Projectile trajectories

Zigoteau wrote:
So the fact that there are things in closed orbits implies
that everything is in a closed orbit?

When do you think Voyager is due back?


In another 100 million years or so.
It's in a closed orbit around the center of the galaxy.

What is the escape velocity from our galaxy?
It seems we have enough data that this should
be determinable.

--
Rich

RichD wrote:
Zigoteau wrote:
So the fact that there are things in closed orbits implies
that everything is in a closed orbit?

When do you think Voyager is due back?


In another 100 million years or so.
It's in a closed orbit around the center of the galaxy.

What is the escape velocity from our galaxy?
It seems we have enough data that this should
be determinable.

--
Rich


Since we don't know the total mass of the galaxy including dark matter
(WIMPs, MACHOs) and where its distribution ends, we are unable to
calculate our galaxy's escape velocity at this time. There may be more
dark matter distributed outside of the bright matter that we can see,
and that would add to the escape velocity.

http://www.madsci.org/posts/archives...5096.As.r.html

Double-A

Double-A wrote:

RichD wrote:

snip

What is the escape velocity from our galaxy?
It seems we have enough data that this should
be determinable.

Since we don't know the total mass of the galaxy including dark matter
(WIMPs, MACHOs) and where its distribution ends, we are unable to
calculate our galaxy's escape velocity at this time. There may be more
dark matter distributed outside of the bright matter that we can see,
and that would add to the escape velocity.

http://www.madsci.org/posts/archives...5096.As.r.html


Moreover escape velocity varies according to the distance from the
centre of mass and, in the case of a dispersed 'body' like a galaxy,
how much of the mass is interior to that position. The escape
velocity will vary from one location to another, so a starting-point
needs to be specified for the problem to be defined.

From here, assuming as a 'first approximation' that the Sun is in a
circular orbit around the centre of the Galaxy, one can make a rough
estimate from its speed, making use of the fact that (above a solid
body) escape velocity is orbital speed times the square root of two.
Given that the Sun is thought to take about 225 million years to
cover an orbit 50,000 parsecs long, making its average speed about
220 km/s, I'd expect the escape velocity at this distance from the
hub to be somewhat over 300 km/s.

In the above I've been ignoring what was said before and on the page
you linked to: while this approach gets around the problem of an
unknown 'interior' mass there's still the unknown size of the 'halo'
to consider. This calculation provides a minimum value, though; I
think we can say with some confidence that the escape velocity can't
be less than 300-odd km/s -- assuming the 'conventional wisdom'
regarding the Sun's orbit is reasonably accurate to start with.

(Starting with the figure of 250 km/s for the orbital speed of the
outer part of the Galaxy's disc given at the above link, we already
have to revise the estimate upward to about 350 km/s *plus* the speed
that would be lost by a projectile between here and the 'rim' on its
way out. If aimed at the Solar Apex that implies a delta-vee of at
least 150 km/s, or something like 600 km/s in the opposite direction.)

--
Odysseus

On a related subject,

'dark matter' is postited to account for spiral galaxies' non-Keplerian
(or more unitary) rotation. The stuff is obviously transparent,
invisible, and non-refractive. Yet it purports to exert a huge
gravitational effect on the visible galaxy. Gravitational effects of
such magnitude should show a corresponding degree of gravitational
lensing. Yet the lensing that *is* oberved such as in this classic HST
image http://csep10.phys.utk.edu/astr162/l.../gravlens.html

doesn't appear to be in excess of lensing caused by 'normal' matter.
Should not the presence of 'dark matter' induce a much higher degree of
lensing? Or does its gravity somehow affect only mass while ignoring
light?
Or, is DM's effect considered present in the
observed lensing?
Just wonderin' oc

Bill Sheppard wrote:

On a related subject,

'dark matter' is postited to account for spiral galaxies' non-Keplerian
(or more unitary) rotation. The stuff is obviously transparent,
invisible, and non-refractive. Yet it purports to exert a huge
gravitational effect on the visible galaxy. Gravitational effects of
such magnitude should show a corresponding degree of gravitational
lensing. Yet the lensing that *is* oberved such as in this classic HST
image http://csep10.phys.utk.edu/astr162/l.../gravlens.html

doesn't appear to be in excess of lensing caused by 'normal' matter.
Should not the presence of 'dark matter' induce a much higher degree of
lensing? Or does its gravity somehow affect only mass while ignoring
light?
Or, is DM's effect considered present in the
observed lensing?

