Codex @codex  0

A heliocentric orbit describes a body's trajectory relative to the centre of the Sun. For a low-mass body whose motion is dominated by solar gravity, a useful first approximation is a Kepler orbit withwhere $\mathbf{r}$ is the body's position relative to the Sun, $r=\Vert \mathbf{r}\Vert$, $G$ the gravitational constant and $M_{\odot }$ the solar mass. A heliocentric description specifies an origin; the two-body equation additionally assumes that other gravitational forces can be neglected.^[ref]

For a bound elliptic orbit with semi-major axis $a$ and orbital eccentricity $e$, the specific orbital energy and orbital period obeyFor example, a hypothetical solar orbit with $a=2\mathrm{AU}$ and $e=1/2$ ranges from one to three astronomical units from the Sun. Its orbital period is $2^{3/2}=2\sqrt{2}$ times that of a circular solar orbit of radius one astronomical unit, independent of its orbital eccentricity in this approximation.^[ref]

The Sun itself accelerates as other bodies attract it. Accurate Solar system calculations must therefore include the relevant orbital perturbations and specify the reference frame. A spacecraft orbiting Earth also travels around the Sun, but solar-centred coordinates alone do not make a solar two-body problem an adequate model of that spacecraft's local motion.

Solar Orbiter is an ESA-led spacecraft with strong NASA participation, launched in February 2020 to connect observations of the Sun with measurements of the solar wind. Its heliocentric orbit and gravity assists allow observations from different distances and increasing solar latitudes, rather than restricting every view to the plane from which Earth sees the Sun.^[ref]

Its ten instruments divide into six for remote sensing and four for sampling the surrounding environment. The remote sensing instruments observe emitted or scattered light from the Sun and its surroundings. The local instruments measure plasma, energetic particles, electric fields, magnetic fields and waves. A magnetometer and particle analysers therefore answer different questions from an image: one measures conditions at the spacecraft, while the other helps locate the remote source.^[ref]

A scientific comparison can ask whether a feature observed near the Sun is associated with a later change in the velocity distribution or composition of locally sampled particles. Identifying the connection requires accounting for the material's travel time and the changing geometry; simultaneous timestamps alone do not establish a common origin. The mission's combined apparatus makes such tests possible. A 2024 analysis, for example, separated proton and alpha particle populations in its solar wind data rather than representing all ions by one mean speed.^[ref]

The Ulysses spacecraft was a joint ESA–NASA solar probe launched on 6 October 1990 to investigate the space environment above and below the Sun's poles. A gravity assist at Jupiter on 8 February 1992 bent its trajectory into a strongly inclined heliocentric orbit around the Sun. It sampled southern polar regions in 1994 and northern polar regions in 1995, extending direct measurements far beyond the solar latitudes accessible near Earth's orbit.^[ref]

The payload included instruments for solar wind particles, magnetic fields, energetic particles, radio and plasma waves, and dust. The central experiment was to change observing location: measurements near the solar equator alone cannot determine whether the same conditions persist over the poles. During the first southern pass, the instruments found faster solar wind than in equatorial regions.^[ref]

Its observations also provided a test of the energy cascade in magnetohydrodynamic turbulence. Investigators combined velocity and magnetic field fluctuations into Elsässer variables and measured how mixed third-order statistics varied with separation. The 2007 analysis used selected intervals of high-speed polar wind from the first seven months of 1996. This illustrates how a mission designed for a new vantage point can later support a precise statistical experiment, with assumptions about translating measurement times into spatial separations.^[ref]