greywolf42 wrote in message news:...
greywolf42 wrote in message news:...

In a parallel thread (Georges Louis Le Sage -Pushing Gravity), Steve
stated:

If you want to show me where my back-of-the-envelope calculation is
drastically wrong, I'd be glad to listen.

{snip}

Steve has not properly modelled the aberrational relationships for bodies
of differing mass. In fact, he hasn't actually modelled anything. His
starting point is nothing more than three handwaving assumptions about the
acceleration (force) that he presumes will result from a LeSagian system:
"1. It can't depend explicitly on properties of the Sun."
"2. It must be proportional to Jupiter's mass m_J."
(later changed to "independent of mass m_J")
"3. It must be proportional to v_J/c."

If Steve had simply sat down and actually modelled a general gravitational
system, between masses m and M, orbiting their common center of mass, he
would have found that all three of his (original) assumptions were
incorrect to varying degrees.

A basic geometrical evaluation of the effect of the delay due to
propagation shows that there are several competing effects in the
aberrative
forces:

1. The total gravitational 'force' is offset from a line through the
center of mass by the angle 'alpha'. This may be broken down into a
'central' force and a tangential 'aberrative' force.

2. The distance travelled by the gravitating force from the 'source' to
the 'target' body is shorter than the orbital diameter. This results in
an increased inward force that tends to counteract the offset.

If you actually perform the analysis (including the orbits about the
common center of mass), I believe you will find that the general
aberrative angle is given (where m = M by convention) by:

alpha = sqrt[2 - delta(1+m/M) + ((m/M)^2 -1)/(delta(1+m/M))]

where delta is the distance reduction factor (mentioned in #2, above):
delta = 1 / sqrt[1 + m/M (v/v_g)^2]

For the case m = M, this reduces to the 'popular' and simpler aberration
equation:

alpha = v / v_g

However, for cases where m M, the aberration angle is further reduced by
roughly the ratio of the masses of the bodies. (This results
straightforwardly from the reduced moment arm affecting the more massive
body.) In the case of Jupiter, your numbers are off by a factor of
roughly m_J / m_S.

No response in a week (not counting Wormley's and DVM's null responses).
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S) than
commonly claimed (as by Steve)? Or does somebody have a different result
from the general solution of orbiting bodies of different mass?

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

"greywolf42" wrote in message ...
greywolf42 wrote in message news:...
greywolf42 wrote in message news:...

In a parallel thread (Georges Louis Le Sage -Pushing Gravity), Steve
stated:

If you want to show me where my back-of-the-envelope calculation is
drastically wrong, I'd be glad to listen.

{snip}

Steve has not properly modelled the aberrational relationships for bodies
of differing mass. In fact, he hasn't actually modelled anything. His
starting point is nothing more than three handwaving assumptions about the
acceleration (force) that he presumes will result from a LeSagian system:
"1. It can't depend explicitly on properties of the Sun."
"2. It must be proportional to Jupiter's mass m_J."
(later changed to "independent of mass m_J")
"3. It must be proportional to v_J/c."

If Steve had simply sat down and actually modelled a general gravitational
system, between masses m and M, orbiting their common center of mass, he
would have found that all three of his (original) assumptions were
incorrect to varying degrees.

A basic geometrical evaluation of the effect of the delay due to
propagation shows that there are several competing effects in the
aberrative
forces:

1. The total gravitational 'force' is offset from a line through the
center of mass by the angle 'alpha'. This may be broken down into a
'central' force and a tangential 'aberrative' force.

2. The distance travelled by the gravitating force from the 'source' to
the 'target' body is shorter than the orbital diameter. This results in
an increased inward force that tends to counteract the offset.

If you actually perform the analysis (including the orbits about the
common center of mass), I believe you will find that the general
aberrative angle is given (where m = M by convention) by:

alpha = sqrt[2 - delta(1+m/M) + ((m/M)^2 -1)/(delta(1+m/M))]

where delta is the distance reduction factor (mentioned in #2, above):
delta = 1 / sqrt[1 + m/M (v/v_g)^2]

For the case m = M, this reduces to the 'popular' and simpler aberration
equation:

alpha = v / v_g

However, for cases where m M, the aberration angle is further reduced by
roughly the ratio of the masses of the bodies. (This results
straightforwardly from the reduced moment arm affecting the more massive
body.) In the case of Jupiter, your numbers are off by a factor of
roughly m_J / m_S.

