Ever seen an artificial satellite?
The Sun. (Alpha Centauri's companion, Proxima Centauri, is 2nd nearest.)
For a pool-shot
where a is the distance from cue-ball to object-ball,
b is the distance from the latter to the intended pocket,
and θ is the angle between these two lines,
the shot's difficulty D is roughly:
(This ignores various other factors, such as the aspect of approach to a pocket, table-tilt, etc.)
Simple:
turn switches A & B to On for a minute.
Then turn B to Off. Upon then promptly entering the room,
you know that the lit bulb correlates to switch A;
and, of the two non-lit bulbs, the warm one correlates to switch B.
(With good timing and sensitivity to heat, one could extend this method
to correlate four (easily) or even five bulbs pretty reliably.)
Crux — the [Southern] Cross.
No, it's not a parabola. Try again.
Near the terminator on
Mercury near perihelion.
[This was realized soon after the explosion of the durable myth
that Mercury kept the same face to the Sun, and it was realized
that Mercury instead synchronously rotated thrice while revolving twice.
This meant that (since its orbital eccentricity is slightly greater than 1/5)
its perihelion speed exceeds the mean speed by more than (5/4)-squared,
a factor which itself exceeds 3/2.]
[The old error is preserved with deliberate anachronism
in the 1982 Baltimore-based B.Levinson film Diner,
one scene of which was filmed in DR's Roland Park neighborhood,
right on Roland Avenue.]
Celestial Billboards: Rearing the Mod God Bod:
Christians' brightest asterism
Crux was
— aptly some might say —
formed from the west end of an eastbound horse.
[OK, so Centaurus is part human.
But the part which Christians grabbed to form Crux (the Southern Cross)
was all horse.
Have Christians ever previously been made aware
of the potential here for pagan-snickers?
DIO is ever pioneering….]
The bright but small constellation Crux
[Southern Cross] is a post-classical-Greece invention,
rearing into the sky a permanent free ad for the Christian business.
(In the northern sky, Cygnus' main stars were less officially converted into
the “Northern Cross”, by turning a bird-rump into Jesus' brain
and a bird-bill into his nailed feet.)
Crux's few stars (displayed upon the flags of Australia & New Zealand)
include the closest pair of 1st magnitude stars in the sky.
Crux's stars were, back in the pre-Christian era, the Centaur's hind legs.
I.e., when those puckish pagans
ever-so-generously relinquished ancient stellar-turf to the modern Christians,
what had borne an old-mythic horse's ass was replaced by what had reared
the very-dead body of the mod-cult-mythic “god”….
Due to the huge (25%) eccentricity of Pluto's orbit, it moved unusually quickly between 1930 and 2006: its heliocentric longitude increased 156° (from 109° to 265°); and 156°/360° = 43% > 33%.
Hipparchos of Nicaea,
whose best astronomy was carried out near Lindos
on the island of Rhodos.
(Is the tiny post-Hipparchos constellation Equuleus a memorial to him? —
whether meant seriously or [pre-Crux] jocularly?)
[“Hipp” = horse;
and the Greek word
“archos” (“archon” is from the same root)
can mean either leader or rectum.
(Thus, the common ancient name Hipparchos just meant horse-leader.)
An implicit ancient comment on Athens' archons?
Not that such an equation would retain the slightest applicability
to the wise&pure leaders of today's astronomy-history institutions.
Who, after decades of DR's calling them “archons”, may now recall
the old (equally mature) joke: why did the Lone Ranger shoot Tonto?
He found out “Kimo-Sabey” was Indian for poophead.]
Cantab John Couch Adams, double
loser of the France-vs-England race to find Neptune
(finished calculations 2nd, & no connexion to 1846/9/23 Berlin discovery),
somewhat redeemed himself by swiftly using
post-discovery Autumn observations in conjunction with
J.Challis' pre-discovery 1846 Summer observations, to compute
and announce (1846/10/15-17) the 1st nearly accurate orbit of Neptune.
However, note the CONTRAST between this speed — taking only 2 weeks
to not only write his report but do the required calculations —
versus the fact that he waited over 6 weeks after
Cambridge learned (1846/10/1) of Neptune's 1846/9/23 Berlin discovery before
producing (1846/11/13) his allegedly-already-computed-in-1845
“Hyp.1” orbital elements!
This is one of the strangest of several evidences against
Brit-mythology's long-accepted — now collapsing — claim
of priority, entirely based upon that curiously reluctant “1845”
orbit for Uranus' perturber. On his Dr.Cookian slowness to produce elements
(not detailed calculations) that could have been immediately published, see:
DIO 2.3 [1992]
‡9 §§D6&E3 [pp.127&128]; also
DIO 9.1 [1999]
‡9 §H11 [p.21].
[North Pole faker Cook's furtive 1909 shiftiness regarding producing
his records was amusingly and correctly weighed by W.Hobbs (D.Rawlins
Peary at the North Pole: Fact or Fiction? 1973 pp.85&172).
Cook's fellow-N.Pole faker Peary also delayed (1910/3/7-1911/1/7)
in publicly producing his own records.
