connecting the north and south poles of the satellite that passes through the sub-primary point. So if you walk directly north or south from the sub-primary point, you're walking along the Zero Meridian. And that's how the maps in Celestia are set up too.

Is that clearer?

This is absolutely clear to me if you're talking about a tide-locked body...
How does all of this relate to a normal planet though? Or, am I missing the
point again? Is Mercury a tide-locked planet? Sorry, just do not know. In
other words, does Mercury keep the same face always pointed at the Sun?

Sorry to be such a pain, but I'm really trying to understand what you were
saying... Having had your second explanation, I now know a lot more
than I did when I read your first message.

I thank you very much for the explanation, and I'd just like to
point out that more people than myself will benefit from your second
explanation.

If I may, you scientist-types seem to forget that us "normal" people have
an interest in space, astronomy and the universe too. You should be
encouraging "normal" people with simple explanations where applicable.

I know that this might be difficult to do, but you already know that I
am Brain-Dead.

At any rate, thanks again for taking the time to explain it to me in terms
that my feeble brain can understand. This is much appreciated.

Take care, Bob

[Bob Hegwood]

Bob:
You've got my grid overlays add-on, don't you? Try turning on the grids while you watch a tidally locked body like Io revolve around its parent planet.

Grant,

I do now. Thanks very much. A picture is worth a thousand
words...

I still don't understand what the tidal-lock property has to do with a
central meridian though. What defines the meridian for non tidal-locked bodies?

Is this just at the whim of someone at the USGS? The IAU? Or, is there
some other rational used to determine where the meridian should be
placed?

Thanks, Bob

[granthutchison]

I still don't understand what the tidal-lock property has to do with a central meridian though. What defines the meridian for non tidal-locked bodies?

The central meridian is defined pretty much randomly for bodies that rotate relative to their primary ... often observers will have agreed an approximate meridian, and then when a spacecraft flies by and takes photographs, the definition is tightened down by the people doing the mapping ... perhaps using a particular small crater as a marker. For asteroids, the prime meridian is often at one end of the long axis.
So the "sub-primary" definition is only relevant for tidal-locked objects ... its just a handy standardization for these bodies.

Just to bend your brain a little further, gas giants have a defined prime meridian! The rotation period of a gas giant's core is known (from the length of time it takes its magnetic field to rotate). So astronomers have just said, randomly: "The prime meridian is the bit of the core that was facing the Earth at X time on X date". After that, they can predict where this invisible prime meridian is at any other time, because they know how long it would take to go once around the planet. And the point of that is so that they can give coordinates for cloud features (relative to this invisible prime meridian), and then track them as the clouds move around.

Mercury is an odd, intermediate situation. It's locked into a tidal resonance in which it rotates three times for every two orbits around the Sun. So it's going around 1.5 times each orbit, instead of once each orbit like a true synchronous rotator. This means whichever area of Mercury is pointing directly at the Sun when Mercury is at its closest to the Sun is pointing directly away from the Sun at the next closest approach, and then directly toward it again next time. So two spots on Mercury, 180 degrees apart, are alternately baked and frozen. The prime meridian of Mercury was chosen to run through one of these points, and the Caloris Basin lies at the other ("Caloris" meaning "hot" in Latin).

Grant

[Evil Dr Ganymede]

I suspected the "tidelocked" part might be what was confusing you. Evidently the word is less commonly used than I thought.

Sorry, did not know what a tide-locked body was. Now I do, so thanks for that explanation. If I understand you correctly now, any
tide-locked body orbiting a planet will always maintain the same face to
the planet in question. Yes?

Basically, yep. It may wobble a bit, but basically the same face always points toward whatever it's orbiting.

Ah, but they do rotate in an exact synchronous state, or the same face would not remain locked to the planet's surface. Yes?

Yeah. Basically the rotational period of the planet is exactly the same as the orbital period around whatever it's orbiting. So the planet IS still rotating, its just that it's day is the same length as its year.

How does all of this relate to a normal planet though? Or, am I missing the
point again? Is Mercury a tide-locked planet? Sorry, just do not know. In
other words, does Mercury keep the same face always pointed at the Sun?

Nope. Astronomers once (way back in the dim and distant 1940s and 50s ) thought that it was tidelocked, but as Grant says, it's in this weird spin:orbit resonance whereby it rotates three times for every two orbits.

No planets in our solar system are tidelocked to the sun, but if you have a world orbiting a K or M V star in the habitable zone, then chances are that it will be tidelocked because it's so close to the star.

If I may, you scientist-types seem to forget that us "normal" people have
an interest in space, astronomy and the universe too. You should be
encouraging "normal" people with simple explanations where applicable.

Well, I thought my first explanation WAS fairly simple . To be honest, I'd assumed that since you play around with Celestia you'd know what tidelocking was from reading things on the boards. Guess I'll just have to remember to start further back down the chain of explanation next time .

Oh well, it's all clear now

[Bob Hegwood]

Just to bend your brain a little further, gas giants have a defined prime meridian! The rotation period of a gas giant's core is known (from the length of time it takes its magnetic field to rotate)...

Now YOU have a gift for explanations that I can understand.

My brain wasn't bent even a tiny bit. Thank you, sir...

As to your grid texture, it does show Hun Kal at the 20-degree mark just
as it should. Appreciate the help.

Take care, Bob