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Mars comes closer to Earth more than any other planet save Venus at its nearest—56 million km is the closest distance between Mars and Earth, whereas the closest Venus comes to Earth is 40 million km. Mars comes closest to Earth every other year, around the time of its opposition, when Earth is sweeping between the Sun and Mars. Extra-close ...
Representative porkchop plot for the 2005 Mars launch opportunity (horizontal axis: departure dates in mm/dd notation, vertical axis: arrival dates (mm/dd)) A given blue contour represents a solution with a constant C 3. The center of the porkchop is the optimal solution for the lowest C 3.
true anomaly at time t 1 = −7.577° true anomaly at time t 2 = 92.423° This y-value corresponds to Figure 3. With r 1 = 10000 km; r 2 = 16000 km; α = 260° one gets the same ellipse with the opposite direction of motion, i.e. true anomaly at time t 1 = 7.577° true anomaly at time t 2 = 267.577° = 360° − 92.423° and a transfer time of ...
The former equation (gravitation) may look foreboding, but its calculation is no problem. The latter equations (motion laws) seem simpler, but yet they cannot be calculated. Computers cannot integrate, they cannot work with infinitesimal values, so instead of dt we use Δt and bringing the resulting variable to the left:
If the same sphere were made of lead the small body would need to orbit just 6.7 mm above the surface for sustaining the same orbital period. When a very small body is in a circular orbit barely above the surface of a sphere of any radius and mean density ρ (in kg/m 3), the above equation simplifies to (since M = Vρ = 4 / 3 π a 3 ρ)
The equation of time vanishes only for a planet with zero axial tilt and zero orbital eccentricity. [5] Two examples of planets with large equations of time are Mars and Uranus. On Mars the difference between sundial time and clock time can be as much as 50 minutes, due to the considerably greater eccentricity of its orbit.
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 ...
Orbit determination has a long history, beginning with the prehistoric discovery of the planets and subsequent attempts to predict their motions. Johannes Kepler used Tycho Brahe's careful observations of Mars to deduce the elliptical shape of its orbit and its orientation in space, deriving his three laws of planetary motion in the process.