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Seeka
2009-Feb-08, 08:57 PM
Hello fellow bauter's,
This is a fairly basic question but i need it clarified so if you can help please do:)

The words mass, size and density can you explain their meaning?

What is a solar mass?
If something is 5 solar masses does this mean 5 times the mass of our sun?

Much appreciated

Steffanie

EDG
2009-Feb-08, 09:27 PM
Mass is really simply just a measure of how much stuff is contained within the volume of an object - a bag of sugar may have a mass of 1 kilogram, for example.

Where potential confusion arises is between mass and weight - but mass is the same no matter what, whereas weight depends on the local gravity. You could be on Earth, or on Mars, or in interstellar space, and that bag of sugar will still have a mass of 1 kg even though its weight will be higher or lower. The only way that mass can change (in normal circumstances - let's not get into relativity here) is if you add or remove stuff to or from the object. Add 250 grams (0.25kg) more sugar to the bag, and you have 1.25 kg - remove 250 grams of sugar from the bag and you'll have 0.75 kg.

Size is just the radius, which is the distance from the centre of the planet to its surface. Usually it refers to a "mean radius", because planets aren't perfectly spherical -they're actually squished a bit, the distance from pole to pole through the centre of the Earth is smaller than the distance between two opposite points on the equator through the centre of the earth. However, the difference in radius is very small compared to the radius itself.

Density is the amount of stuff per unit volume, measured in kilograms per cubic metre (kg/m). In other words, it's mass divided by volume. Liquid water has a density of 1000 kg/m, which means that one cubic metre (a volume equal to that enclosed by a cube that is 1 metre by 1 metre by 1 metre) of water will have a mass of 1000 kg. The Earth's density is about 5500 kg/m.

And yes, five solar masses is five times the mass of the Sun. Similarly, three Earth masses is three times the mass of the Earth, and 15 Jupiter masses is 15 times the mass of Jupiter.

Nowhere Man
2009-Feb-08, 09:39 PM
Size is kind of vague, when used popularly. Usually, you have to ask for clarification. If cube A is twice the size of cube B, what has doubled? The length of an edge, the area of a face, or the volume? Three very different results.

Fred

Seeka
2009-Feb-08, 10:18 PM
Definitely mass and volume have been hazy to me.
So i have read that Jupiter needs to have 80 times more mass to be able to ignite nuclear fusion, this means its current size does not have to change, just the amount of stuff contained within the volume of itself?

EDG
2009-Feb-08, 11:04 PM
Jupiter's a bit weird - since it's mostly made of gas (which is very compressible), you can pile in more mass and the volume won't actually change much because the gas just gets more compressed. So you could have a planet that has 10 jupiter masses, but it'd still be around the same radius as Jupiter - so the density of the whole body is going to be much higher (a 70-80 Jupiter Mass brown dwarf will be bigger though, just not as much as you'd expect).

Rock on the other hand isn't so easy to compress. If you triple the mass of the Earth, the radius will increase quite a bit (and to complicate things further, the density will increase too because that rock is still being compressed)

Tobin Dax
2009-Feb-08, 11:26 PM
Like Nowhere Man said, size is a tricky word. I try not to use it in lectures, but to specify radius/length or mass instead.

Mass is how much stuff there is in an object. Volume is how much space something takes up. Since I usually have a water bottle with me during class lectures, I've been explaining mass vs. volume this way:

Say you have a 1-liter bottle full of water. The volume of the water is 1 liter. The mass of the water is the mass of the water. Imagine that the water is replaced with, say, lead (melted, poured in, solidified and cooled, and magically leaving the plastic container intact). Is the bottle now heavier? (Yes) Is there still the same volume? (Yes) So the volume hasn't changed, but there's more stuff inside the bottle-there's more mass. (Mass is related to weight, but different, like EDG_ says.)

