I will still be answering questions as I receive them, however, I have been asked to add something additional. As we move forward I will be adding resources for science learning in the online environment. These will not, for the most part be sites for taking classes but rather sites for learning aids or for fun science learning.
The first request was for mathematics resources, so here are some of my favorites...
Math Warehouse
This is an interactive site for students, teachers and just about anyone who needs to brush up on math concepts. The site is easy to navigate by math type or searching.
Math is Fun
Another site that covers a wide range of math topics from geometry and algebra. Each topic has a ton of images, great definitions and activities to reinforce the information. The site is easy to understand and breaks all the topics down to easy to understand and manage topics.
Math.com
This is a self tutoring site for Kindergarten to Calculus and some other advanced topics in math. The site includes things like study tips and test prep guides as well as practice problems. It is a great all around source for learning new or brushing up on older math knowledge.
Cool Math Games
Learn basic math concepts with some fun flash games.
Numberphile
A great youtube channel that tackles complicated and interesting math topics through series of weekly videos. Also the Numberphile 2 Channel which covers many of the topics more in-depth than the main channel.
TecMath
A youtube channel that shows tricks and tips for doing math and remembering mathematical information.
Mathantics
Youtube channel to review or learn various math principles.
3Blue1Brown
Ever wanted to learn math as entertainment? Then this is the youtube channel for you. Sadly it has been almost a month since they uploaded their last video.
Mathologer
A really fun math channel that explore theories and properties with visual demonstrations.
ViHart
A really fun channel that explores math concepts with humor and a free form style that one might imagine a journal being written in. Bonus for the riotously funny sketches and images that go with it. (And it covers some other topics too.)
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Wednesday, September 16, 2015
Sunday, May 26, 2013
Question #4 Why is there so much space between things in the universe?
From Zach on Facebook.
This question is directly related to the Metric Expansion of Space or the increase of distance between objects and particles in space. To really get a grip on this topic lets go all the way back to the Big Bang then work forward.
At the moment just prior to the Big Bang all the matter and energy of the universe was in a single point. Technically it had not volume it was crushed in so tiny. At the moment of the Big Bang all of this energy and matter flew out of this volumeless point at speeds at (or some speculate even faster than ) the speed of light. Now all this matter is flying away from this point and starting to spiral and form early gas clouds and accretion disks and so forth. However, even these larger items that are forming are still being acted upon by the energy that came out of the Big Bang so they are being shoved away on all directions at the speed of light.
Gravity can hold these moving objects together. For example, every star in the Milky Way galaxy is being acted on by this initial Big Bang force, however, the gravity between all those stars keep them moving as a group. Think of it as a bunch of people swimming in the ocean. If a huge wave comes in they'll be pushed around in different directions and away from each other. If those swimmers are holding hands (the hand holding is gravity) then they will be moved as a unit by that big wave.
The Universe is 13.7 billion years old +/-. For these 13+ billion years everything has been moving at the speed of light or near the speed of light at least.
The speed of light is 299,792,458 m/s. Let's convert this term to meters per year (m/yr) so that we can compare it to our 13.7 billion years.
After we cross out all of our units we are left with the following calculation which will give us meters per year.
299,792,458*60*60*24*365= 9.454255 * 10^15 or written out it would look like this....
9,454,255,000,000,000 m/yr.
If you are not comfortable with meters that would be 5,874,601,701,065.775391 mi/yr.
That's a lot of distance to cover in a year. To put it in perspective it is 10 million times the distance from the sun to Saturn. This should start getting to the reason why things in the universe are so far apart.
While doing these calculations why don't we look at how far a particle, say a hydrogen atom, may have moved from the Big Bang if it were present at the exact moment of the bang and traveling away the entire time.
5,874,601,701,065.775391 mi/yr * 13.7 billion years. = 80,482,043,000,000,000,000,000 miles
or... 13,690,622,873.69648 light years.
How do we know this calculation makes sense?
We know that our hydrogen atom was traveling at the speed of light (i.e. one light year per year) for 13.7 Billion years. Our answer for how far it traveles is 13.7 billion light years (if we round.)
So what does this all mean? That means that 13.7 light years is the farthest distance two objects can be from each other. i.e. one object on one end of the universe to another object on the exact opposite side of the universe. Any distance smaller than this is a possible distance between two objects somewhere in space.
Let's take this back to something more concrete. This Hubble article and video explains it without all the math.
This NOVA article covers it as well.
An awesome Visible Universe poster from National Geographic. The timeline at the top may be very helpful.
This question is directly related to the Metric Expansion of Space or the increase of distance between objects and particles in space. To really get a grip on this topic lets go all the way back to the Big Bang then work forward.
 |
| The Metric Expansion of Space from Astronomy Magazine and NASA: http://cs.astronomy.com/ |
At the moment just prior to the Big Bang all the matter and energy of the universe was in a single point. Technically it had not volume it was crushed in so tiny. At the moment of the Big Bang all of this energy and matter flew out of this volumeless point at speeds at (or some speculate even faster than ) the speed of light. Now all this matter is flying away from this point and starting to spiral and form early gas clouds and accretion disks and so forth. However, even these larger items that are forming are still being acted upon by the energy that came out of the Big Bang so they are being shoved away on all directions at the speed of light.
Gravity can hold these moving objects together. For example, every star in the Milky Way galaxy is being acted on by this initial Big Bang force, however, the gravity between all those stars keep them moving as a group. Think of it as a bunch of people swimming in the ocean. If a huge wave comes in they'll be pushed around in different directions and away from each other. If those swimmers are holding hands (the hand holding is gravity) then they will be moved as a unit by that big wave.
The Universe is 13.7 billion years old +/-. For these 13+ billion years everything has been moving at the speed of light or near the speed of light at least.
The speed of light is 299,792,458 m/s. Let's convert this term to meters per year (m/yr) so that we can compare it to our 13.7 billion years.
299,792,458*60*60*24*365= 9.454255 * 10^15 or written out it would look like this....
9,454,255,000,000,000 m/yr.
If you are not comfortable with meters that would be 5,874,601,701,065.775391 mi/yr.
That's a lot of distance to cover in a year. To put it in perspective it is 10 million times the distance from the sun to Saturn. This should start getting to the reason why things in the universe are so far apart.
While doing these calculations why don't we look at how far a particle, say a hydrogen atom, may have moved from the Big Bang if it were present at the exact moment of the bang and traveling away the entire time.
5,874,601,701,065.775391 mi/yr * 13.7 billion years. = 80,482,043,000,000,000,000,000 miles
or... 13,690,622,873.69648 light years.
How do we know this calculation makes sense?
We know that our hydrogen atom was traveling at the speed of light (i.e. one light year per year) for 13.7 Billion years. Our answer for how far it traveles is 13.7 billion light years (if we round.)
So what does this all mean? That means that 13.7 light years is the farthest distance two objects can be from each other. i.e. one object on one end of the universe to another object on the exact opposite side of the universe. Any distance smaller than this is a possible distance between two objects somewhere in space.
Let's take this back to something more concrete. This Hubble article and video explains it without all the math.
This NOVA article covers it as well.
An awesome Visible Universe poster from National Geographic. The timeline at the top may be very helpful.
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