Why do things fall?
Because they gain weight as they move down.
If, for instance, they are in orbit and weightless they do not fall.
Don’t orbiting space-craft fall around the Earth?
No, if they were to fall they would gain weight.
The reason that objects in orbit curve is that they curve with the gravitational field.
Essentially, if they are in a circular orbit then they stay at exactly the same distance from the centre of the gravitational field.
Elliptical orbits are a bit more complicated in that for part of the orbit the object does fall and gain weight, but this increases its velocity which eventually causes it to move further away again and lose weight which slows it down until it starts to fall again, etc.
The question is : What is the connection between weight and mass?
I used to think that the mass of an object could change until FTSE pointed out that it was unlikely. I’m starting to think FTSE was absolutely right.
Perhaps we keep confusing mass and weight because we don’t really understand what weight is!
If you think about it, it doesn’t really make any sense to try and imagine a Universe without mass, because so many things depend on mass.
How could gravity create a Universe without mass?
Yet, a Universe without weight would be an altogether simpler concept so perhaps the Higgs is a weighty bosun.
Comments
Mangone | January 9, 2011 - 05:12
The common usage of the term ‘weight’ is something like “the downward force exerted by a body as a result of gravity” and it is usually taken to be directly proportional to the body's mass.
I think that ‘weight’ should actually be the instantaneous downward force exerted by a body… this would still give the normal weights that we are used to if we, say, stand on a weighing scale if we take the measurement once it had settled. The point being that if you jump onto a weighing scale the reading is much higher at first.
If you now consider the new measurement of weight it would be equal to total downward force of the body at any instant. So if we drop a ball from a particular height its weight would increase until it hit the ground and then actually become negative as it bounced.
For, say, an aircraft, it would have to be relative weight in that the body of the aircraft could be considered to have little or no weight due to the lift of its wings but the people in it would have essentially their normal weight supported by the floor of the plane.
The use of instantaneous weight would clearly reveal that falling is simply gaining weight by moving toward the centre of the local gravitational field.
What really interests me is, in a vacuum, how long would a super ball continue to bounce?
Perhaps, theoretically, a ‘perfect ball’ would continue bouncing forever but, in practice would a large ball bounce as long as a small ball if they were both otherwise identical?
The reason I see this as important is simply because it would reveal how important the geometry of size is when it comes to curving surfaces - ie.. assuming that the surface the balls are bouncing off is flat how much difference does the size of the sphere (its relative curvature) make to the reflection (bounce)?
Mangone | January 10, 2011 - 17:20
Further thought inclines me toward keeping the common usage of weight and calling the instantaneous weight ‘Effective Weight”…
both of course are proportional to the mass of the body.
So now we need a ratio that will give us the strength of the gravitational field at the point in space where the body lies and for this the mass/weight ratio should suffice as I posit that mass remains constant.
I suggest that since it is abitary a value of 1 should give a gravitational acceleration of 10 meters per second per second.
Since we don't need space to curve for our planets to orbit what do we need? Just a balance between gravity and inertia with gravity preventing the planet from moving out and inertia preventing it from moving in.
So how would a body get into orbit?
The further a body falls toward its ‘sun’ the faster it moves and the greater its weight.
Its effective weight increases both because it is nearer the centre of gravity and because of its momentum and there is a very small chance that the body will be moving almost straight down and will dive into the sun.
However, usually it will have enough of a horizontal vector to cause it to tend to curve its trajectory because the gravitational field is curved and obviously the closer the body approaches to its sun the steeper the curve becomes - simply because the radius of the gravitational field is shrinking.
At some stage the velocity of the body perpendicular to its sun will be enough to start slowing its decent and its effective weight will begin to reduce and it will begin its dance with inertia.
Once it has settled into an orbit then essentially it can’t move too far away from the sun because it lacks the energy to break free of its gravitational bond but it can’t fall too far because when it falls it increases its orbital velocity which moves it father away from the sun again.