No response in a week (not counting Wormley's and DVM's null responses).
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S) than
commonly claimed (as by Steve)? Or does somebody have a different result
from the general solution of orbiting bodies of different mass?

I think we can safely agree that Beckman was an idiot and
that his book was a complete failure.



Dirk Vdm

Dirk Van de moortel wrote in
message ...

"greywolf42" wrote in message
...
greywolf42 wrote in message news:...
greywolf42 wrote in message news:...

In a parallel thread (Georges Louis Le Sage -Pushing Gravity), Steve
stated:

If you want to show me where my back-of-the-envelope calculation is
drastically wrong, I'd be glad to listen.

{snip}

Steve has not properly modelled the aberrational relationships for
bodies
of differing mass. In fact, he hasn't actually modelled anything.
His
starting point is nothing more than three handwaving assumptions about
the
acceleration (force) that he presumes will result from a LeSagian
system:
"1. It can't depend explicitly on properties of the Sun."
"2. It must be proportional to Jupiter's mass m_J."
(later changed to "independent of mass m_J")
"3. It must be proportional to v_J/c."

If Steve had simply sat down and actually modelled a general
gravitational
system, between masses m and M, orbiting their common center of mass,
he
would have found that all three of his (original) assumptions were
incorrect to varying degrees.

A basic geometrical evaluation of the effect of the delay due to
propagation shows that there are several competing effects in the
aberrative
forces:

1. The total gravitational 'force' is offset from a line through the
center of mass by the angle 'alpha'. This may be broken down into a
'central' force and a tangential 'aberrative' force.

2. The distance travelled by the gravitating force from the 'source'
to
the 'target' body is shorter than the orbital diameter. This results
in
an increased inward force that tends to counteract the offset.

If you actually perform the analysis (including the orbits about the
common center of mass), I believe you will find that the general
aberrative angle is given (where m = M by convention) by:

alpha = sqrt[2 - delta(1+m/M) + ((m/M)^2 -1)/(delta(1+m/M))]

where delta is the distance reduction factor (mentioned in #2, above):
delta = 1 / sqrt[1 + m/M (v/v_g)^2]

For the case m = M, this reduces to the 'popular' and simpler
aberration
equation:

alpha = v / v_g

However, for cases where m M, the aberration angle is further
reduced by
roughly the ratio of the masses of the bodies. (This results
straightforwardly from the reduced moment arm affecting the more
massive
body.) In the case of Jupiter, your numbers are off by a factor of
roughly m_J / m_S.

No response in a week (not counting Wormley's and DVM's null responses).
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S)
than
commonly claimed (as by Steve)? Or does somebody have a different
result
from the general solution of orbiting bodies of different mass?

I think we can safely agree that Beckman was an idiot and
that his book was a complete failure.




Hey, Dinky, you pathetic coward. This post has nothing to do with Beckmann.
Do you even read posts before posting your crap?

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

On Fri, 28 May 2004 20:28:20 GMT, "Dirk Van de moortel"
wrote:

"greywolf42" wrote in message ...
greywolf42 wrote in message news:...
greywolf42 wrote in message news:...

In a parallel thread (Georges Louis Le Sage -Pushing Gravity), Steve
stated:

If you want to show me where my back-of-the-envelope calculation is
drastically wrong, I'd be glad to listen.

{snip}

Steve has not properly modelled the aberrational relationships for bodies
of differing mass. In fact, he hasn't actually modelled anything. His
starting point is nothing more than three handwaving assumptions about the
acceleration (force) that he presumes will result from a LeSagian system:
"1. It can't depend explicitly on properties of the Sun."
"2. It must be proportional to Jupiter's mass m_J."
(later changed to "independent of mass m_J")
"3. It must be proportional to v_J/c."

If Steve had simply sat down and actually modelled a general gravitational
system, between masses m and M, orbiting their common center of mass, he
would have found that all three of his (original) assumptions were
incorrect to varying degrees.

