Orbit Flashcards

Roughly 160–2,000 km above the surface, so orbital radii of about 6,540–8,380 km. The period runs 90–120 minutes, giving 14 to 16 revolutions per day at a speed near 7.8 km/s.

The dominant perturbation is atmospheric drag. Residual atmosphere removes energy every revolution, lowering the semi-major axis and gradually circularising the orbit, so every LEO satellite has a finite lifetime unless it carries propellant to reboost. J2 is also strong here, and it is what makes sun-synchronous orbits possible.

LEO, a few hundred kilometres up.

Two independent arguments point the same way. Ground resolution for a fixed aperture scales with range, so 500 km buys roughly seventy times the detail that the same optics would give from geostationary distance. And free-space path loss goes as the square of range, so 2 W closes a link that would need a far larger amplifier from 35,786 km. A small satellite simply cannot buy its way out of either penalty.

What is given up is continuity: each pass over the station lasts about five to ten minutes, so the mission is store-and-forward, not live.

False. A typical visible pass lasts five to fifteen minutes.

The satellite is moving at nearly 7.8 km/s and the horizon-to-horizon geometry seen from the ground is only a few thousand kilometres wide, so it crosses the visible sky quickly. This single number is why continuous LEO service requires a constellation with handover between satellites rather than one spacecraft.

Everything between the LEO ceiling and the geostationary radius — roughly 2,000 to 35,786 km. Navigation constellations sit near 20,000–23,000 km with periods of about twelve hours.

Against LEO you gain a much larger footprint, visibility measured in hours rather than minutes, and global coverage from 24 to 30 satellites instead of hundreds. You pay in higher path loss, one-way delay of roughly 50 to 70 ms, and repeated passage through the Van Allen belts, so the electronics must be radiation hardened.

Signal strength is not the binding constraint; visibility duration and constellation size are.

At 550 km a satellite is usable for a few minutes and its geometry changes continuously, so global continuous service would need hundreds of satellites, constant handover and very frequent ephemeris updates. At 20,000 km a satellite stays usable for hours and its geometry drifts slowly, so 24 to 30 satellites suffice.

LEO signals are now being added on top of GNSS, precisely because their fast geometry change speeds up carrier-phase convergence — but as a supplement to the MEO backbone, not a replacement for it.

An orbit whose inclination is near 90°, so the orbital plane contains, or nearly contains, Earth's rotation axis.

The plane stays essentially fixed in inertial space while Earth turns eastward beneath it. Each successive ground track is therefore displaced westward by the angle Earth rotates in one orbital period — about 22.5° for a 90-minute orbit. The track runs almost north–south and, over a day, the satellite overflies every latitude, poles included.

A polar LEO.

An orbit at inclination i never carries its ground track beyond latitude ±i, so an inclination near 90° is the only choice that reaches the poles at all. Coverage in longitude then costs nothing: Earth's rotation sweeps a fresh strip of surface under the satellite on every revolution, so the tracks fill in westward without any manoeuvring.

One satellite therefore builds global coverage over hours to days. The trade being made is revisit time, not coverage — you see everywhere, but not often.

Earth's equatorial bulge — the J2 term — makes the right ascension of the ascending node Ω drift. A sun-synchronous orbit is one whose altitude and inclination are chosen so that this drift exactly matches Earth's mean motion around the Sun, about +0.9856° per day eastward. The orbit plane then holds a constant angle to the Sun–Earth line all year.

Prograde orbits regress westward under J2, so achieving an eastward drift needs a slightly retrograde inclination — roughly 96° to 99° for altitudes of 600 to 900 km. The satellite then crosses each latitude at the same local solar time on every orbit.

False. Sun-synchronous fixes the local solar time of the sub-satellite point, not the illumination of the spacecraft. Most sun-synchronous satellites are eclipsed once per revolution, roughly every 90 minutes.

The special case that does stay lit is the dawn–dusk sun-synchronous orbit, whose plane lies close to the terminator. That is exactly why it is chosen for power-hungry radar satellites, which cannot afford either the eclipse power gap or the thermal cycling.

A sun-synchronous LEO, typically 700 to 800 km, with a repeating ground track.

The limiting factor in change detection is not resolution but consistency. A scene imaged at 10:30 local time and again at 14:00 differs in shadow length, shadow direction and atmospheric path length, and those differences look exactly like change. Fixing the local solar time turns illumination into a controlled variable, so a difference between two images is a real difference on the ground.

Adding a repeating ground track fixes the viewing geometry too, so the same pixel is seen from the same angle each cycle.

The orbit must be circular (e ≈ 0), equatorial (i = 0°) and prograde, with a period of one sidereal day — 86,164 s, not the 86,400 s solar day.

Kepler's third law then gives a semi-major axis of 42,164 km, so the altitude is 42,164 − 6,378 ≈ 35,786 km and the orbital speed is about 3.07 km/s.

All three conditions matter. Break any one and the satellite no longer holds a fixed position in the sky.