Now, we could get the same mass of water as we have in our liter of lead, but that would require a larger volume of water. This is because of the density of water and lead. Density is how concentrated a certain material is. Higher density, like lead has, means that there is more mass in the same volume. Density is how much mass (stuff) there is in a certain volume.

Hopefully that explanation helps.

Seeka
2009-Feb-08, 11:29 PM
Of course i should have realised that gas and rock are different regarding mass.
You have helped alot thank you.

Seeka
2009-Feb-08, 11:39 PM
Yep Tobin Dax that was a good description also:) I tend to respond to 'imagine if....' alot better. It took a revolving porsche before i grasped the moons rotation :lol: It is crystal clear to me now :)

cosmocrazy
2009-Feb-08, 11:53 PM
Yep Tobin Dax that was a good description also:) I tend to respond to 'imagine if....' alot better. It took a revolving porsche before i grasped the moons rotation :lol: It is crystal clear to me now :)

When we were children we were taught lots of things using pictures and objects, a simple example would be to ask a child to count the oranges in a bowl.. etc I find this method still very useful today, even at very technical levels.

Picturing explanations tends to be far more useful. Its always a good idea to ask for an example or an analogy so that you can picture the situation first, then you can start to understand the dynamics and then further, the relative math.

Good question to ask and there are billions of people who never understand them.

Seeka
2009-Feb-09, 12:11 AM
So with relation to gravity, if i weigh 9 stone on earth i could weigh more or less depending on what planet i am on, but still have the same mass?

cosmocrazy
2009-Feb-09, 12:40 AM
So with relation to gravity, if i weigh 9 stone on earth i could weigh more or less depending on what planet i am on, but still have the same mass?

Exactly! now you've got it!:)

Seeka
2009-Feb-09, 12:46 AM
Cheers David:D

So stars, do we know how big stars can get in terms of solar masses? I would just like an idea of where our sun fits in, is it average or very massive?
The red giant Beltelgeuse in orion, how many solar masses is it?

cosmocrazy
2009-Feb-09, 12:51 AM
Cheers David:D

So stars, do we know how big stars can get in terms of solar masses? I would just like an idea of where our sun fits in, is it average or very massive?
The red giant Beltelgeuse in orion, how many solar masses is it?

I have heard of some reaching 150 solar masses but these tend to be short lived stars. The more massive a star the shorter its life span. IIRC betelgeuse has a mass of around 20 solar masses, but i'm not 100% sure on that.

I'm sure the good folks who know these details will better inform you than i can. but I'll check it out in the meantime and see if i can find you a link. :)

Here is a couple of links listing the most massive and least massive known stars
http://en.wikipedia.org/wiki/List_of_most_massive_stars
http://en.wikipedia.org/wiki/List_of_least_massive_stars

Neverfly
2009-Feb-09, 01:12 AM
I have heard of some reaching 150 solar masses but these tend to be short lived stars. The more massive a star the shorter its life span. IIRC betelgeuse has a mass of around 20 solar masses, but i'm not 100% sure on that.
http://www.youtube.com/watch?v=bov9M2gEgcE

EDG
2009-Feb-09, 01:17 AM
Cosmo's about right on his mass estimates. 150 is about the maximum possible stellar mass, and Betelgeuse is about 20 solar masses (so is Antares in Scorpio).

From the numbers I've gathered from stellar distribution tables, it seems that between 85% and 90% of stars are actually red and orange main sequence stars (type K V and M V) that are less massive than Sol, so the sun is not an "average" star by any means. However, it is also by no means the most massive star possible either, so call it an "above average" star ;).

Our sun appears to be a fairly normal type of star for its class (a G2 main sequence star) - and for that we can be grateful, because if it wasn't we'd all be dead :). Some other stars similar to the sun (e.g. Kappa Ceti) are known to "superflare", which means that every now and then they produce flares so gigantic that they would blast our atmosphere away if we were orbiting them.

