If you like to calculate, it can help you learn cosmo basics. Partly just by making it fun. Partly because it gives a hands-on dimension to what you are learning. If you don't find calculating basic cosmo numbers fun, then this thread is not for you. There are other less number-crunchy approaches to understanding.(adsbygoogle = window.adsbygoogle || []).push({});

Google calculator changes the circumstances somewhat. You type something in the window and press return (or "search") and it evaluates it. It knows constants like G, hbar, k, pi. It knows units like lightyear and parsec and nanopascal. So it makes it easy. You don't have to look up constants and convert units and so on.

So suppose you want to try this out with a few basic cosmo quantities. Let's say you know that the present value of H is 71 km/s per megaparsec, and that the total energy density is very close to the critical density needed for spatial flatness, and that dark energy is estimated about 73 percent of total. Essentially you know two numbers 71 and 0.73. What can you calculate from that?

Hubble radius (in lightyears)

The Hubble radius is the distance at which objects at rest wrt background are receding at speed c. If an object's present distance from us is twice that radius, then it is receding from us at 2c. So put this into google:

"c/(71 km/s per megaparsec) in lightyears"

You get out:

c / (71 ((km / s) per megaParsec)) = 1.37720275 × 10^{10}lightyears

So 13.77 billion lightyears.

Total energy density (in nanopascal)

One joule per cubic meter is a metric unit of energy density called the Pascal. It is equivalent to one Newton per square meter, the corresponding unit of pressure. To find the energy density of the universe, in nanojoules per cubic meter, put this in:

"3 c^2 (71 km/s per megaparsec)^2/(8 pi G) in nanopascal"

You get out:

(3 * (c^2) * ((71 ((km / s) per megaParsec))^2)) / ((8 * pi) * G) = 0.85... nanopascals

We've used the critical density as an estimate of the real density, because of near flatness.

Dark energy density (in nanopascal)

Just take 73 percent of the above, put this in:

"0.73*3 c^2 (71 km/s per megaparsec)^2/(8 pi G) in nanopascal"

You get out 0.62... nanopascal.

So that's how much dark energy there is. 0.62 nanojoules per cubic meter, or if it seems easier to imagine, 0.62 joules per cubic kilometer. I like the latter. It is easy to imagine a joule of energy---raise a book a few centimeters up off the table, drop it, the satisfying thump is a joule of energy. About that much in a cubic kilometer.

If you are new and want to know where the formula for critical density comes from, that's good. This approach is meant to motivate you to find the underlying equations involved in a calculation. Just googleFriedmann equations. You can read what critical density is from one of the two equations discussed there. Flat meansk=0, so put it equal zero and solve for the density rho.

I'll get some other examples.

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# Google calculator impact on basic cosmo explanations

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