How To Fly

Due to the previous, more technical posts, I decided to write a less serious one this time. Douglas Adams, in his "Hitchikers Guide to the Galaxy" series, offers the following advise to those who aspire to fly.

"There is and art, it says, or, rather, a knack to flying.


The knack lies in learning how to throw yourself at the ground and miss.

Pick a nice day, it suggests, and try it.

The first part is easy.

All it requires is simply the ability to throw yourself forward with all your weight, and the willingness not to mind that it's going to hurt.

That is, it's going to hurt if you fail to miss the ground.

Most people fail to miss the ground, and if they are really trying properly, the likelihood is that they will fail to miss it fairly hard.

Clearly, it is this second part, the missing, which presents the difficulties.

One problem is that you have to miss the ground accidentally. It's no good deliberately intending to miss the ground because you won't. You have to have your attention suddenly distracted by something else when you're halfway there, so that you are no longer thinking about falling, or about the ground, or about how much it's going to hurt if you fail to miss it.

It is notoriously difficult to prize your attention away from these three things during the split second you have at your disposal. Hence most people's failure, and their eventual disillusionment with this exhilarating and spectacular sport.

If, however, you are lucky enough to have your attention momentarily distracted at the crucial moment by, say, a gorgeous pair of legs (tentacles, pseudopodia, according to phyllum and/or personal inclination) or a bomb going off in your vicinity, or by suddenly spotting an extremely rare species of beetle crawling along a nearby twig, then in your astonishment you will miss the ground completely and remain bobbing just a few inches above it in what might seem to be a slightly foolish manner.

This is a moment for superb and delicate concentration.

Bob and float, float and bob.

Ignore all considerations of your own weight and simply let yourself waft higher.

Do not listen to what anybody says to you at this point because they are unlikely to say anything helpful.

They are most likely to say something along the lines of "Good God, you can't possibly be flying!"

It is vitally important not to believe them or they will suddenly be right.

Waft higher and higher.

Try a few swoops, gentle ones at first, then drift above the treetops breathing regularly.

DO NOT WAVE AT ANYBODY.

When you have done this a few times you will find the moment of distraction rapidly becomes easier and easier to achieve.

You will then learn all sorts of things about how to control your flight, your speed, your maneuverability, and the trick usually lies in on not thinking too hard about whatever you do, but just allowing it to happen as if it were going to anyway.

You will also learn about how to land properly, which is something you will almost certainly screw up, and screw up badly, on your first attempt.

There are private flying clubs you can join which help you achieve the all-important moment of distraction. They hire people with surprising bodies or opinions to leap out from behind bushes and exhibit and/or explain them at the critical moments. Few genuine hitchhikers will be able to afford to join these clubs, but some may be able to get temporary employment at them."

Time dilation

    According to Euclid, we live in a 3-dimensional world, being able to pinpoint our position using three coordinates: x, y and z. Einstein saw this in a different light- 4 dimensions. According to his special theory of relativity "The four dimensional space-time continuum of the theory of relativity , in its most essential formal properties, shows a profound relationship to the Euclidian geometrical space. In order to give due prominence to this relationship, we must replace the usual time coordinate t by an imaginary magnitude by (√-1)* ct proportional to it." Just as space is fluctuary, time changes as well.
    One feature that distinguishes time from space in how it is changed, is that motion changes time relatively. To illustrate that, imagine that an observer, person A, is on a stationary platform, and I have another person, person B, also on that platform, sitting in a spaceship. They are both experiencing, at that moment the same rate of time. Now the spaceship launches and it is accelerating. If he is traveling at 0.5c (half the speed of light) What feels like one day to person B, is 1.15 relative days for person A. As he gets closer to the speed of light, 0.99c, one day for person B is over a week back at the platform. Time goes up rapidly from there. at0.99999999999999c, for one day for person B, person A is long dead having almost 2000 years pass on his platform.
     This data is all based upon the Lorentz factor, which is represented by the equation below, with:
t = time
v = velocity
c = constant, the speed of light

 Rest Frame Time Elapsed per Day on Ship        
v/c                           Days        Years
0.0                           1.00         0.003  
0.1                           1.01         0.003  
0.2                           1.02         0.003  
0.3                           1.05         0.003  
0.4                           1.09         0.003  
0.5                           1.15         0.003  
0.6                           1.25         0.003  
0.7                           1.40         0.004  
0.8                           1.67         0.005  
0.9                           2.29         0.006  
0.95                          3.20         0.009  
0.97                          4.11         0.011  
0.99                          7.09         0.019  
0.995                        10.01         0.027  
0.999                        22.37         0.061  
0.9999                       70.71         0.194  
0.99999                     223.61         0.613  
0.999999                    707.11         1.937  
0.9999999                  2236.07         6.126  
0.99999999                 7071.07        19.373 
0.999999999               22360.68        61.262 
0.9999999999              70710.68       193.728
0.99999999999            223606.79       612.621
0.999999999999           707114.60      1937.300       
0.9999999999999         2235720.41      6125.261       
0.99999999999999        7073895.38     19380.535      
0.999999999999999      22369621.33     61286.634      
Sincerely,
Space Cadet



High-Quality Photograph of a Black Hole



Black holes are an well-known effect that is consistent with Einstein's theory. Black holes are an extremely dense region of space where even light cannot escape. The premise of this phenomena is that a massive object bends space-time. If that massive object was extremely dense, it would ultimately bend space-time so that the walls of the dent are vertical. If a light beam is traveling and encounters the black hole, it will be bent at a consistently increasing angle so that it loops back upon itself and continues circling. It is now trapped. Objects of mass can be caught in the same way. When they spiral to the center they will be crushed to extreme density.