But the key difference between Cook and either Adams or Peary is:
Cook couldn't fake navigational data or use real data (which is harder),
whereas Adams and Peary were genuinely expert
at the relevant math of their endeavors —
and so eventually produced data that for decades convinced onlookers
that they had legitimate claims of priority.]
The bottle of bugs was half-full
at 7:59.
[Almost no-one answers this question correctly —
and most are educationally shocked at its powerful lesson:
that exponential population-growth can sneak up
on societies who aren't anticipating its
sudden,
explosive danger.]
On the twin-planets:
[a] Both pairs are of contiguous planets.
[b] The relative contiguity is closer
than for other contiguous planets.
[c] Each pair's inner member rotates in retrograde.
[d] No other major planets do so.
[The foregoing set appears to constitute an original DIO discovery.]
These peculiarities may provide hints regarding the origin of the System.
(DIO 1.1 [1991]
‡2 §G2 [p.14].)
Never.
Venus' atmosphere refracts (bends) horizontal light-rays' paths
far more than the curvature of Venus' sphere.
(DIO 2.3 [1992]
‡8 n.8 [p.100].)
Answer:
Sunlight on Pluto is not dimmer but ordmag 1000 times
brighter than full-moonlight on Earth.
(DIO 2.1 [1992]
‡1 §A3 [p.3].)
The full Moon is about 15 magnitudes
dimmer than the Sun, i.e., roughly a million times dimmer.
The Earth is about 31 times nearer the Sun than Pluto.
Multiplying a millionth by the square of 31, we find a factor of about 1/1000.
Set p2 = n + 3.
If p is integral, closed orbits
will occur for F = krn.
And p will provide the number of approaches to
the gravitating center per revolution: obviously 1 for Newton
(as we realize every January at Earth's perihelion) and 2 for Hooke
(as is obvious from the 2-dimensional horizontal motion of a pendulum).
So for n = 6, 13, 22, 33, 46, etc, orbits will be closed.
(For n = −3, the orbiting body will steadily drift either
towards or away from the central force.
For values of n less than −3, the motion is unstable.)
ii is not imaginary or even complex. It is a real (if irrational) number. Hint: try Euler's Equation. Answer at our Defynitions page.
Most sources have listed Wm.Lassell as Umbriel's discoverer in 1851.
However,
DR and Chas.Kowal showed decades ago that Wm.Herschel
(Uranus' 1781 discoverer) spotted
Umbriel first, on 1801/4/17, and published his accurate positional data
long before Lassell.
NOTE: By the time it was possible reliably to check
Herschel's claim, Lassell's name had been attached for decades to Umbriel,
thus creating an inertia that resembles the present difficulty
astronomers are having in demoting Pluto from planethood.
Though E.Bower and E.Brown warned immediately upon Pluto's 1930 discovery that
Pluto was not the huge 7-Earth-mass planet P.Lowell had predicted in 1915,
few noted or appreciated their simple logic: in the period
between the last Uranian data (used by Lowell) and 1930,
Uranus' path had followed normal ephemerides,
not the motion entailed by the gravity of Lowell's large predicted body.
Yet not until DR's widely-read 1968 March S&T article
did the process of publicly facing Pluto's true puniness begin.
But, as with the Umbriel situation, it was too late:
for over a third of a century, Pluto had been wishfully
or fallaciously deemed ordmag an Earth-mass,
so it was naturally included in the list of planets.
This has created traditions
— even childhood-engendered loyalties —
that will take a long time to overcome.
(One bright sign of hope on the Pluto front:
see the excellent New York Times editorial of 2006/8/19.)
The Earth pulls on the Moon only half as hard as the Sun pulls on the Moon!
Because the Earth is roughly 1/300000 the Sun's mass
(which is 400 times farther away from the Moon than is the Earth's mass),
and 1/300000 divided by the inverse-square of 400 is about 1/2.
[If this seems strange, consider that: if the Earth vanished,
the Moon would continue revolving around the Sun.]
Four. (Useful for patio-restaurants,
where bothersome asymmetry is due more to floor than table.)
It's obvious that a 3-legged table will immediately find stability.
But a 4-legged table just requires rotating until stability is achieved.
[This assumes that the table stands on a surface with
a vertical gradient which is
[a] continuous, and
[b] of sufficient magnitude that one is not left
with an impossible situation, e.g., the extreme case of two over-short
diagonally-opposite legs on a table upon a perfectly planar floor.]
So that the man-hole cover cannot fall in the hole and hurt the man.
Answer: Uranus. Neptune hasn't been within 18AU of Pluto for millions of years, whereas Uranus was roughly 11AU from Pluto in recent decades. (Situation shown to be long-term-stable resonance in AJ 1969.)
A tossed rock is an artificial satellite — for a moment, anyway. But the general opinion that the motion is parabolic — a very close [flat-Earth] approximation to the truth — fails to comprehend that the correct viewpoint is that one is seeing the rock during just a tiny fraction of one sharpish end of the 6400 km long (and extremely eccentric) ELLIPTICAL orbit it would follow if it didn't crash into the ground.