View Full Version : Radius of planets

cjackson

2012-Nov-29, 03:35 AM

Does the radius of a planet matter as much as it's circumference, and diameter?

Why do most sites only list a planet's radius, but not it's diameter, and circumference?

What can be learned by knowing the radius of an object?

Hornblower

2012-Nov-29, 03:53 AM

Does the radius of a planet matter as much as it's circumference, and diameter?

Why do most sites only list a planet's radius, but not it's diameter, and circumference?

What can be learned by knowing the radius of an object?What do you mean by "does it matter as much?"

Jens

2012-Nov-29, 04:17 AM

Does the radius of a planet matter as much as it's circumference, and diameter?

Why do most sites only list a planet's radius, but not it's diameter, and circumference?

What can be learned by knowing the radius of an object?

Well, diameter is 2 x radius, so if you know one you don't have to write the other. And the circumference is 2 x radius x pi. So why would you wonder whether one is more important than the other?

George

2012-Nov-29, 04:30 AM

The radius of something is a better geometric term. Longitude and lattidue are much better to understand when looking from the center of a sphere outward (i.e. radius). A radius vector is important, and you never here of a "diameter vector" except in skewed humor. :)

I enjoyed being at the F1 race in Austin, and the curves of the track were built by the contractor who was given the radius for each curve. It is a more common and useful term. Diameter is ok to use if you are comparing sizes, but consistency is also important, so using radii seems prefered even in size comparisons, as in planet comparisons.

chornedsnorkack

2012-Nov-29, 11:57 AM

Where is the centre of Earth?

Is it at an equal distance to North Pole and South Pole, or is it 2800 m closer to North Pole than to South Pole?

antoniseb

2012-Nov-29, 12:08 PM

Where is the centre of Earth? Do you count the ice on Antarctica as surface or above the surface? ...

Geometric center, center of mass, center of pressure? It isn't a perfect equally distributed sphere, so it has a number of centers you could give it.

Jens Riggelsen

2012-Nov-29, 12:59 PM

Where is the centre of Earth?

Approximately 6400 km directly below you :)

Sent from my phone (seriously! I mean, how awesome is that!)

Glom

2012-Nov-29, 02:47 PM

Circumference might be interesting if your were comparing airline operations on different planets since it would relate to the maximum sizes of their routes. But still that really isn't an applicable topic, it does come up much.

Approximately 6400 km directly below you :)

Sent from my phone (seriously! I mean, how awesome is that!)

Tapatalk is great for browsing this forum. I prefer it to regular view.

jfribrg

2012-Nov-29, 07:46 PM

I would think that radius is used more in calculations. Gravitational calculations use distance from the center of each object, so the radius is more useful. Area of a circle uses the radius of the Circle. Volume of a sphere involves the radius of the sphere. If you need the other numbers, you can easily get them from the radius, but I suspect that most of the time you will need the radius.

Jens

2012-Nov-30, 12:11 AM

Where is the centre of Earth?

Is it at an equal distance to North Pole and South Pole, or is it 2800 m closer to North Pole than to South Pole?

My somewhat flippant answer would be that geometrically, the center of a line is the point that is equidistant from the two ends of the line. So if you draw a line from the north pole to the south pole, the center of that line will be equally close to both. Now whether you want to define that point as the "center of the earth" is where it gets tricky, as antoniseb said.

Ara Pacis

2012-Nov-30, 12:16 AM

In most calculations, you use radius directly, so if someone tells you the diameter, you'd have to divide it by two before you start calculating area of the disc, volume, etc except for circumference which you can calculate straight from diameter.

grapes

2012-Nov-30, 04:44 AM

Geometric center, center of mass, center of pressure? It isn't a perfect equally distributed sphere, so it has a number of centers you could give it.

It seems like that might complicate things, but it doesn't really. If you take the shape of the earth to be the geoid, the equipotential surface that corresponds to sea level, the center of figure of an equipotential surface is the center of mass, so that very naturally is taken as the center of the earth.

In most calculations, you use radius directly, so if someone tells you the diameter, you'd have to divide it by two before you start calculating area of the disc, volume, etc except for circumference which you can calculate straight from diameter.I dunno, if you have the diameter D of a sphere, the surface area is just pi times D2.

Ivan Viehoff

2012-Nov-30, 05:18 PM

Radius, circumference and diameter are only equivalent when we know we are talking about a circle, or in the case of a planet when the cross-section is circular. When we are talking about something more like an ellipse, it is much harder to interpret the circumference. Although in principle if one has one axis and the circumference of an ellipse one can (with difficulty) deduce the other axis, the cross-sectoin probably isn't even a proper ellipse, but rather a circle flattened in a different way.

Saturn is heavily flattened at the pole, so one might say it has 2 distinct radiuses. The equatorial circumference is equivalent to the equatorial radius and diameter as a piece of information, as the equator is close to circular. Though giving a polar circumference wouldn't be interesting, rather we would want to know the length of the polar axis.

Haumea, a dwarf planet, is apparently an ellipsoid which is not only heavily flattened at the pole, but its equator is far from being circular too. No cross section is a circle, so circumference information is not useful. 3 quite different diameters are given.

Radius and diameter are at least equally useful when there is symmetry. If a body were materially prolate, then this ceases to be true, and indeed radius might not be well-defined as the centre may be unclear. So in this case there is a tendency to give diameter, as for example in the smaller irregular planetary bodies, Haumea, etc.

Hornblower

2012-Nov-30, 06:33 PM

Radius, circumference and diameter are only equivalent when we know we are talking about a circle, or in the case of a planet when the cross-section is circular. When we are talking about something more like an ellipse, it is much harder to interpret the circumference. Although in principle if one has one axis and the circumference of an ellipse one can (with difficulty) deduce the other axis, the cross-sectoin probably isn't even a proper ellipse, but rather a circle flattened in a different way.

Saturn is heavily flattened at the pole, so one might say it has 2 distinct radiuses. The equatorial circumference is equivalent to the equatorial radius and diameter as a piece of information, as the equator is close to circular. Though giving a polar circumference wouldn't be interesting, rather we would want to know the length of the polar axis.

Haumea, a dwarf planet, is apparently an ellipsoid which is not only heavily flattened at the pole, but its equator is far from being circular too. No cross section is a circle, so circumference information is not useful. 3 quite different diameters are given.

Radius and diameter are at least equally useful when there is symmetry. If a body were materially prolate, then this ceases to be true, and indeed radius might not be well-defined as the centre may be unclear. So in this case there is a tendency to give diameter, as for example in the smaller irregular planetary bodies, Haumea, etc.

Usefulness is in the eye of the beholder, depending on the needs of the task at hand. If I were planning an overland trek around an oddly shaped asteroid, I might want to know the circumference of a particular cross section, regardless of how difficult it might be to calculate it.

Ara Pacis

2012-Dec-01, 06:03 PM

I dunno, if you have the diameter D of a sphere, the surface area is just pi times D2.

Wha? No, I don't think so. It's not πd2, it's πr2 or (πd2)/4 or ½r*2πr.

Though I could be wrong, I suppose.

http://en.wikipedia.org/wiki/Area_of_a_disk

Amber Robot

2012-Dec-01, 06:20 PM

Wha? No, I don't think so. It's not πd2, it's πr2 or (πd2)/4 or ½r*2πr.

Though I could be wrong, I suppose.

http://en.wikipedia.org/wiki/Area_of_a_disk

I believe he said surface area of a sphere, not a disk.

Ara Pacis

2012-Dec-05, 09:19 AM

Ah, so he did. I wasn't paying attention.

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