A basic geometrical evaluation of the effect of the delay due to
propagation shows that there are several competing effects in the
aberrative forces:

1. The total gravitational 'force' is offset from a line through the
center of mass by the angle 'alpha'. This may be broken down into a
'central' force and a tangential 'aberrative' force.

2. The distance travelled by the gravitating force from the 'source' to
the 'target' body is shorter than the orbital diameter. This results in
an increased inward force that tends to counteract the offset.

If you actually perform the analysis (including the orbits about the
common center of mass), I believe you will find that the general
aberrative angle is given (where m = M by convention) by:

alpha = sqrt[2 - delta(1+m/M) + ((m/M)^2 -1)/(delta(1+m/M))]

where delta is the distance reduction factor (mentioned in #2, above):
delta = 1 / sqrt[1 + m/M (v/v_g)^2]

For the case m = M, this reduces to the 'popular' and simpler aberration
equation:

alpha = v / v_g

However, for cases where m M, the aberration angle is further reduced by
roughly the ratio of the masses of the bodies. (This results
straightforwardly from the reduced moment arm affecting the more massive
body.) In the case of Jupiter, your numbers are off by a factor of
roughly m_J / m_S.

No response in a week (not counting Wormley's and DVM's null responses).
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S) than
commonly claimed (as by Steve)? Or does somebody have a different result
from the general solution of orbiting bodies of different mass?

I think we can safely agree that Beckman was an idiot and that his book was
a complete failure.

Hmmm, this conclusion certainly demonstrates a total lack of credibility...

http://209.197.94.171/people/beckmann.htm
http://en.wikipedia.org/wiki/Petr_Beckmann
http://www.accesstoenergy.com/view/ate/s41p901.htm

Dr. Beckmann my have had held controversial views but, by any objective
measure, he was NOT an idiot. Further, in the argument presented (you
know, the 'on topic', physics) does NOT depend upon Dr. Beckmann's
analysis. For the reading impaired, such as youself, let's revisit the
only section of this original post where Dr. Beckmann was even mentioned...

"But this is the 'hard' way. Beckmann approaches the problem much
more elegantly in "Einstein Plus Two." Now that I've shown you
additional errors in your approach, I recommend you crack the book.
If only to see the competing arguments."

Please note the, "But this is the 'hard' way", meaning the argument does NOT
depend 'AT ALL' upon Beckmann's approach! If you think otherwise show it,
explicitly.




Typical Dickhead ad homimen attacks, totally devoid of ANY physics or
on topic substance.

If you've got a viable counter, great, spit it out, thats what the thread
needs. Otherwise you're showing yourself to be a thoughtless under-achiever
attempting to compensate for this by constantly demeaning others... A
classic psychological behavior

Paul Stowe

On Fri, 28 May 2004 "greywolf42" wrote:
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S) than
commonly claimed... ?

Commonly claimed? This is pretty standard stuff. The aberration
angle for a theory of the kind you are talking about is obviously
(m/M)*(v/v_g). For Jupiter and the Sun the factor of m/M is about
1/1000 if I recall correctly. Even with this factor, the aberration
is still far too great to be compatible with the observed stability of
Jupiter's orbit (unless v_g is many orders of magnitude greater than
the speed of light, in which case the planet is vaporized). The
aberration effect can be offset by ultra-mundane drag, but only at one
orbital radius, sqrt(m/(k v_g), for a given mass m. This conflicts
with observation.

On Fri, 28 May 2004 20:28:20 GMT, "Dirk Van de moortel"
wrote:

"greywolf42" wrote in message ...
greywolf42 wrote in message news:...
greywolf42 wrote in message news:...

In a parallel thread (Georges Louis Le Sage -Pushing Gravity), Steve
stated:

If you want to show me where my back-of-the-envelope calculation is
drastically wrong, I'd be glad to listen.

{snip}

Steve has not properly modelled the aberrational relationships for bodies
of differing mass. In fact, he hasn't actually modelled anything. His
starting point is nothing more than three handwaving assumptions about the
acceleration (force) that he presumes will result from a LeSagian system:
"1. It can't depend explicitly on properties of the Sun."
"2. It must be proportional to Jupiter's mass m_J."
(later changed to "independent of mass m_J")
"3. It must be proportional to v_J/c."

