Water Ball with Sun's Mass - It's Diameter?

[zforgetaboutit]

(For recreation)

Assuming (from Wikipedia) that the mass of the Sun is 2 x $10^{30}$ Kg,

I wondered what would be the size of an equivalently-massed ideal ball of water at STP with uniform density?

I read there the Sun is about 109 Earth diameters. My water ball model calculation is ~123 Earth diameters.

Anybody care to please confirm/correct?

 

[mfb]

The number looks reasonable, as the density of the sun is a bit above the density of water.
It is impossible to have such a ball, of course.

 

[zforgetaboutit]

Keep in mind I already used the word 'ideal'.

 

[mfb]

Sure, I just wanted to mention it. Such a ball would probably collapse until fusion of its hydrogen atoms starts inside. Alternatively, if the object stays too cold to start fusion, it might become a white dwarf.

 

[CellCoree]

I would like to clarify that the size of a water ball with the mass of the Sun would depend on several factors, including the density of the water and the temperature and pressure at which it is kept. Assuming that the water is at standard temperature and pressure (STP), the diameter of the water ball can be estimated using the following formula:

D = (3m/4πρ)^1/3

Where D is the diameter, m is the mass of the water ball (2 x 10^30 kg in this case), and ρ is the density of water (1000 kg/m^3 at STP).

Plugging in the values, we get a diameter of approximately 1.4 x 10^9 meters, which is equivalent to about 175 Earth diameters. This is slightly larger than the estimated 123 Earth diameters mentioned in the original content.

However, it is important to note that this is simply a theoretical calculation and there are many other factors that could affect the actual size of a water ball with the mass of the Sun. For example, the water would likely not be able to maintain its liquid state at such a large size and may need to be compressed or heated to maintain its form. Additionally, the gravitational force of the water ball would also play a role in its size.

In conclusion, while this calculation provides an estimate of the size of a water ball with the mass of the Sun, it should be taken with caution and further research and experimentation would be needed to accurately determine its size.