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Venus was 0.7205 au from the Sun on the day of transit, decidedly less than average. [9] Moving far backwards in time, more than 200,000 years ago Venus sometimes passed by at a distance from Earth of barely less than 38 million km, and will next do that after more than 400,000 years.
More importantly, the radius of curvature of a north-south line on the earth's surface is 1% greater at the poles (≈6399.594 km) than at the equator (≈6335.439 km)—so the haversine formula and law of cosines cannot be guaranteed correct to better than 0.5%.
Venus's equator rotates at 6.52 km/h (4.05 mph), whereas Earth's rotates at 1,674.4 km/h (1,040.4 mph). [ note 2 ] [ 153 ] Venus's rotation period measured with Magellan spacecraft data over a 500-day period is smaller than the rotation period measured during the 16-year period between the Magellan spacecraft and Venus Express visits, with a ...
[2] [3] The general equation describing the radius of the sphere of a planet: [4] / where a {\displaystyle a} is the semimajor axis of the smaller object's (usually a planet's) orbit around the larger body (usually the Sun).
The quantity of the time unit [CTU] can be solved in another unit system (e.g. the metric system) if the mass and radius of the central body have been determined. Using the above equation and applying dimensional analysis , set the two equations expressing μ {\displaystyle \;\mu \;} equal to each other:
Kepler used his two first laws to compute the position of a planet as a function of time. His method involves the solution of a transcendental equation called Kepler's equation. The procedure for calculating the heliocentric polar coordinates (r,θ) of a planet as a function of the time t since perihelion, is the following five steps:
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
Radius of the Moon: s: Radius of the Sun: t: Radius of the Earth: D: Distance from the center of Earth to the vertex of Earth's shadow cone d: Radius of the Earth's shadow at the location of the Moon n: Ratio, d/ℓ (a directly observable quantity during a lunar eclipse) x: Ratio, S/L = s/ℓ (which is calculated from φ)