I should think so -- to the extent that it's relevant. AFAICT they're
modelling the mass concentration in Abell 2218 from its lensing
properties, not its visible appearance -- and it's the whole cluster
that's involved, not just a single galaxy. At that kind of distance
(over 700 Mpc according to the cluster's red-shift) a lot more of the
matter is "dark" than would be in our own neighbourhood: the cluster
could contain any number of dwarf galaxies, extended galactic haloes
or arcs too faint to detect from here, comprising perfectly ordinary
stars &c. But that alone doesn't merit the term "dark matter" as it's
usually understood; I would reserve it for situations where we
believe we *ought to* be able to see all (or most) of the material
whose presence is inferred indirectly.

--
Odysseus

From Ody, re 'dark matter':

...At that kind of distance (over 700 Mpc
according to the cluster's red-shift) a lot
more of the matter is "dark" than would
be in our own neighbourhood: the cluster could contain any number of
dwarf
galaxies, extended galactic haloes or
arcs too faint to detect from here,
comprising perfectly ordinary stars &c.
But that alone doesn't merit the term
"dark matter" as it's usually understood; I would reserve it for
situations where we
believe we *ought to* be able to see all
(or most) of the material whose presence is inferred indirectly.

Ody, you seem pretty astute and level headed in these matters. Maybe you
could speak to an issue i've put forth a couple of times recently, but
nobody responded to except Painius.
Non-Keplerian (or more unitary) rotation of galaxies
seems to present a quandary requiring 'dark matter' to account for. But
when you look at mass distribution in a typical spiral galaxy, why
should it display Keplerian rotation? That is to say, our solar system
has over 99% of its mass concentrated in the center, in the Sun. Whereas
the galaxy has much more of its mass spread out through the periphery.
This spread-out mass has to be under mutual gravitation, which would
force the rotation to be more unitary (less Keplerian).
Painius counters that the galaxy *does* mirror the solar
system by having 99% of its mass in the central black hole, and
therefore *should* display Keplerian rotation, but doesn't.
To my uneducated perception, the 'missing mass' is
already present and accounted for in the galaxy's periphery, and 'dark
matter' is a solution without a problem.
So maybe you could expound a bit more of your
learned view on the matter (no pun intended)?g oc

Bill Sheppard wrote:

snip
Non-Keplerian (or more unitary) rotation of galaxies
seems to present a quandary requiring 'dark matter' to account for. But
when you look at mass distribution in a typical spiral galaxy, why
should it display Keplerian rotation? That is to say, our solar system
has over 99% of its mass concentrated in the center, in the Sun. Whereas
the galaxy has much more of its mass spread out through the periphery.
This spread-out mass has to be under mutual gravitation, which would
force the rotation to be more unitary (less Keplerian).

I only know what I've read in popular accounts, but I understand
"Keplerian rotation" to refer not only to a situation like that in
the solar system, but to include all cases where the mass inside a
given orbit acts as if it's concentrated at the centre. Within the
part of the disc where the majority of the mass is located, it's true
that the motion tends to be somewhat unitary because the weaker
gravity in the regions more distant from the centre is partly
compensated for by the greater quantity of mass contained within the
larger orbits. Near the edge of the disk the Keplerian principle
dominates; once there's little additional mass to be 'taken up' by
orbits of increasing radius, their rotational velocity should drop
off quite quickly.