If Steve had simply sat down and actually modelled a general gravitational
system, between masses m and M, orbiting their common center of mass, he
would have found that all three of his (original) assumptions were
incorrect to varying degrees.

A basic geometrical evaluation of the effect of the delay due to
propagation shows that there are several competing effects in the
aberrative forces:

1. The total gravitational 'force' is offset from a line through the
center of mass by the angle 'alpha'. This may be broken down into a
'central' force and a tangential 'aberrative' force.

2. The distance travelled by the gravitating force from the 'source' to
the 'target' body is shorter than the orbital diameter. This results in
an increased inward force that tends to counteract the offset.

If you actually perform the analysis (including the orbits about the
common center of mass), I believe you will find that the general
aberrative angle is given (where m = M by convention) by:

alpha = sqrt[2 - delta(1+m/M) + ((m/M)^2 -1)/(delta(1+m/M))]

where delta is the distance reduction factor (mentioned in #2, above):
delta = 1 / sqrt[1 + m/M (v/v_g)^2]

For the case m = M, this reduces to the 'popular' and simpler aberration
equation:

alpha = v / v_g

However, for cases where m M, the aberration angle is further reduced by
roughly the ratio of the masses of the bodies. (This results
straightforwardly from the reduced moment arm affecting the more massive
body.) In the case of Jupiter, your numbers are off by a factor of
roughly m_J / m_S.

No response in a week (not counting Wormley's and DVM's null responses).
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S) than
commonly claimed (as by Steve)? Or does somebody have a different result
from the general solution of orbiting bodies of different mass?

I think we can safely agree that Beckman was an idiot and that his book was
a complete failure.

Hmmm, this conclusion certainly demonstrates a total lack of credibility...

http://209.197.94.171/people/beckmann.htm
http://en.wikipedia.org/wiki/Petr_Beckmann
http://www.accesstoenergy.com/view/ate/s41p901.htm

Dr. Beckmann my have had held controversial views but, by any objective
measure, he was NOT an idiot. Further, in the argument presented (you
know, the 'on topic', physics) does NOT depend upon Dr. Beckmann's
analysis. For the reading impaired, such as youself, let's revisit the
only section of this original post where Dr. Beckmann was even mentioned...

"But this is the 'hard' way. Beckmann approaches the problem much
more elegantly in "Einstein Plus Two." Now that I've shown you
additional errors in your approach, I recommend you crack the book.
If only to see the competing arguments."

Please note the, "But this is the 'hard' way", meaning the argument does NOT
depend 'AT ALL' upon Beckmann's approach! If you think otherwise show it,
explicitly.




Typical Dickhead ad homimen attacks, totally devoid of ANY physics or
on topic substance.

If you've got a viable counter, great, spit it out, thats what the thread
needs. Otherwise you're showing yourself to be a thoughtless under-achiever
attempting to compensate for this by constantly demeaning others... A
classic psychological behavior

Paul Stowe

"Paul Stowe" wrote in message ...
On Fri, 28 May 2004 20:28:20 GMT, "Dirk Van de moortel"
wrote:

"greywolf42" wrote in message ...
greywolf42 wrote in message news:...
greywolf42 wrote in message news:...

In a parallel thread (Georges Louis Le Sage -Pushing Gravity), Steve
stated:

If you want to show me where my back-of-the-envelope calculation is
drastically wrong, I'd be glad to listen.

{snip}

Steve has not properly modelled the aberrational relationships for bodies
of differing mass. In fact, he hasn't actually modelled anything. His
starting point is nothing more than three handwaving assumptions about the
acceleration (force) that he presumes will result from a LeSagian system:
"1. It can't depend explicitly on properties of the Sun."
"2. It must be proportional to Jupiter's mass m_J."
(later changed to "independent of mass m_J")
"3. It must be proportional to v_J/c."

If Steve had simply sat down and actually modelled a general gravitational
system, between masses m and M, orbiting their common center of mass, he
would have found that all three of his (original) assumptions were
incorrect to varying degrees.

