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An orbit will be Sun-synchronous when the precession rate ρ = dΩ / dt equals the mean motion of the Earth about the Sun n E, which is 360° per sidereal year (1.990 968 71 × 10 −7 rad/s), so we must set n E = ΔΩ E / T E = ρ = ΔΩ / T , where T E is the Earth orbital period, while T is the period of the spacecraft ...
The value of a solar beta angle for a satellite in Earth orbit can be found using the equation = [ + ()] where is the ecliptic true solar longitude, is the right ascension of ascending node (RAAN), is the orbit's inclination, and is the obliquity of the ecliptic (approximately 23.45 degrees for Earth at present).
An inclination of 0° means the orbiting body has a prograde orbit in the planet's equatorial plane. An inclination greater than 0° and less than 90° also describes a prograde orbit. An inclination of 63.4° is often called a critical inclination, when describing artificial satellites orbiting the Earth, because they have zero apogee drift. [3]
These are executed as thruster burns orthogonal to the orbital plane. For Sun-synchronous spacecraft having a constant geometry relative to the Sun, the inclination change due to the solar gravitation is particularly large; a delta-v in the order of 1–2 m/s per year can be needed to keep the inclination constant. [citation needed]
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 ...
However, maximum efficiency of inclination changes are achieved at apoapsis, (or apogee), where orbital velocity is the lowest. In some cases, it can require less total delta-v to raise the satellite into a higher orbit, change the orbit plane at the higher apogee, and then lower the satellite to its original altitude. [1]
To retain a Sun-synchronous orbit as the Earth revolves around the Sun during the year, the orbit must precess about the Earth at the same rate (which is not possible if the satellite passes directly over the pole). Because of Earth's equatorial bulge, an orbit inclined at a slight angle is subject to a torque, which causes precession. An angle ...
ϖ = Ω + ω in separate planes. In celestial mechanics, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) would occur if the body's orbit inclination were zero.