The "missing mass" problem appears when the rotational speeds of the
outer haloes of galaxies are measured: they don't seem to decline
nearly as much as the decrease in visibly radiating matter would
imply. Therefore they behave as if the observed disk were embedded in
a very much larger, invisible one. The quandary, then, is not that
non-Keplerian rotation occurs within the areas whose emissions of EMR
show them to be densely 'populated': that's entirely to be expected.
It's that the outlying regions behave much the same way, despite
their sparse appearance.

Painius counters that the galaxy *does* mirror the solar
system by having 99% of its mass in the central black hole, and
therefore *should* display Keplerian rotation, but doesn't.

I don't know where he that 99% comes from; it seems very exaggerated.
The figures I've seen bandied about for the "super-massive" black
hole in the hub of our Galaxy run from about two to five million
solar masses; IIRC the Milky Way's total mass is estimated to be
somewhere in the 100 to 150 *billion*-sun range, making the black
hole account for 0.005% of it at best!

To my uneducated perception, the 'missing mass' is
already present and accounted for in the galaxy's periphery, and 'dark
matter' is a solution without a problem.

The problem AIUI is that, in the periphery or not, we can't see the
stuff -- or conversely, what we *can* see is simply insufficient to
account for the observed effects. It's not a small discrepancy either
-- for some reason a food-related analogy occurs to me: must be
getting near dinnertime -- we're not talking about a few crumbs that
have fallen off the plate, but all five courses that should have
followed the appetizer.

This subthread started with the motions of galaxies within clusters.
Note that it was from observations of these that astronomers first
suspected missing mass, without being able to tell whether it
belonged to the individual members or was distributed in
intergalactic space. But we hear much more about the more recently
discovered galactic-rotation evidence, in part because modelling the
space-motions of galaxies solely on the basis of their red-shifts is
a very tricky and uncertain business, yielding little firm evidence,
while by looking at different parts of a rotating spiral (the closer
to edgewise, the better) one can get a pretty precise "rotation
curve", the red-shift of the centre serving to calibrate the other measurements.

--
Odysseus

Excellent synopsis, Ody. Based on the visible evidence then, one has to
conclude that the posited dark matter's gravity selectively affects only
mass while having no effect on light passing thru it, which is contrary
to the nature of gravity. Strange stuff indeed.

I don't know where he that 99% comes
from; it seems very exaggerated.

It's a representative figure, meaning "a very large percentage", like
the amount of the solar system's mass that's concentrated in the Sun. Or
the galaxy's mass that's supposedly concentrated in the central BH
(which as you pointed out is grossly and hugely exaggerated).

It might be interesting to computer model rotation curves in the
protostellar cloud and see how they compare to those of galaxies. oc

"BS" babbled in message
...

Excellent synopsis, Ody. Based on the visible evidence then, one has to
conclude that the posited dark matter's gravity selectively affects only
mass while having no effect on light passing thru it, which is contrary
to the nature of gravity. Strange stuff indeed.

Google: dark matter gravitational lense



I don't know where he that 99% comes
from; it seems very exaggerated.

It's a representative figure, meaning "a very large percentage",

99% is actually very specific BS, and represents 99%.


like
the amount of the solar system's mass that's concentrated in the Sun.

Google: 99.8% solar system


Or
the galaxy's mass that's supposedly concentrated in the central BH
(which as you pointed out is grossly and hugely exaggerated).

It might be interesting to computer model rotation curves in the
protostellar cloud and see how they compare to those of galaxies. oc

Bill Sheppard wrote:

Excellent synopsis, Ody. Based on the visible evidence then, one has to
conclude that the posited dark matter's gravity selectively affects only
mass while having no effect on light passing thru it, which is contrary
to the nature of gravity. Strange stuff indeed.


I'm inclined to doubt that it would have *no* effect on light; I
don't think there's any reason to believe dark matter's gravitational
effects would be restricted to the kinematics of the surrounding
matter and not include e.g. gravitational lensing. But it doesn't
emit or absorb EMR in any way that we can recognize so far:
definitely a strange property.

--
Odysseus