A basic geometrical evaluation of the effect of the delay due to
propagation shows that there are several competing effects in the
aberrative forces:

1. The total gravitational 'force' is offset from a line through the
center of mass by the angle 'alpha'. This may be broken down into a
'central' force and a tangential 'aberrative' force.

2. The distance travelled by the gravitating force from the 'source' to
the 'target' body is shorter than the orbital diameter. This results in
an increased inward force that tends to counteract the offset.

If you actually perform the analysis (including the orbits about the
common center of mass), I believe you will find that the general
aberrative angle is given (where m = M by convention) by:

alpha = sqrt[2 - delta(1+m/M) + ((m/M)^2 -1)/(delta(1+m/M))]

where delta is the distance reduction factor (mentioned in #2, above):
delta = 1 / sqrt[1 + m/M (v/v_g)^2]

For the case m = M, this reduces to the 'popular' and simpler aberration
equation:

alpha = v / v_g

However, for cases where m M, the aberration angle is further reduced by
roughly the ratio of the masses of the bodies. (This results
straightforwardly from the reduced moment arm affecting the more massive
body.) In the case of Jupiter, your numbers are off by a factor of
roughly m_J / m_S.

No response in a week (not counting Wormley's and DVM's null responses).
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S) than
commonly claimed (as by Steve)? Or does somebody have a different result
from the general solution of orbiting bodies of different mass?

I think we can safely agree that Beckman was an idiot and that his book was
a complete failure.

Hmmm, this conclusion certainly demonstrates a total lack of credibility...

http://209.197.94.171/people/beckmann.htm
http://en.wikipedia.org/wiki/Petr_Beckmann
http://www.accesstoenergy.com/view/ate/s41p901.htm

Dr. Beckmann my have had held controversial views but, by any objective
measure, he was NOT an idiot.

Let me guess...
He was an *engineer*, right?
Just like.... Androcles, right?

Dirk Vdm

On Sat, 29 May 2004 03:43:01 GMT, (Rod Lassiter) wrote:

On Fri, 28 May 2004 "greywolf42" wrote:
Can we all now agree that the aberrational force on the Earth (and
the aberrational angle) is on the order of a million times less
(m_E / m_S) than commonly claimed... ?

Commonly claimed? This is pretty standard stuff. The aberration
angle for a theory of the kind you are talking about is obviously
(m/M)*(v/v_g).

OK, let's let v_g - c... Then it's a' = a(m/M)(v/c), right?


For Jupiter and the Sun the factor of m/M is about 1/1000 if I
recall correctly. Even with this factor, the aberration
is still far too great to be compatible with the observed
stability of Jupiter's orbit (unless v_g is many orders of
magnitude greater than the speed of light, ...

Why?

in which case the planet is vaporized).

Why?

aberration effect can be offset by ultra-mundane drag, but
only at one orbital radius, sqrt(m/(k v_g), for a given mass
m. This conflicts with observation.

Given that ultra-mundane drag [a''] is,

a'' = k(v/c)

and to balance we need (let's forget about LeSagian vector
potential for the moment),

a' = a''

and thus,

a(m/M)(v/c) = k(v/c)

or,

am = kM

Let's take a as,

a = GM/r^2

Then,

(GM/r^2)m = kM

Gm/r^2 = k

Thus, finally we get,

r = Sqrt(Gm/k)

Given that for LeSagian theory

G = Qu^2

Where Q = the LeSagian momentum flux
u = mass attenuation coefficient

and k is simply,

k = Qu,

then we simplify the above to,

r = Sqrt(um)

We note that no speed, either c or v is present and the
radius r is uniquely different for each mass m.

But, there's the problem of field 'back-action' spin-up
resulting from the circular orbital condition. This acts
to reduce the ultra-mundane drag, reducing the effective
magitude of v in the drag equation. This in turn acts
to increase the radius where a balance will be achieved.
Next there's the multi-body problem and the interaction of
each other AND their field back actions... Not an easily
solved problem, eh?

