Astronomy & Celestial Mechanics
the sky, computed
Concept

Frozen orbit — where it appears

An orbit whose eccentricity and argument of perigee are chosen so that perturbations leave their mean values unchanged. Round the Earth the balance is between the flattening and the pear shape, at an eccentricity of about 0.001. The height over each latitude then repeats, which altimetry needs.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

6 satellites over the Moon's south pole. The horizontal (solid) and vertical (dashed) dilution of precision for a receiver near the Moon's south pole over 48 hours, with 6 satellites in elliptical frozen orbits — semi-major axis 6541.4 km, eccentricity 0.6, inclination 56.2°, apolune over the south pole, each in its own plane — and a 5° horizon mask, logarithmic. Gaps are times with fewer than four satellites in view, when no fix is possible: 28 per cent of the time. When there is a fix, the horizontal geometry is good — median HDOP 1.7 — and the vertical is bad, median VDOP 6: the satellites near apolune all stand at much the same elevation, and a receiver cannot tell whether every range is long because it is lower or because its clock is late.

A height the map already knows

A navigation service for the Moon's south pole needs only a handful of satellites, if they are put in elliptical orbits that hang for hours over the pole at the high point of each lap. But satellites hanging over a pole all stand at much the same height in the sky, on a cone, and four ranges from a cone cannot tell whether the receiver is lower or its clock is late. On the surface the receiver knows its height already, from a map of the terrain — and that one number, used as a measurement, does more for the service than two more satellites.

spaceflight · Ground tracks An eccentricity that goes round a point that is not zero. The eccentricity vector of a near-circular orbit at 800 km and 98.6 degrees, with its component along the line of nodes across and its perpendicular component up, in thousandths. Under J₂ alone it would circle the origin. J₃ moves the centre to 1.03 thousandths, on the axis where the argument of perigee is 90 degrees, and every orbit circles there once in 123 days. A satellite placed at that centre does not move.

An orbit held still by the Earth's pear shape

A satellite's eccentricity does not stay put. The Earth's flattening turns it once every few months, in a circle around zero, as anyone would expect. A coefficient four hundred times smaller, the slight pear shape of the planet, moves the centre of that circle to a value of about one part in a thousand. A satellite placed exactly there goes nowhere at all, and its height above every latitude repeats, for no fuel. Nothing else in orbital mechanics costs so little for so much.

spaceflight · Station-keeping

Named alongside it

The objects these essays reach for when they reach for this one.

Argument of perigeeClock biasCoverageCritical inclinationDilution of precisionEccentricity vectorElevation maskGeometry matrixLeast-squaresSatellite altimetrySatellite navigation

All concepts