False. Visibility is limited by the horizon.

For zero elevation the station can be at most about 81.3° of longitude from the sub-satellite point at the equator, and that limit shrinks as station latitude rises, vanishing near 81.3° latitude. Real systems also demand a working minimum elevation, often 5° to 10°, for rain margin and to clear terrain, which tightens the window further.

This is exactly why New York sees none of the Arabsat slots at 20°E, 26°E or 30.5°E — it is roughly 94° to 105° of longitude away, far outside the limit for its latitude.

Geostationary.

The economics live on the ground, not in space. A fixed position in the sky means a cheap dish bolted to a wall once and never moved — no tracking motor, no handover, no scheduling — multiplied by millions of receivers. One satellite illuminates the whole country continuously, so there is no constellation to build or operate.

The usual objection to GEO does not apply here: broadcasting is one-way, so the ~120 ms one-way delay that would ruin a phone call is invisible to a viewer. The high path loss is absorbed by a large satellite with high-power transponders — a cost paid once, in orbit, rather than millions of times on the ground.

e ≈ 0.74 and a ≈ 26,600 km, giving a period of about twelve hours — two revolutions per sidereal day, so the ground track repeats daily.

i ≈ 63.4°, the critical inclination at which the J2-driven drift of the argument of perigee vanishes, so apogee stays where it is put.

ω = 270°, which places apogee over the northern hemisphere at its highest latitude.

By Kepler's second law the satellite sweeps equal areas in equal times, so it crawls near apogee and races through perigee — spending roughly eight of its twelve hours high in the northern sky.

ω = 270° puts perigee at the lowest point of the orbit, and therefore apogee at its highest northern latitude — which is where the long dwell time is wanted.

i = 63.4° is not chosen for coverage at all. J2 makes ω itself drift, at a rate proportional to (5 cos²i − 1), and that expression is zero at 63.4°. Off the critical inclination the apogee would slowly migrate away from the northern hemisphere and the mission would quietly degrade over months.

Note the design idea: the orbit is built around a perturbation rather than fighting it — the same reasoning as sun-synchrony, applied to a different orbital element.

Large eccentricity, so apogee and perigee radii differ greatly. By Kepler's second law the satellite spends most of its period in the apogee half of the orbit.

That buys two things a circular orbit cannot. First, long dwell at high altitude over a chosen region — Molniya at a twelve-hour period, Tundra at twenty-four. Second, a single orbit that samples a wide range of altitudes, which is why magnetospheric and radiation-belt missions fly HEOs: one revolution crosses many plasma regimes.

A highly elliptical orbit.

Notice that coverage of the ground is irrelevant here — the spacecraft is the probe, and the orbit's job is to move the instrument through the region of interest. A single HEO sweeps continuously through the inner belts, the plasmasphere, the ring current and the outer magnetosphere, twice per revolution.

The alternative — several circular satellites at different altitudes — would reach the same altitudes but would compare measurements made by different instrument sets, so every gradient would be contaminated by cross-calibration error. One spacecraft on one calibration is the scientific argument.

A geosynchronous orbit — one sidereal-day period — that is deliberately inclined, around 40°, and slightly eccentric, with apogee placed over the target region.

The ground track is an asymmetric figure-of-eight, and the phasing is chosen so the satellite lingers in the northern loop. From the service region it then appears close to the zenith for roughly eight hours a day, which is where the name comes from. Three or four satellites in staggered planes keep one near the zenith at all times.

A small quasi-zenith constellation — three or four satellites, so that one is always near the zenith.

The reasoning matters more than the name. This country's positioning failures are not caused by a shortage of satellites in orbit; they are caused by satellites being blocked. In an urban canyon the low-elevation members of the MEO constellation are masked or multipathed, which both reduces the number of usable signals and wrecks the geometry of those that remain.

Adding satellites at near-zenith elevation restores usable geometry exactly where it collapses, and it does so regionally — so the bill is a handful of satellites rather than thirty. It augments the MEO constellation; it does not replace it.

Inclination 0°: the orbit lies in Earth's equatorial plane, so the ground track runs along the equator itself.

The satellite repeatedly covers a band centred on the equator and never reaches mid or high latitudes. Geostationary orbit is the special case that is also circular and geosynchronous; a low equatorial orbit is a much faster animal with a completely different mission profile.

A low equatorial orbit. Two independent arguments converge on it.

Coverage: with i = 0° every revolution passes over the same latitude band, so the satellites revisit the service area roughly every 100 minutes instead of spending most of each orbit over regions with no users. An inclined orbit would waste most of its time off-target.

Launch: from an equatorial site an eastward launch keeps the full 0.465 km/s of Earth's rotation and needs no plane change, so the same rocket delivers more mass than to any inclined orbit.

The trade is stark and must be stated: the system serves nothing above about ±20° latitude.