Paul Stowe

Rod Lassiter wrote in message
...
On Fri, 28 May 2004 "greywolf42" wrote:
Can we all now agree that the aberrational force on the Earth (and the
aberrational angle) is on the order of a million times less (m_E / m_S)
than commonly claimed... ?

Commonly claimed? This is pretty standard stuff.

Not in the books I've seen. The 'aberration angle' is given as simply
'v/c'. Which is what Steve provided. To which I responded.

The aberration
angle for a theory of the kind you are talking about is obviously
(m/M)*(v/v_g).

It's certainly not self-evident. And I get a more complex answer. Though
it is roughly in agreement.

For Jupiter and the Sun the factor of m/M is about
1/1000 if I recall correctly.

Yes.

Even with this factor, the aberration
is still far too great to be compatible with the observed stability of
Jupiter's orbit (unless v_g is many orders of magnitude greater than
the speed of light, in which case the planet is vaporized).

Reference, please.

The
aberration effect can be offset by ultra-mundane drag, but only at one
orbital radius, sqrt(m/(k v_g), for a given mass m. This conflicts
with observation.

How?

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

On Sat, 29 May 2004 Paul Stowe wrote:
Rod Lassiter wrote:
The aberration angle for a theory of the kind you are talking about
is obviously (m/M)*(v/v_g)... The aberration effect can be offset by
ultra-mundane drag, but only at one orbital radius, sqrt(m/(k v_g),
for a given mass m. This conflicts with observation.

then we simplify the above to r = Sqrt(um) and the radius r is
uniquely different for each mass m.

That's what I said. (Is there an echo in here?) In other words, if
you try to offset the aberration with drag, it works only for one
orbital radius for a given mass. This conflicts with observation.

We note that no speed, either c or v is present...

The constant that you call "u" is equal to the constant that I called
1/(k v_g). Understand? Since this is a constant, the balance between
aberration and drag works for only one radius for any given mass, in
conflict with observation.

...the aberration is still far too great to be compatible with the
observed stability of Jupiter's orbit (unless v_g is many orders of
magnitude greater than the speed of light, ...
Why?

The aberration effect with v_g = c is large enough to produce
noticeable instabilities in the planetary orbits. Laplace computed
that v_g would need to be about 7 million times the velocity of light
in order to give the observed stability, and this estimate has been
greatly increased since then. For certain orbital radii and masses
you could offset the effect with drag, but this conflicts with the
existence of stable orbits for different masses at the same radii.

in which case the planet is vaporized).
Why?

The amount of energy conveyed by a particle is (mv^2)/2 and its
momentum is mv, so for a given amount of momentum conveyed to a
planet the amount of energy to be absorbed goes up in proportion to
v_g. If v_g is set high enough to avoid the aberration (and drag)
problems, it is high enough to vaporize the planet. (Thomson's idea
of having the excess energy absorbed by the ultra-mundane particles
has long since been debunked.)

...let's forget about LeSagian vector potential for the moment...

Yes. In fact, let's forget about it permanently, since there's no
such thing.

But, there's the problem of field 'back-action' spin-up
resulting from the circular orbital condition. This acts
to reduce the ultra-mundane drag...

No, the most basic necessity of a Lesage model is that the
ultra-mundane particles have almost infinite mean free path lengths,
i.e., they do not interact with each other, so there is no way for the
field of particles to be "spun up" like a fluid whose particles are
all interacting with each other. Also, another pre-requisite for a
Lesage model is that ordinary matter is virtually transparent to the
ultra-mundane particles, so the passage of a planet through the field
can have no significant effect on the agregate field (even if the
field particles did interact - which they don't). Furthermore, the
requirement to minimize drag implies that v_g is very much greater
than the speed of the planets, so on the time scale of the
ultra-mundane particles the planets are virtually stationary. Any
one of these reasons, by itself, would be adequate to ensure that
there is no appreciable "spin up" of the radiation field. Considering
all of them together, the idea of "spinning up" the radiation field is
so idiotic that no one with even a marginal competence for rational
thought could possibly take it seriously.

Not an easily solved problem, eh?

To the contrary, it's quite easily solved... by anyone with the
ability to think rationally. Debunking Lesage theories is not
difficult. It's recreational physics.