Thread: What is the escape velocity of VY Canis Majoris, and the relation between mass and volume?

As above, I've been wondering how fast an object would need to travel to escape its gravity? As if we were launching from the pad on Earth.

I did Google it, and the one thought out answer was:

Alright, so @wonderingwhy provided the formula for escape velocity and from there it’s just a matter of plugging a couple of values. G is the gravitational constant and it’s equal to about 6.67 * 10^-11. M is the mass of the star, which according to your link is not known exactly but estimated to be about 30 to 40 solar masses. A solar mass is about 2 * 10^30 kg, so if this star is, say, 35 solar masses, that’d put it at 70 * 10^30 kg. Finally, r is radius of the star, which according to the wikipedia article is about 1.5 * 10^9 km. We need that in meters to do this calculation, so add three more zeroes: 1.5 * 10^12 m.
So v = sqrt(2GM/r). Plug in the above values:
v = sqrt(2 * 6.67 * 10^-11 * 70 * 10^30 / 1.5 * 10^12)
v = 78,900 meters per second, or 176,500 miles per hour, or about 7 times more than earth’s escape velocity.
So why is it less than the sun’s? Because you chose the largest star by volume, not by mass. This star is only about 35 times more massive than the sun, but its radius is about 1000 times larger. Since escape velocity increases with the square root of mass/radius, having such a large radius means a smaller escape velocity even though the mass is also larger.
Interestingly, this must mean that this star has very low density. If it were the same density as the sun and had a radius 1000 times larger, its mass would be one billion times more than the sun’s (mass increases proportionate to the cube of radius). However, if it were this dense, I’m pretty sure it would be a black hole.

I'm wondering if this is accurate or not. After reading it, I realize that I don't really understand the relation between Mass & volume. I'm thinking that it's

Mass = density (weight) of an object
Volume = the space it occupies

I know that you can have a balloon the size of a house and yet a truck could have more mass, but at the same time I thought that a star of that size would also have an insane amount of mass? How do they determine that?

Originally Posted by Bay Ridge

As above, I've been wondering how fast an object would need to travel to escape its gravity? As if we were launching from the pad on Earth.

I did Google it, and the one thought out answer was:

Alright, so @wonderingwhy provided the formula for escape velocity and from there it’s just a matter of plugging a couple of values. G is the gravitational constant and it’s equal to about 6.67 * 10^-11. M is the mass of the star, which according to your link is not known exactly but estimated to be about 30 to 40 solar masses. A solar mass is about 2 * 10^30 kg, so if this star is, say, 35 solar masses, that’d put it at 70 * 10^30 kg. Finally, r is radius of the star, which according to the wikipedia article is about 1.5 * 10^9 km. We need that in meters to do this calculation, so add three more zeroes: 1.5 * 10^12 m.
So v = sqrt(2GM/r). Plug in the above values:
v = sqrt(2 * 6.67 * 10^-11 * 70 * 10^30 / 1.5 * 10^12)
v = 78,900 meters per second, or 176,500 miles per hour, or about 7 times more than earth’s escape velocity.
So why is it less than the sun’s? Because you chose the largest star by volume, not by mass. This star is only about 35 times more massive than the sun, but its radius is about 1000 times larger. Since escape velocity increases with the square root of mass/radius, having such a large radius means a smaller escape velocity even though the mass is also larger.
Interestingly, this must mean that this star has very low density. If it were the same density as the sun and had a radius 1000 times larger, its mass would be one billion times more than the sun’s (mass increases proportionate to the cube of radius). However, if it were this dense, I’m pretty sure it would be a black hole.

I'm wondering if this is accurate or not. After reading it, I realize that I don't really understand the relation between Mass & volume. I'm thinking that it's

Mass = density (weight) of an object
Volume = the space it occupies

I know that you can have a balloon the size of a house and yet a truck could have more mass, but at the same time I thought that a star of that size would also have an insane amount of mass? How do they determine that?

Mass does not equal density. Density is mass per volume.

But to address how a large star can have a comparably small mass you have to consider the following: Stars are essentially big balls of gas. How much volume that gas takes up depends on what the star is doing. Because of the way stars burn their fuel, they can contract or expand in size with out changing their mass. Our own star, as it ages will change so that it will expand into a Red giant who's surface could extend all the way out to Mars' orbit. When it does so, it will actually be slightly less massive than it is now.

VW Canis Majoris is a red hyper-giant. it has more in common with the future red giant out star will become than it does with the sun as it is now.

Okay so looking back on the original post, I realize I worded the question poorly. I didn't mean as in the star escaping itself as I know that can't be done. I meant as in "how fast an object (say, rocket) would need to travel to escape its (its meaning this particular star) gravity?"

As for mass/density/volume and all that, I don't know why I have such a hard time wrapping my head around it.

So mass doesn't = density, but density = mass?

Is density separate from weight, or is it synonymous? I feel dumb.

Density = mass per volume. If you shove more mass into a smaller volume, you get a greater density.

For instance: kilogram is a unit of mass. cubic meter is a unit of volume. Kilogram per cubic meter is a measure of density.

Originally Posted by Bay Ridge

Okay so looking back on the original post, I realize I worded the question poorly. I didn't mean as in the star escaping itself as I know that can't be done. I meant as in "how fast an object (say, rocket) would need to travel to escape its (its meaning this particular star) gravity?"

As for mass/density/volume and all that, I don't know why I have such a hard time wrapping my head around it.

So mass doesn't = density, but density = mass?

Is density separate from weight, or is it synonymous? I feel dumb.

Density is mass/volume.

So for example, if you have something that has a mass of 2 kg and a volume of 10 m^3, then it has a density of

2kg/10m^3 = 0.2 kg/m^3 or 0.2 kilogram per cubic meter.

If you had another object that massed the same 2 kg but had a volume of 4 m^3, then it would have a density of

0.5 kilogram per cubic meter. Same mass, different density.

Weight is how much downward force is exerted by a mass due to gravity. On the surface of the Earth, Kilograms are sometimes used for both mass and weight, thus you will hear that something "weighs" 10 kg. But using kg as a weight is only valid in Earth's gravity, because it is only there that something that masses 10 kg also "weighs" 10 kg. If you were to take the same object to the moon, it would still have a mass of 10 kg, but it would have a different weight than that on the Earth.

Originally Posted by AlexG

Density = mass per volume. If you shove more mass into a smaller volume, you get a greater density.

For instance: kilogram is a unit of mass. cubic meter is a unit of volume. Kilogram per cubic meter is a measure of density.

Okay, this helps a bit.

I think what makes it harder for me is I follow what most people seem to think about mass/weight and such. As in mass=massive=big object, more mass. And pounds/kilograms being weight, rather than mass.

Your explanation helps too, PhDemon. How come when we talk about weight (most of us), we say we weigh like 170lbs rather than newtons? I'm guessing it's because the vast majority of us stay on the same planet? Would be less confusing though if everyone used newtons. I guess the same goes for kilograms, celsius & driving on the right lol.

Kilogram is a measure of mass. When the mass is resisting a gravitational field, for instance, sitting on the table, that resistance is weight.

So you can say weight is mass in gravity.