True. Earth's surface speed is greatest at the equator, about 0.465 km/s, and an eastward equatorial launch uses all of it with no plane-change penalty.

Launching into a high-inclination or polar orbit forfeits most of that contribution, because only the component of the rotation velocity along the target orbit is useful. That is one reason polar launch sites are sited at high latitudes — there is little left to give up.

Inclination i is the angle between the orbital plane and the equatorial plane, measured at the ascending node. It fixes the highest latitude the ground track reaches: |latitude|_max = i for a prograde orbit, and 180° − i for a retrograde one.

Classification: prograde 0° ≤ i < 90°, polar i = 90°, retrograde 90° < i ≤ 180°.

Changing inclination once in orbit is the most expensive manoeuvre in orbital mechanics, so inclination is effectively a launch-time decision that the mission lives with.

An inclined LEO with an inclination a little above the highest target latitude — around 45°.

Low altitude supplies the resolution. Choosing i just above the target band means the satellite spends nearly all of its time over latitudes of interest rather than crossing empty polar regions, and the ground track turns over near those latitudes, so passes bunch there and revisit frequency rises. Because the track shifts west each revolution and the plane precesses under J2, overflight times drift instead of repeating on a fixed daily schedule.

What is traded away is continuity and polar coverage. A geostationary satellite would watch the region without interruption, but from 35,786 km the resolution simply is not there.

True for a prograde orbit, where the ground track oscillates between +i and −i in latitude.

For a retrograde orbit (i > 90°) the maximum latitude is 180° − i. So a sun-synchronous satellite at i = 98° reaches 82° latitude, not 98°, and leaves a small uncovered circle around each pole — a real operational limitation for polar ice and ozone monitoring.

The orbital plane is essentially fixed in inertial space, while Earth rotates eastward beneath it at 360° per sidereal day. A track laid down one revolution later therefore starts further west, by the angle Earth turned during that period — about 22.5° for a 96-minute orbit.

A geostationary satellite has a period exactly equal to the sidereal day and travels eastward in the equatorial plane at the same angular rate as the ground below. The westward shift is exactly zero, so the ground track degenerates to a single point.

This is also why the sidereal day, not the solar day, is the right number: what matters is Earth's rotation relative to the fixed stars, which is the frame the orbit lives in.

LEO — atmospheric drag. It removes energy on every revolution, lowering the semi-major axis and setting a finite lifetime, so the design carries propellant for reboost and a deorbit plan. J2 is also strong here, and is the effect that sun-synchronous orbits exploit.

GEO — third-body attraction. There is no drag, but the Sun and Moon tip the orbit plane at roughly 0.8° per year, so the satellite needs north–south station-keeping, which is by far the largest item in a GEO fuel budget. Solar radiation pressure acts on the large solar arrays and perturbs eccentricity and east–west position.

In short: LEO missions budget for decay, GEO missions budget for station-keeping. In both cases the fuel load sets the operational lifetime.

An orbit whose period is chosen so that a whole number of revolutions fits an exact whole number of nodal days — for example 233 revolutions in 16 days. The satellite then passes over precisely the same points on a fixed, predictable cycle.

Remote sensing wants it because comparing two images is only meaningful when the viewing geometry matches: the same look angle, the same swath, the same incidence. Combined with sun-synchrony you get the same place, the same lighting and the same geometry every cycle — which is what change detection needs, and what radar interferometry absolutely requires.

They answer different questions, so neither substitutes for the other.

A geostationary weather satellite stares at one hemisphere continuously and produces an image every few minutes, so it captures the evolution of a storm — that is the animated loop in a forecast. What it cannot do is resolve fine detail from 35,786 km, and it sees the polar regions badly or not at all.

A sun-synchronous polar weather satellite gives global coverage including the poles, at much higher resolution, with consistent illumination and well-calibrated atmospheric soundings — but only about twice a day for any given point.

Continuous coarse motion plus infrequent detailed global sampling. Operational meteorology needs both.

The orbit choice is right; the constellation sizing is what was missed.

A Molniya orbit has a period of about twelve hours, and the satellite is usefully high in the northern sky for roughly eight of them. That leaves a gap of several hours per orbit while it swings through perigee over the southern hemisphere — so a single satellite cannot deliver continuous service, whatever its elevation at apogee.

The fix is three satellites, in planes spaced 120° apart in right ascension and phased eight hours apart, so that as one drops toward perigee the next has already climbed into the usable arc. The ground station tracks and hands over between them.

No. The orbit is perfectly good engineering and completely wrong for this requirement.

From 550 km each pass over the service area lasts under ten minutes, and a single satellite in one sun-synchronous plane returns only a couple of times a day. Continuous voice needs either a constellation with handover, or a single satellite that never sets — which means a geosynchronous slot.

Note also what sun-synchrony is for: it solves an illumination-consistency problem, which a voice relay does not have. The team would be paying, in inclination and altitude, for a property the mission cannot use.

Cheap access to the wrong orbit is still the wrong orbit.