Swartzschild Radius
Formula

A black hole is formes when a star collapses to a diameter equivelant to or past its Swartzschild Radius. The Swartzschild radius is a ratio of a spherical object's mass to its radius. The formula(left): Rs is the Radius, G is Gravitational Constant, m is the mass of the object , and c  is the speed of light in a vaccum. To put this in proportion,  if the earth were to become a black hole, the mass would have to be contained within a 9 millimeter radius. However most black holes are not quite as small. The chart below shows a few examples of their massive size:

sincerely,

Space Cadet

Gravitational lensing



Einstein's Cross- example of lensing.

 Einstein's Relativity theory allows for certain effects that would not be possible according to the Newtonian theory. Because Gravity does not involve a force, massless objects can be affected. A straight beam of light, passing by a dent in space-time caused by a object of mass, will be bent to follow that geodesic path. The implication of this is a phenomena called gravitational lensing.

The main idea of Gravitational Lensing is if a massive object is in front of a star, or other bright object, the rays from the star will be bent around the massive object, appearing to the observer to be two or more distinct objects.

This is far from being just an interesting effect. Using geometry, one can derive the approximate distance of the object. Also Astronomers are using gravitational lensing to predict the placement and size of pockets of dark matter, as it also bends light.
Sincerely,
Space Cadet

Newton and Einstein- Gravity

     In 1916, Einstein published his theory of General Relativity, radically changing the way we view gravity. Over 200 years earlier, Newton published his "law of universal gravitation" in Principia Mathematica. Newton's view of gravity held that gravity was a force. This force is the attraction of mass to mass, the larger mass having a stronger pull on the smaller mass, and the smaller mass pulled upon the larger with less force. To this day Newton's gravitational equation is used to approximate a given object's weight upon a given planet.

 However, Einstein saw gravity in a different light. He supposed that mass could bend the fabric of space-time, much like a bowling ball on a trampoline. A smaller mass, like a planet, would simply follow the geodesic curve in an acceleration percieved as a force.

Since 1916, Einstein's theory has been shown to be accurate over the years, as certain  points are proven, such as the GP-B probe and the proof that gravity acts at the speed of light. His theory also covers other important points (such as Gravitational lensing) to be mentioned in a later post.

Sincerely,

Space Cadet

Gravity Probe B - Testing Einstein's Theories

Gravity Probe B has tested- and proven,  two effects of the general relativity theory developed by Albert Einstein developed in 1916. Orbiting around the earth, the spacecraft has the perfect opportunity to measure this, as the earth itself is a large enough mass to warp space-time noticably. The sensitive gyroscopic sensors were able to prove:
"1.The geodetic effect—the amount by which the Earth warps the local spacetime in which it resides.


2.The frame-dragging effect—the amount by which the rotating Earth drags its local spacetime around with it."(GP-B Mission)
The Geodetic effect is an essential component of the General Relativity theory, as it rests upon the tenet that mass can warp space-time. This allows for the existence of black holes, quasars, and other space phenomena.
The frame dragging effect had never been tested before. It can be visualized as a ball spinning in a bowl of a thick liquid such as syrup. As it spins it drags the syrup in a spiral around it.
In theory testing relativity is a simple concept. According to GP-B Mission;
 
"1.Place a gyroscope and a telescope in a polar-orbiting satellite, 642 km (400 mi) above the Earth. (GP-B actually uses four gyroscopes for redundancy.)


2.At the start of the experiment, align both the telescope and the spin axis of each gyroscope with a distant reference point—a guide star.

3.Keep the telescope aligned with the guide star for a year, as the spacecraft makes over 5,000 orbits around the Earth, and measure the change in the spin-axis alignment of each gyro over this period in both the plane of the orbit (the geodetic precession) and orthogonally in the plane of the Earth's rotation (frame-dragging precession).

The predicted geodetic gyro-spin-axis precession is a tiny angle of 6,606 milliarcseconds (0.0018 degrees) in the orbital plane of the spacecraft. The orthogonal frame-dragging precession is a minuscule angle of 39 milliarcseconds (1.1x10-5 degrees). "
Links:
Official Site
NASA GP-B Mission
Paper model of the Spacecraft

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Sincerely, Space Cadet

50th Anniversary of Human Space Flight

     The 12th of April marked the 50th anniversary of human spaceflight. On that day in 1961 Yuri Gagarin, a soviet Military Pilot, became the first human to orbit the earth. This event had a lot of political implications, as it seemed the Russians would beat the Americans in the dominance of space. Previously the Russians had already put the first satellite, sputnik 1, and the first animal, a dog named Laika (literally translated means "Barker") . All of these victories to the Russians. were a major blow to the Americans and their pride. The Americans caught up soon, and ultimately won the race to dominate space in 1969 as Neil Armstrong stepped upon the moon.
Sincerely, Space Cadet