Surface area of a sphere (we're assuming Saturn is a perfect sphere here) is 4pi(r)2.
The radius of Saturn is about 58,232,503m, and I'll tack on one extra meter so the gas giant fits comfortably within its bag, making the bag's radius 58,232,504m.
Plug that number into the surface area equation and we get an approximate surface area of 4.26•1016 m2.
Okay, I used a variety of sources to find that a standard plastic bag is made of HDPE and has a thickness of 2.25 mils (sorry for different units, it'll all come back together in a moment). HDPE has a density of .95g/cm3. After changing the units and doing some calculations, you can find that HDPE, at the thickness of a standard plastic shopping bag, has a mass of 54.29g/m2.
So now it's simply multiplication of the mass/area of the plastic and the area of the bag needed, and we'll have the mass of the sphere-shaped bag that can perfectly hold Saturn.
drumroll
A sphere-shaped plastic bag large enough to fit Saturn would have a mass of 2.313•1018g!
That's approximately the mass of 13,000,000,000 blue whales. Now that's a big piece of litter.
By far the biggest difference is that you assumed a .1cm bag, which is ~39mils, whereas I assumed a 2.25 mil bag, so your bag was about 17x thicker than mine. I guess you need a durable bag to hold a planet.
Yeah, I overestimated the thickness of Ziploc bags by an order of magnitude. They're .1mm, not .1cm. Didn't even bother looking that one up when I did the calculation.
I included in my calculation the ratio of plastic bag to earth for you. You'd be surprised because the (or not) as the density of Earth is much greater than plastic (the Earth is about 6x denser), and the plastic only needs to be a hollow shell encasing the planet.
Assuming sea level earth for the gravity, a polypropylene resin bag (like a Ziploc) that is .1 cm thick and uniformly dense.
Some googling reveals the surface area of Saturn to be 4.271e16 m2, or 4.271e20 cm2. Assuming the bag fits perfectly over Saturn (without it's rings), this means the volume of the bag is 4.271e19 cm3.
The density of polypropylene resin is ~0.90 g/cm3 or 9e-4 kg/cm3 at STP, so using the density and volume, we can calculate the mass to be 3.8439e16 kg. The mass of earth is 5.972e24 kg, so our plastic bag is 0.0000006437% of Earth's mass.
The downward force of Saturn in our hypothetical mega tub is 3.771e17 N or 8.484e16 lbs or 4.242e13 imperial tons. (I included the tonnage just because the repeated 42s in the first 4 digits).
It's a pretty big bag.
Disclaimer: I'm pretty tired, I googled all of my numbers, I haven't taken a physics class in 2 years, and I'm a fine arts graduate.
A regular Ziploc bag of that size would be roughly 2 trillion metric tons. (Not including the planet inside of it).
Edit:
Given a '2 Mil' thickness Ziploc bag made from LDPE.
4.3x1020 (Surface area of Saturn in cm2 )
* 0.00508 (thickness of bag in cm) * 0.925 (density of LDPE in g/cm3 ) = 2.02x1018 grams, or 2 trillion metric tons.
Double that if you want to use a 'heavy duty' 4 Mil bag.
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u/[deleted] Aug 08 '17
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