In many ways it is like a weight being swung in circles by an elastic band - to move further out it must move faster - so if its speed is constant so is the length of the elastic band - but if its speed constantly varies then it starts to be effected by the continuously changing relationship between its inertia and its effective weight and it takes on an elliptical orbit.
Of course with an elastic band swinging the weight faster to extend its orbit also increases the pull on the elastic where as with gravity the pull weakens with distance and so in practice planets actually travel slower the further their orbit is from the sun but still require the extra energy to move them out against gravity.
I still can’t decide how much difference the size ratio between the planet and its sun makes - but it could be far more important to orbits than mass.
If you think about it the curvature of the Earth is not particularly noticeable to us and you can understand why people might have once believed it to be flat...
My point being that things which are relatively small might notice far less curvature than things which are relatively large and so the smaller might find it easier to orbit nearer the sun.
Mangone | January 11, 2011 - 05:40
Here are more ramblings :O)
The nutshell of orbits is gravity’s ability to apply a constant ‘downward’ force.
In Newtonian physics this force constantly attempts to tip the direction of a body downward but since an orbit circles the gravitational centre then, in effect, it cancels itself out over a complete orbit.
The effective weight is simply an indication of the orbiting body’s vertical vector… in other words the strength of its inclination to move up or down.
The only other really important factor is ‘attitude’ which is the resultant vector of the orbital velocity with the effective weight and the bodies inertia - or in simple terms the ‘tipping factor‘.
Imagine that the Earth was flat and an object is fired horizontally from an enormous gun.
If there was no atmosphere the projectile would eventually hit the Earth with the distance travelled depending on the ratio of the object’s forward velocity in relation to the force of gravity on it.
Obviously the faster the object was moving the further it would get before it hit the ground.
Now, all you need to do is to realise that since the Earth isn’t flat then to get the object to orbit all you need to do is get the object to move fast enough that it ‘falls’ almost precisely the same amount as the ground retreats from it… in its curve. Since the object never gets any nearer to the centre of gravity it cannot be said to be truly falling - unless you want to call it falling sideways :O)
So we can see that for a simple, circular orbit the ‘planet’ has a constant ‘attitude’ (and altitude) and so it is the most efficient path around the ‘sun’.
With an elliptical orbit the planet’s ‘attitude’ varies causing its distance to the sun to vary.
As always the ‘attitude’ depends on the ratio of forward force to the downward force and the bodies inertia and so if the effective weight becomes positive and the object starts to fall so its velocity increases too but the object’s inertia resists the change and so the ‘dance’ of inertia, orbital velocity and effective weight continuously influence the ‘attitude’ of the body and hence its orbit.
Mangone | February 13, 2011 - 04:35
Summing up: it is simply the mistaken idea, that even NASA seems to promote, that if things don’t fall then they are in zero gravity or a gravity free environment that causes the confusion about orbiting bodies.
Gravity is a force and what NASA terms ‘zero gravity’ really means a ‘weightless environment’ as the force of gravity is still there but it is either balanced by an equal but opposite force or the objects which appear weightless are all accelerating together at the same speed and hence seem ‘weightless’ to each other.
As Einstein pointed out it is probably impossible to tell the difference between the force of gravity and any other force that causes a constant acceleration.
Hence a man in a spaceship accelerating at approximately 10 meters per second per second might be forgiven for thinking he was falling to Earth due to gravity… but of course not for long.
The difference would be noticeable after a time as the force of gravity increases with the decrease of the square of the distance between the falling body and that to which it is falling…
In other words the acceleration is not constant and would increase if the spaceship was indeed falling.
So it is with the planes that ‘dive’ to Earth to produce ‘zero gravity’ they are simply using enough power to overcome air-resistance so that they might match the acceleration due to gravity.
It’s worth remembering that although all mass is accelerated at the same speed in a vacuum in the presence of an atmosphere things fall at different speeds depending on their density and shape.