What Happens if a Scale Model of the Sun Weighs as Much as the Real Sun?

[lvanb]

I'm writing an article in a plastic modeling magazine talking about scale weight. Plastic models come in many scales, i.e. 1/72 or 1/48, etc., so my article talks about what weight a model would be if it was also scaled properly for weight. For instance, a 2000 lb car, at 1/72 scale, would weigh 27.78 (real) lbs to be 1/72 it's real weight. So...here's a hypothetical question...say I built a model of the sun and the diameter of that model is 3 inches (typical size of a Christmas ornament or a small orange). That is approximately 1/18,266,404,199 scale. That would put the real weight of this "model", (1/18,266,404,199 of the sun's actual weight), at a jaw dropping 108,893,900,423,881,000,000 kg. Here are my questions:

1) Would something that small weighing so much collapse in on itself creating a black hole?

2) Let's say I have a magic box I am carrying this model around in (I'm a strong guy). Also, for the sake of argument let's say that this model doesn't collapse into itself and become a black hole, but stays a 3 inch diameter model (at this huge scale weight). Everything is fine until I take this model out of the box and set it on the display table at the next model club meeting. What would happen? I would think that the first thing is that the tidal forces would rip me and everyone else in the room apart, or instantly suck us all (in the room) into the 3 inch model, but how far out (in real distance) from the table would people be ripped apart or sucked into this model?

3) I would also assume that the model would (nearly) instantly start sinking through the crust and sink to the center of the earth. I would assume this would also cause massive quakes and destruction...any guesses as to how strong of quakes or what kinds of destruction? For sake of argument say I was located in Wyoming or Nevada (so not right on the west coast, but the Rocky Mountain region).

Thanks for any help on pointing me in the right direction on this.

 

[Janus]

Volume, and therefore mass would decrease by the "cube" of the scale, not directly by the scale. Thus your 1/72 scale car would weigh 1/373248 of 2000 lb or 3 1/3 oz. and a 1/18,266,404,199 scale Sun would weigh ~11.5 oz.

Another way to look at it is that the Sun's density is 1.41 g/cm³. A 3 in diameter sphere has a volume of 231.66 cc and would weigh 326.64 g = ~11.5 oz. ,

 

[lvanb]

Thanks, Janus. Constant density...makes perfect sense!

 

[DaveC426913]

For instance, a 2000 lb car, at 1/72 scale, would weigh 27.78 (real) lbs to be 1/72 it's real weight.

No.

A car that is 1/72 scale is, at once 1/72 shorter as well as 1/72 narrower as well as 1/72 thinner.

A 2000 lb car, scaled down to 1/72 would mass 1/(72)³ as much, or 0.005lbs. (~2.2 grams)


Your model sun would mass 1/(18,266,404,199)³ of the real sun.

That works out to 0.32kg.

Sanity check:
m_sun = 2x10³⁰kg
scale = 1.65x10^-31
= 3.2x10^-1.

Yup. ~300g.

Hm. My answer is more than an order of magnitude different from Janus'...

Still, less than 1kg.

 

[pmacias]

I find this hypothetical model of the Sun to be an interesting thought experiment. However, it is important to remember that this model is purely hypothetical and does not accurately reflect the actual properties of the Sun.

To address your questions, let's start with the first one. At a scale of 1/18,266,404,199, the model of the Sun would weigh an immense amount, as you have calculated. However, it is important to note that weight is a measurement of the force of gravity on an object, and at such a small size, the force of gravity would not be strong enough to cause the model to collapse into a black hole. In fact, the force of gravity would be so small that it would not even be noticeable.

Moving on to your second question, if you were to take this model out of the magic box and place it on a display table, the effects would be catastrophic. The model would have a mass equivalent to that of the actual Sun, but at a much smaller size. This would create an incredibly strong gravitational pull, causing the tidal forces you mentioned. Anyone in the room would likely be ripped apart or sucked into the model, as you suggested.

As for the third question, it is difficult to predict the exact effects of such a model sinking through the Earth's crust. However, it is safe to say that it would cause massive earthquakes and destruction, potentially on a global scale. The strength of these earthquakes would depend on the location and depth of the model's descent, as well as the surrounding geological conditions.

Overall, while this hypothetical model may be an interesting thought experiment, it does not accurately reflect the properties and behavior of the Sun. It is important to remember that scale models are simply representations and cannot be used to accurately predict real-world scenarios.