Showing posts with label maths. Show all posts
Showing posts with label maths. Show all posts

Wednesday, March 11, 2020

Probing in Dark Places

I've been bouncing around the Internet Spaceship galaxy again ...
That's a black hole ... and the galaxy. More of that later ...

In real life stuff, things are getting a bit more scary no ? If you are worried about what's going on, you're in a good place. It's ok. I'm right there with you on it. I think the situation will develop further as time goes on, then it'll hit a plateau and start reducing again. But in the meantime, keep being wary of it, take your precautions, don't be silly about it and I hope you and your people will come through this ok. I suspect that Comic Con Birmingham will disappear, that one is 9 days from now. I reckon London Comic Con at the end of May is probably 50:50 at the moment. I think the Lords day will still happen ... but that's an event held at a wide open stadium, not something in a closed in exhibition centre.

I had a mission accomplished last night from the shopping trip. I was out of Mini Eggs so had to indulge the panic of running out to get more. Also acquired loo roll because that was a due purchase. Looks like the locusts had hoovered up most of the loo roll but they'd rolled out a fresh pallet of the stuff ... sorted. The thing of 4 will keep me going for a bit. I was feeling as if I was being judged for having my loo roll in the trolley though.

May also have acquired more popcorn and a big Toblerone.

Internet spaceships ? As the thumbnail (and the title!) suggests, I've been getting braver with the black holes ...
That one was rather pretty. The game lets you get pretty close to them and I got curious enough to do a little research on what we're seeing there.

You'll probably already know about the Event Horizon, the point at which even light cannot escape. This is also known as the Schwarzchild radius for non rotating, uncharged black holes (simple ones). If you were to pack our Sun into a size smaller than its Schwarzchild radius (I'm just gonna call this the S Radius), it would become a black hole. Our Sun's S Radius is 2.95km. That's not very big ... (The radius of our Sun averages as 696,000 km).

The stars you see in the picture that look like an eyeball globe is the Photon Sphere. This is at 1.5x the S Radius. The game lets you approach to maybe double that. It doesn't let you get any closer than that and depending on the size of the hole, the ship starts getting hotter. The small black holes are the best because you can orbit them quicker.
This one was stunning. The orangey/yellow type thing in the background is actually the straightness of the Milky Way ribbon bent around the black hole by the gravitational lensing. You can also see the lensing within the photon sphere. At some point, I'll do a video because the screenshots don't do justice to how the lensing folds and unfolds as you approach and ...
Retreat.

I'm curious about the gravity though, so if you don't mind I'm gonna think aloud through the numbers for a minute ... The Gravity equations is :
Force = Gravitational Constant * Mass of Object 1 * Mass of Object 2
Radius ^2
The Gravitational Constant is known : 6.674 * 10 ^ -11.
Mass of Object 1 will be our black hole. For our Sun, that's 1.9884 * 10 ^ 30 kg.
And we can ignore Mass of Object 2 because :
Force = Mass x Acceleration.
To calculate the Acceleration, we divide Force by Mass, which means Mass Of Object 2 cancels out.

So big number time : Acceleration per solar mass = 13.27 * 10 ^ 19 / Radius in m squared. (1.327 * 10 ^ 20)

That makes the acceleration at the Schwarzchild Radius of a 1 Solar Mass object =
1.327 * 10 ^ 20 / (3 * 10 ^ 3) * (3 * 10 ^ 3)
By the way, you can cheat with the powers of 10. Multiplying them adds, dividing subtracts, so that works out to 1.47 * 10 ^ 13 m/s/s. Or about 1,500,000,000,000g. 1 g = about 10m/s/s (actually 9.81 but that needs a calculator and I'm lazy!)

Going out to 10km reduces that to 1.327 * 10 ^ 12 or 132,700,000,000g.
25km makes that 2.12 * 10 ^ 11 m/s/s or 21,200,000,000g.
1000km is 1.327 * 10 ^ 8 or 13,270,000g.
696,000km or the current surface of the Sun is 2.74 * 10 ^ 2 or 27.9g. Phew - wiki agrees.

I do hope this math is right. Either way, you'd want pretty strong engines or Space Magic to keep you out of the black holes at that range.
That's a considerably bigger black hole ... and my 4th trip to Sagittarius A* at the centre of the galaxy. Sagittarius A* is estimated to be 4 million Solar masses and its Schwarzchild Radius is 1.187 * 10 ^ 10 m (11.87 billion km). It's chunky.

I think that's enough math for one day.
I found this place while on the travels, attempted to join the dots. Need brighter ship lights.
If a star isn't big enough to collapse into a black hole (our Sun is not, the threshold is about 2.17 stellar masses according to Wiki) after exploding, then it may crush down into degenerate subatomic particles. As these squish together, a neutron star may form ... or pulsar. In the game, these have streamers running off of varying levels of violence. The one above was pretty gentle and the idea is to run the streamer just long enough to super charge the jump drive so you can bounce huge distances between stars. For my current ship, that takes the range from 65 light years up to 261. Neat for crossing vast distances quickly.

And they look rather pretty too.
I found some planets along the way too, here's a water world. These seem to be generated a fair amount by the game.
That one is an Ammonia world.
Another black hole, this time with a star behind it ... or maybe in front. Or behind me and the lensing has turned it all the way around. This one was from today and it's the GRS 1737-31 black hole, coming in at 48.2 solar masses giving a S Radius of 142km. The game let me approach to 185km, which was closer than I predicted, that Photon Sphere should have been at 213km.

But ... alas, my hand was starting to complain at too much probing of the dark holes so I called it a night not long after visiting GRS 1737-31. I found a curious canyon system :
And a good place to settle in.

Nite all. Apologies for me letting the geek out in the middle there :-D. Wait. Sorry not sorry ! :-D

Wednesday, June 22, 2011

Daft advert claims - debunk time !

Just caught an ad for energy saving tyres that promised to save 80 litres of fuel over the life of the car.

Sounds ok - What's that mean exactly though ?

My Focus does between 28 and 36 miles to the Imperial Gallon. Call it 32. That's 7 miles per litre. (7.04 - close enough). So over the life of the tyre, which I'd expect to be 20,000 miles on the fronts, that's an extra 560 miles.

The 20,000 miles should take 2857 litres of fuel, with the oh-so-green energy saving tyres it'll take 2777. Petrol here costs about 133.9p/litre, so those 80 litres saved works out to about £107. I'll do those 20,000 miles over just under 3 year so that's a saving of £36 per year.

That's kinda - meh. And it's even worse with the rear tyres as they did 40,000 miles.

Mind you, I paid £80 per corner on my last set of tyres, so that £107 saved actually means Free Tyres ! Probably at the cost of having less grip around corners though, like my current pair of Famous Brand (not saying who - ads = bad) tyres on the back of the Focus.

With the next car it's better, because it's expected to do double the economy. 68mpg instead of 32. Not looked at the Next Car yet, although it's just the other side of Bristol. Friday pm is looking like a good opportunity to go peek, plus I'm having a sense of looking to out cagey the apparently cagey garages. I'm feeling a bit like Truck Roadkill at the moment, so I'm shepherding my energy carefully at the mo with just crashing out in the evenings. Gaming is really suffering to the point where it goes several days between putting the pooter in Game Mode.

Saying that though, Otis Cookies from the canteen were Awesome earlier. It even resulted in one of those Crazy Just Bounced Off Wall Emails to the long-suffering Mrs Sunshine.

I guess the lesson which I just distracted myself from is : Don't trust adverts. When they make a claim that sounds believable, see if you can work out what it actually means and from there, whether the claim is actually relevant to you.