Tim Thompson
2009-Feb-09, 01:59 AM
In most cases it is good enough (but not really correct) to say that the mass of something is a measure of how much matter there is in it. The old idea of "conservation of mass" (or "conservation of matter") comes from classical chemistry, where the total number of atoms that go into a chemical reaction must be equal to the total number of atoms that come out (that particular rule is every bit as valid today as it was 100 years ago).

The correct definition of mass comes from Newton's 2nd law: F=ma or Force equals mass times acceleration. So mass is really a measure of how strongly an object resists a force. If the force is constant, increasing the mass will decrease the acceleration of the object being pushed (or pulled), and decreasing the mass will increase the acceleration. As long as we don't stray into Einstein territory we can say that the mass of an object is constant if we don't add anything to it, or take anything from it, and that will be good enough.

So for our non-Einstein purposes, where special relativity is not a consideration, then we can say that the mass is a measure of the amount of stuff (matter); more matter, more mass; less matter, less mass.

Density is just a measure of mass per unit volume. So, if the mass remains constant but the volume gets larger (a balloon expanding as the gas in it is heated, for instance) then the density gets smaller (it is the ratio mass / volume).


So stars, do we know how big stars can get in terms of solar masses? I would just like an idea of where our sun fits in, is it average or very massive?
The red giant Beltelgeuse in orion, how many solar masses is it?
It's quite common to read or hear that the Sun is an "average" star, but that's not really true. It does have an "average" color, if one thinks that yellow-green is an "average" of orange/red & blue/white. But the Sun is more massive than well over 90% of the stars in the galaxy, so in terms of its mass, the Sun is definitely a heavy weight star.

The most massive stars we know of today are about 100 solar masses, though high mass stars (over say 5 solar masses) have a strong tendency to be double or multiple stars. So Eta Carinae, which comes in at about 100 or 120 solar masses is now known to be a double star, with both stars in the double being very massive stars. See the Wikipedia list of most massive stars (http://en.wikipedia.org/wiki/List_of_most_massive_stars), but keep in mind that the stars showing 150 solar masses are probably not single stars, but multiple stars.

The size of a star, its radius (or diameter) or volume depend less on the mass of the star and more on which stage of its lifetime it is in. So Betelgeuse is a red supergiant star, one of the largest stars known. Look at the famous 1996 HST image of Betelgeuse (http://hubblesite.org/newscenter/archive/releases/1996/04/image/a/). The image is in ultraviolet light and shows Betelgeuse to extend farther across than the orbit of Jupiter around the sun. The photosphere ("surface" of the star) is actually not that big, and lies between Mars & Jupiter, because ultraviolet light sees the upper atmosphere of the star. But it is still very big; according to Kaler's Betelgeuse page (http://www.astro.uiuc.edu/~kaler/sow/betelgeuse.html) a new distance measurement puts the radius of Betelgeuse at 87% of Jupiter's orbital radius, and its mass at 20 solar masses. Rigel (http://www.astro.uiuc.edu/~kaler/sow/rigel.html), on the other hand, despite being about the same mass as Betelgeuse, is only 70 solar radii in extent, instead of the 950 solar radii of Betelgeuse. The two stars of nearly equal mass are radically different in radius because Betelgeuse has moved farther through the stellar life cycle and has reached the red supergiant (http://en.wikipedia.org/wiki/Red_supergiant) stage, while Rigel is still a blue supergiant (http://en.wikipedia.org/wiki/Blue_supergiant) and therefore rather smaller (The orbit of Earth, 1 Astronomical Unit, is about 215 solar radii). Alnilam (http://www.astro.uiuc.edu/~kaler/sow/alnilam.html), the center star in Orion's belt, is probably 40 solar masses and 375,000 times brighter than the sun.

