Sidereal day in the context of "Diurnal motion"

Mercury is the first planet from the Sun and the smallest in the Solar System. It is a rocky planet with a trace atmosphere and a surface gravity slightly higher than that of Mars. The surface of Mercury is similar to Earth's Moon, being heavily cratered, with an expansive rupes system generated from thrust faults, and bright ray systems, formed by ejecta. Its largest crater, Caloris Planitia, has a diameter of 1,550 km (960 mi), which is about one-third the diameter of the planet (4,880 km or 3,030 mi). Being the most inferior orbiting planet, it always appears close to the sun in Earth's sky, either as a "morning star" or an "evening star". It is the planet with the highest delta-v required for travel from Earth, as well as to and from the other planets in the Solar System.

Mercury's sidereal year (88.0 Earth days) and sidereal day (58.65 Earth days) are in a 3:2 ratio, in a spin–orbit resonance. Consequently, one solar day (sunrise to sunrise) on Mercury lasts for around 176 Earth days: twice the planet's sidereal year. This means that one side of Mercury will remain in sunlight for one Mercurian year of 88 Earth days; while during the next orbit, that side will be in darkness all the time until the next sunrise after another 88 Earth days. Above the planet's surface is an extremely tenuous exosphere and a faint magnetic field just strong enough to deflect solar winds. Combined with its high orbital eccentricity, the planet's surface has widely varying sunlight intensity and temperature, with the equatorial regions ranging from −170 °C (−270 °F) at night to 420 °C (790 °F) during sunlight. Due to its very small axial tilt, the planet's poles are permanently shadowed. This strongly suggests that water ice could be present in the craters.

The atmosphere of Venus is the very dense layer of gases surrounding the planet Venus. Venus's atmosphere is composed of 96.5% carbon dioxide and 3.5% nitrogen, with other chemical compounds present only in trace amounts. It is much denser and hotter than that of Earth; the temperature at the surface is 740 K (467 °C, 872 °F), and the pressure is 93 bar (9.3 MPa; 1,350 psi), roughly the pressure found 900 m (3,000 ft) under water on Earth. The atmosphere of Venus supports decks of opaque clouds of sulfuric acid that cover the entire planet, preventing, until recently, optical Earth-based and orbital observation of the surface. Information about surface topography was originally obtained exclusively by radar imaging. However, the Parker Solar Probe was able to capture images of the surface using IR and nearby visible light frequencies, confirming the topography.

Aside from the very surface layers, the atmosphere is in a state of vigorous circulation. The upper layer of troposphere exhibits a phenomenon of super-rotation, in which the atmosphere circles the planet in just four Earth days, much faster than the planet's sidereal day of 243 days. The winds supporting super-rotation blow at a speed of 100 m/s (≈360 km/h or 220 mph) or more. Winds move at up to 60 times the speed of the planet's rotation, while Earth's fastest winds are only 10% to 20% rotation speed. However, wind speed decreases with decreasing elevation to less than 2.8 m/s (≈10 km/h or 6.2 mph) on the surface. Near the poles are anticyclonic structures called polar vortices. Each vortex is double-eyed and shows a characteristic S-shaped pattern of clouds. Above there is an intermediate layer of mesosphere which separates the troposphere from the thermosphere. The thermosphere is also characterized by strong circulation, but very different in its nature—the gases heated and partially ionized by sunlight in the sunlit hemisphere migrate to the dark hemisphere where they recombine and downwell.

A geosynchronous orbit (sometimes abbreviated GSO) is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds (one sidereal day). The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky may remain still or trace out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of 35,786 km (22,236 mi).

A special case of geosynchronous orbit is the geostationary orbit (often abbreviated GEO), which is a circular geosynchronous orbit in Earth's equatorial plane with both inclination and eccentricity equal to 0. A satellite in a geostationary orbit remains in the same position in the sky to observers on the surface.

A Molniya orbit (Russian: Молния, IPA: [ˈmolnʲɪjə] , "Lightning") is a type of satellite orbit designed to provide communications and remote sensing coverage over high latitudes. It is a highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of 270 degrees, and an orbital period of approximately half a sidereal day. The name comes from the Molniya satellites, a series of Soviet/Russian civilian and military communications satellites which have used this type of orbit since the mid-1960s. A variation on the Molniya orbit is the so-called Three Apogee (TAP) orbit, whose period is a third of a sidereal day.

The Molniya orbit has a long dwell time over the hemisphere of interest, while moving very quickly over the other. In practice, this places it over either Russia or Canada for the majority of its orbit, providing a high angle of view to communications and monitoring satellites covering these high-latitude areas. Geostationary orbits, which are necessarily inclined over the equator, can only view these regions from a low angle, hampering performance. In practice, a satellite in a Molniya orbit serves the same purpose for high latitudes as a geostationary satellite does for equatorial regions, except that multiple satellites are required for continuous coverage.