The Physics
Opus in profectus

Angular Momentum

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the idea


L =  r × p
L =  r × mv
L =  mr × (ω × r)
L =  mω(r · r) − mr(r · ω)
L =  mr2ω − 0
L =  mr2ω
L =  Iω

Moment of inertia again

I = ∑r2m = 
r2 dm = ρ
r2 dV

Conservation of angular momentum

τ =  d  L = 0


L = constant

Translational and rotational quantities compared
concept translation connection rotation
momentum p =  mv L =  r × p = mr × v L =  Iω
impulse-momentum ∫ F · dt
F = 
 = ∆p
∫ τ · dt
τ = 
 = ∆L 



Orbital spaceports
country status name
audisusedWoomera Launch Site
aucanceledCape York Spaceport
auproposedChristmas Island Spaceport
bractiveAlcantara Launch Center (Centro de Lançamento de Alcântara)
cnactiveJiuquan Satellite Launch Center (酒泉卫星发射中心)
cnactiveTaiyuan Satellite Launch Center (太原卫星发射中心)
cnactiveWenchang Satellite Launch Center (文昌卫星发射中心)
cnactiveXichang Satellite Launch Center (西昌卫星发射中心)
fractiveGuiana Space Center (Centre Spatial Guyanais)
frdisusedHammaguir Launch Site
itdisusedLuigi Broglio Space Centre
inactiveSatish Dhawan Space Centre (सतीश धवन अंतरिक्ष केंद्र)
inactiveVikram Sarabhai Space Center (विक्रम साराभाई अंतरिक्ष केंद्)
iractiveImam Khomeini Space Center
ilactivePalmachim Air Force Base (בָּסִיס חֵיל-הַאֲוִויר פַּלְמַחִים)
jpactiveTanegashima Space Center
jpactiveUchinoura Space Center (内之浦宇宙空間観測所)
kpactiveTonghae Satellite Launching Ground (동해위성발사장)
kpactiveSŏhae Satellite Launching Station (서해위성발사장)
kractiveNaro Space Center (나로우주센터)
mxproposedMexican Space Agency (Agencia Espacial Mexicana)
nzactiveMahia Launch Complex
ruactiveBaikonur Cosmodrome (Космодром Байконур)
ruactiveVostochny Cosmodrome (Космодром Восточный)
ruactiveKapustin Yar Cosmodrome (Космодром Капустин Яр)
ruactivePlesetsk Cosmodrome (Космодром Плесецк)
ruactiveYasniy Launch Base (Пусковая База Ясный)
rudisusedSvobodniy Cosmodrome (Космодром Свободный)
usactiveKennedy Space Center
usactiveVandenberg Air Force Base
usactiveWallops Flight Facility
usactiveKodiak Launch Complex
usactiveRonald Reagan Ballistic Missile Defense Test Site
usactiveSea Launch

the earth

The earth is not the world's best clock.



types of LOD change … horrible mess …

  1. a linear increase owing to tidal dissipation. Paraphrase, "The tidal friction between the oceans and the Earth's surface causes the Earth's rotation to slow by approximately 0.002 seconds every century. However, ignoring energy lost to heat generated by the tides, the angular momentum of the Earth-Moon system must remain constant. The Earth's angular momentum is decreasing, so the Moon's must increase. The only way it can do this is by moving into a higher orbit around the Earth. Thus, the distance to the farthest point of the lunar orbit is increasing by about 3.8 centimeters per year."
  2. Larger, irregular variations, on the scale of decades, owing to core-mantle interactions
  3. Solar flares are known to abruptly alter the Earth's rotation. For example, the great flares of 1959 and 1972 brought abrupt changes in the LOD. Both long-term and short-term changes in solar activity alter the Earth's rotation. The 11-year, 22-year and 56-year solar cycles are conspicuous in the LOD data. Long-term (secular) changes were noted at times of fluctuations in solar activity in the past, and the evidence indicates that these changes were very likely abrupt. Observations of the LOD, like so many other geophysical phenomena, reveal the solar-FEM linkage.
  4. Seasonal changes from the angular momentum exchange between crust and atmosphere.

The rate of rotation of the Earth is high in summer and low in winter (northern hemisphere).

At time scales of hours to days, tidally driven? ocean currents and variations in the ocean height dominate