Most of the stars you can see naked eye are more massive than the sun, and considerably brighter as well. It is a simple selection effect: In order for us to see a star, it has to be bright enough to see. The absolute magnitude of the Sun (its apparent magnitude if it were 10 parsecs or 32.6 light years away) is 4.83. So it would be clearly visible, but not spectacular or distinctive (the naked eye limit under a dark sky is about magnitude 6), and would be washed out by urban lights. Hence, we see mostly stars more massive and brighter than our Sun, which leads one to the mistaken notion that our Sun is "average", or even just plain wimpy. This kind of observational bias (Malmquist bias (http://astroprofspage.com/archives/81)) is common in astronomy, and professional astronomers are on guard against it constantly (at least, they are supposed to be).

EDG
2009-Feb-09, 02:41 AM
In most cases it is good enough (but not really correct) to say that the mass of something is a measure of how much matter there is in it. The old idea of "conservation of mass" (or "conservation of matter") comes from classical chemistry, where the total number of atoms that go into a chemical reaction must be equal to the total number of atoms that come out (that particular rule is every bit as valid today as it was 100 years ago).

The correct definition of mass comes from Newton's 2nd law: F=ma or Force equals mass times acceleration. So mass is really a measure of how strongly an object resists a force. If the force is constant, increasing the mass will decrease the acceleration of the object being pushed (or pulled), and decreasing the mass will increase the acceleration. As long as we don't stray into Einstein territory we can say that the mass of an object is constant if we don't add anything to it, or take anything from it, and that will be good enough.

This is going to sound odd coming from me, but I am drawing a total blank on how we can directly measure the actual mass (as opposed to the weight) of a (mundane) object.

My old school physics textbook talks about inertial balances and trolley experiments, but in both cases apparently you need to compare with a standard 1 kg mass. Is that the only way to determine the mass of an object?

(and I do know how we can figure out mass of astronomical bodies - it's just the smaller things I've gone blank on).

Tim Thompson
2009-Feb-09, 03:01 AM
... how we can directly measure the actual mass (as opposed to the weight) of a (mundane) object.
You have to remember that all measurements are dimensionless ratios. There is no such thing as an absolute measurement. So we measure the mass of anything by comparing it to a known or defined standard mass, or by measuring its acceleration under a known or defined standard force. And this is generally true for all properties of all things. They are all measured by comparison to a known example, or directly to a defined standard for that property.

Since weight & mass must have a constant proportionality as well, measuring one always reveals the other as a necessary consequence.

Seeka
2009-Feb-09, 04:48 PM
Wow guys thanks so much for those replies. Tim Thompson i will give your reply a few reads and check the links, i am sure i will have more questions:)

geonuc
2009-Feb-09, 05:01 PM
Wow guys thanks so much for those replies.
BAUT is a wonderful place, isn't it? :)

BigDon
2009-Feb-09, 05:40 PM
Isn't the proper convention to use the phrase Jovian masses instead of Jupiter masses?

EDG
2009-Feb-09, 06:32 PM
I use "Jupiter masses" myself - jovian is also used an adjective to generally describe gas giants, so it's not really specific. With "jupiter mass" you know you're talking about Jupiter, not Saturn or any other gas giants.

Seeka
2009-Feb-09, 11:15 PM
Looking at the links from Tim Thompsons post, the idea of a red supergiant having a radius 1500 times that of our sun is just too much to comprehend, imagine or believe! Wow! I mean that is big. It's fascinating, i can't express how much this interests me that a star can swell this size when it enters its final cycle.

How can something be so huge!

Geonuc you're right it's a fantastic place :)

Tobin Dax
2009-Feb-10, 02:03 AM
When we were children we were taught lots of things using pictures and objects, a simple example would be to ask a child to count the oranges in a bowl.. etc I find this method still very useful today, even at very technical levels.
In an epiphany I should have year ago, I explained adding multiples of a single variable with such a method last week. I was trying to get students to do something like 4x+2x, and they weren't answering. My variable became apples instead x. Wow, did that work! I feel stupid saying that last comment, but this is definitely something I'll remember.