Our World

A. The Geoid:

• The true shape of the Earth is not a perfect sphere, but an Oblate Spheroid (often described as a Geoid — literally "Earth-shaped").
• It is slightly flattened at the North and South Poles and bulges at the Equator. This distortion is caused by the centrifugal force generated by the Earth\'s rapid axial rotation over billions of years.
• Measurements:
  • Equatorial Diameter: $12,756\text{ km}$ (Equatorial Circumference: $\approx 40,075\text{ km}$)
  • Polar Diameter: $12,714\text{ km}$ (Polar Circumference: $\approx 40,008\text{ km}$)
  • Polar Flattening Difference: $12,756 - 12,714 = \mathbf{42\text{ km}}$

B. Proofs of Sphericity:

1. Circumnavigation: Ferdinand Magellan\'s fleet sailed continuously west from Spain (1519 – 1522) and returned to the same starting point without encountering a sharp edge.
2. Lunar Eclipse Shadow: During a lunar eclipse, the shadow of the Earth cast upon the Moon is always strictly circular or curved. Only a spherical object casts a circular shadow from all angles.
3. Bedford Level Canal Experiment: In England, three poles of equal height were placed at $1\text{ mile}$ intervals along a straight canal. The center pole appeared slightly higher ($8\text{ inches}$) than the outer poles when viewed through a telescope due to the Earth\'s curvature.
4. Expanding Horizon: The higher one climbs, the wider and more circular the visible horizon becomes. On a flat Earth, the horizon would remain unchanged regardless of elevation.

A. Parallels of Latitude:

• Angular distance of a place north or south of the Equator ($0^\circ$).
• Drawn as full, parallel concentric circles. Lines never meet. Length decreases from Equator ($40,075\text{ km}$) to zero at the Poles ($90^\circ\text{ N}$ and $90^\circ\text{ S}$). Total latitudes: $181$ ($90\text{ North} + 90\text{ South} + 1\text{ Equator}$).
• Distance between $1^\circ$ of latitude is approximately $111\text{ km}$ ($69\text{ miles}$).
• Important Parallels:
  • Equator: $0^\circ$ (Great Circle dividing Northern and Southern Hemispheres).
  • Tropic of Cancer: $23^\circ 30\'\text{ N}$ ($23.5^\circ\text{ N}$)
  • Tropic of Capricorn: $23^\circ 30\'\text{ S}$ ($23.5^\circ\text{ S}$)
  • Arctic Circle: $66^\circ 30\'\text{ N}$ ($66.5^\circ\text{ N}$)
  • Antarctic Circle: $66^\circ 30\'\text{ S}$ ($66.5^\circ\text{ S}$)

B. Meridians of Longitude:

• Angular distance of a place east or west of the Prime Meridian ($0^\circ$), which passes through the Royal Astronomical Observatory at Greenwich near London.
• Drawn as semi-circles running strictly North-South, converging at both poles. All meridians are of equal length. Total longitudes: $360$ ($180^\circ\text{ E} + 180^\circ\text{ W}$, sharing the $180^\circ$ meridian).
• Distance between longitudes is maximum at the Equator ($\approx 111\text{ km}$) and diminishes to zero ($0\text{ km}$) at the Poles.

A. Longitude and Time:

The Earth rotates $360^\circ$ on its axis in $24\text{ hours}$ (from West to East):

• Rule of Thumb:
  • Places to the East of a meridian see the sun earlier → Time is Ahead (East Gain Add — EGA).
  • Places to the West of a meridian see the sun later → Time is Behind (West Lose Subtract — WLS).

B. Indian Standard Time (IST):

• India extends longitudinally from $68^\circ 7\'\text{ E}$ (Gujarat) to $97^\circ 25\'\text{ E}$ (Arunachal Pradesh), spanning nearly $30^\circ$ of longitude (a local time difference of $\approx 2\text{ hours}$).
• To avoid administrative chaos in train and flight schedules, the central meridian of $82^\circ 30\'\text{ E}$ ($82.5^\circ\text{ E}$) passing through Mirzapur near Prayagraj (Allahabad) was chosen as the standard meridian for the entire country.
• $$\text{Time difference from GMT} = 82.5^\circ \times 4\text{ min} = 330\text{ minutes} = \mathbf{+5\text{ hours } 30\text{ minutes}}$$

C. The International Date Line (IDL):

• Follows the $180^\circ$ meridian directly opposite the Greenwich Prime Meridian.
• Calendar Change: Crossing the IDL from West to East (e.g., Asia to North America) → Gain a day (Subtract 24 hrs); crossing from East to West (North America to Asia) → Lose a day (Add 24 hrs).
• Why It Zig-Zags: The IDL deviates and bends at the Bering Strait, Aleutian Islands, Fiji, and Tonga to prevent dividing small island countries into two different calendar days.