Can you give me an estimation of the biggest height delta of a planet?

Question

The biggest delta means - the highest mountain compared to the lowest valley.
On earth for example it's around 20 km(everst ~8km, deepest point in coean ~11km).
The estimation should be of course as a function of the radius, and maybe some other parameters.

1.The question is about a random planet, not only in the solar system. moons included.

2. I need a rough estimation based on physical intuition. not a statistic of the solr system planets.

3. The function doesn't have to be linear in radius, as suggested in one answer. In fact - the same one to offer this also says that the smalle the object the bogger the ratio, so....

Answer 1

The surface irregularity of planets result from different effects. The delta you give for the earth is the result of tectonic processes. Mars also has surface irregularity's that are the result of tectonic
processes. I think the key word is "processes".

There are events creating surfaces irregularity, and there is gravity reducing the irregularity. The effect of gravity is going to depend on the surface gravity, the nature of the surface material ( ductility), effects of the atmosphere,.....

Consider a planet entirely of ice, with a surface gravity equal to that of the earth. The ductile-brittle transition zone is at 30m http://en.wikipedia.org/wiki/Ductile it is hard to imagine a delta much greater than 30m lasting very long.

The ductile-brittle on the earth is 10km down, comparable to the delta of 20km.
I 'think' your formula will look something like this.
Delta = k X dbtr
dbtr = depth of ductile-brittle transition

k = a constant determined by material and dimensional needs

D(earth) = 20km

k(earth) = 20km/10km = 2

Valles Marineris -7km
Olympus Mons 26km
D(mars) = 33km

mars is earth like so
k(mars) = 2
so--
33(km) = 2 (dbtr(mars)
dbtr(mars) = 16.5km

I haven't found any data to confirm this.

Answer 2

I think this is Mars to date*.
The highest point is on the Olympus Mons at about 26 km.
The deepest depression is about 4 km (the impact crater Hellas).
So the delta would be roughly 30 km.

*: Our solar system has not yet been completely explored - not
to mention other solar systems. Fantasy has no limit as to what deltas may exist. I can't say if models have been made that would even enable a rough guess.

After additional details 1.) 2.) and 3.) What do you need such an intuitive guess for? Just for a formula or to investigate possible life on such planets? I could even imagine a planet with a crevest so deep that there could be an atmosphere inside it with life or an elevation so large, that it peaks out of the atmosphere... why not?

Answer 3

First, some disclaimers: I could not say if this is the greatest 'delta' of all planets, but I will assume you mean planets within our solar system and not counting moons (they haven't been studied that well) or unknown dwarf planets (oh, poor Pluto). As a function of radius, I'll assume you mean a ratio of delta:radius. I would disagree that this calculation is an "of course" type thing, since most places for which this information is known are about the same size (excepting the theorized gas planet cores, see note 3 at the end) and that ratio would only be important if there were wide variations in the size of solid planets in the solar system. Since you don't specify what "other parameters", I will ignore that.

With that said, I am pretty sure Mars has that title with a delta of about 31 km, and ratio of 0.0091256.

On Mars, Olympus Mons is "the largest mountain in the Solar System rising 24 km (78,000 ft.) above the surrounding plain" (there is no 'sea level', although there are estimates of average planetary elevation based on a perfect sphere model which is silly since no planet is perfectly spherical - see more in note 1 at the end). Valles Marineris is "a system of canyons 4000 km long and from 2 to 7 km deep."

24 + 7 = 31

The average diameter (a much more interesting value than radius) of Mars is 6,794 km. Therefore its radius is 3,397 km. If you wish to you use the ratio of the height 'delta' to the radius, this would give you...

31 km / 3397 km = 0.0091256......, but this will only be of any use if you have other planets' data to compare.

Note 1: "There is a discrepancy in the actual measurement of Mount Olympus. Because the measurements are actually estimations from the pictures of the Mariner 9, results for the height of the volcano range from 22 to 29 kilometers (14 to 16 miles) high. Also, some of the measurements were made from the base of the mountain, while others were done from the crater surrounding it, Nix Olympica. In terms of Earth's topography, Olympus Mons is taller than three Mount Everests, about as wide as the entire Hawaiian Island chain and it is larger than the entire state of Washington." Read all about it at http://hypertextbook.com/facts/2001/MarinaTsukerman.shtml however this info is a bit old (2001) considering several successful missions to Mars have happened since.

Note 2: It is theorized that the large gaseous planets may have solid cores, and those cores would probably have very irregular surfaces, yielding increased 'deltas', but if their sizes were great, that would lower any ratio of delta:radius.

Note 3: This question would get absolutely crazy if you wanted to compare delta:radius ratios of all known objects in the solar system, since the smaller the object, the less spherical they get. Fortunately for my sanity, you specified planet.


P.S. Darn! This took me so long to type, someone else got their answer in first. I still like mine better, 'of course'.


Addendum following the posting of added details to the question:
A) Please reread my full answer to this point, as I have edited it several times since the first post.

B) Please at least use the "Check Spelling" function before submitting.

C)Concerning your added details:
. 1)"The question is about a random planet, not only in the solar system. moons included."
. What do you mean random planet? Do you want us to talk about a planet we don't have information on? Or do you mean we should speculate what we suppose the greatest value for this delta or ratio could ever be? Either is silly, so I hope you mean something else. I do not include moons, since information on their topographics is sketchy at best, unless again, you wish us to speculate.
. 2)"I need a rough estimation based on physical intuition. not a statistic of the solr system planets."
. You are asking a question in the physics category, specifying terms like radius, delta, etc. Nothing about this suggests estimation or statistics, and intuition does not belong in the same conversation with mathematics (unless, as mentioned above, you expect us to speculate on unknown planets, which would be silly).
. 3)"The function doesn't have to be linear in radius, as suggested in one answer. In fact - the same one to offer this also says that the smalle the object the bogger the ratio, so..."
. If you have a particular function in mind, then let us know. No one should be expected to guess what the questioner means in the non-humorous questions. However, I can't think of any other 'function' using the data of "height delta" and planet radius that would be of any interesting use. Also, I don't see the point of using anything but a linear function, but that may change depending on clarification of your question.

Answer 4

It relies upon on what you mean via "the international." for many folk, "the international" is comparable to "the planet Earth." so the only danger is "the Earth." in case you mean "the photograph voltaic gadget" then the biggest planet is Jupiter, approximately 10 situations the diameter of the Earth. in case you mean "the Galaxy" then there are a number of planets a lot greater effective than Jupiter revolving around different stars, a large form of that they have got not have been given any names, basically catalog numbers.