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These two phenomena are related: A low-altitude spotlight Sun would spend most of the day near the horizon for most locations on Earth, which is not observed, but rise and set fairly close to the horizon. A high-altitude Sun would spend more of the day away from the horizon, but rise and set fairly far from the horizon, which is also not observed.
An illustration explaining why this lemma is called "Rising sun lemma". In mathematical analysis, the rising sun lemma is a lemma due to Frigyes Riesz, used in the proof of the Hardy–Littlewood maximal theorem. The lemma was a precursor in one dimension of the Calderón–Zygmund lemma. [1] The lemma is stated as follows: [2]
The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see Timing).
The typical tidal range in the open ocean is about 1 metre (3 feet) – mapped in blue and green at right. Mean ranges near coasts vary from near zero to 11.7 metres (38.4 feet), [ 4 ] with the range depending on the volume of water adjacent to the coast, and the geography of the basin the water sits in. Larger bodies of water have higher ...
High and low tide in the Bay of Fundy. The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans (especially Earth's oceans) under the gravitational loading of another astronomical body or bodies (especially the Moon and Sun).
Figure 1: Tidal interaction between the spiral galaxy NGC 169 and a smaller companion [1]. The tidal force or tide-generating force is a gravitational effect that stretches a body along the line towards and away from the center of mass of another body due to spatial variations in strength in gravitational field from the other body.
So a small change in the mean temperature of the ocean represents a very large change in the total heat content of the climate system. Winds and currents move heat into deeper parts of the ocean. Some of it reaches depths of more than 2,000 m (6,600 ft). [88] When the ocean gains heat, the water expands and sea level rises. Warmer water and ...
Most of Earth's surface is ocean water: 70.8% or 361 million km 2 (139 million sq mi). [96] This vast pool of salty water is often called the world ocean, [97] [98] and makes Earth with its dynamic hydrosphere a water world [99] [100] or ocean world. [101] [102] Indeed, in Earth's early history the ocean may have covered Earth completely. [103]