[27] CORE 4: Orbits & Resolution

By Kepler's second law, where in an elliptical orbit does a satellite move fastest, and where slowest?

Fastest at perigee (closest to Earth), slowest at apogee (farthest).

What does Kepler's third law say?

The square of the orbital period is proportional to the cube of the semi-major axis: T² ∝ a³. The semi-major axis a is half the ellipse's longest diameter (the radius, for a circle).

How does a circular orbit's speed depend on its radius?

v = √(GM/r) with r measured from Earth's center, so v ∝ 1/√r. Lower orbits are faster. Also v = 2πr/T.

What does orbital inclination measure?

The tilt of the orbit plane relative to Earth's equator: 0° equatorial, 90° polar, above 90° retrograde (moving against Earth's rotation).

What is the typical orbital period of a LEO Earth-observing satellite?

About 90 to 100 minutes (LEO overall about 88 to 128 min).

Which orbit class do GPS satellites use?

MEO (about 20,200 km, 12-hour period). Not LEO.

What is the altitude of geostationary orbit (GEO)?

About 35,786 km (≈36,000 km) above the equator, about 42,164 km from Earth's center.

What is a Molniya orbit?

A highly elliptical orbit with about a 12-hour period whose high apogee sits over high northern latitudes.

What makes a geostationary orbit a special case of geosynchronous?

It is also circular (eccentricity 0) and equatorial (inclination 0°), so the satellite appears fixed over one point on the equator.

How do GOES satellites (NOAA's main weather satellites) stay over the same spot on Earth?

They are geostationary: an equatorial orbit at 35,786 km whose period matches Earth's rotation.

What is the main coverage limitation of a geostationary satellite?

It always sees the same fixed disk of Earth (a bit less than half the globe) and views poorly beyond about 60 to 70° latitude, with no view of the poles.

In a GOES image, why are pixels over Canada much larger and more distorted than near the equator below the satellite?

Canada is viewed far off nadir (far from the point directly below the satellite): a longer slant distance and oblique angle stretch each pixel.

What is the point on Earth's surface directly beneath a satellite sensor called?

The nadir point.

What does off-nadir viewing do to pixels and to the signal?

Pixels get larger and more distorted, and light travels a longer path through the atmosphere (more attenuation).

What is a swath?

The width of the strip of ground imaged in one pass.

IFOV vs FOV: which one sets pixel size and which sets swath width?

IFOV (one detector) sets pixel size. FOV (whole sensor) sets swath width.

What is ground sample distance (GSD)?

The ground distance between adjacent pixel centers, i.e. how much ground one pixel represents.

What are the four types of resolution in remote sensing?

Spatial, spectral, radiometric and temporal.

What does spatial resolution describe?

The size of the smallest ground feature a sensor can distinguish (roughly the pixel size, or GSD).

Which type of resolution is the ability to tell apart small differences in the wavelength (frequency) of light?

Spectral resolution: the number and narrowness of the bands.

What does radiometric resolution describe?

The ability to distinguish small differences in brightness (energy) at a given wavelength, set by bit depth and noise.

What does temporal resolution describe?

How often the same place is observed (revisit time), set by the orbit's repeat pattern, swath width and pointing.

What is a polar orbit?

An orbit with inclination near 90° that passes over or near both poles.

What is a sun-synchronous orbit (SSO)?

A near-polar orbit whose plane turns to keep pace with the Sun, so the satellite crosses the equator at the same local solar time every day (for example, always about 1:30 pm).

Why is a sun-synchronous orbit ideal for climate monitoring and change detection?

The sun angle and shadows are the same on every pass, so differences between images are real changes, not lighting changes.

Sun-synchronous chain, step 1: what feature of Earth makes an inclined satellite orbit's plane slowly rotate (precess)?

Earth's equatorial bulge (its oblateness, called the J2 effect).

Sun-synchronous chain, step 5: the orbit plane turns ~0.986°/day eastward, keeping pace with Earth's trip around the Sun. What is the result?

The plane keeps a fixed angle to the Sun, so the satellite crosses the equator and each latitude at the same local solar time every day.

What is the main drawback of a sun-synchronous orbit for climate studies?

It sees each place only at the same one or two local times, so it cannot sample the diurnal (daily) cycle.

Which is the morning satellite and which is the afternoon satellite: Terra or Aqua?

Terra is morning (~10:30 am), Aqua is afternoon (~1:30 pm).

What kind of orbit do the A-Train satellites share?

One sun-synchronous, near-polar LEO at about 705 km, with the satellites flying in a line minutes apart.

Why did the A-Train satellites fly just minutes apart in the same orbit?

So their different instruments observed nearly the same scene at nearly the same time and could be combined (e.g. CloudSat radar + CALIPSO lidar + Aqua MODIS).

Why do the Jason altimeters avoid a sun-synchronous orbit?

A sun-synchronous orbit samples each spot at the same solar time, so the Sun-driven part of the tide would be caught at the same stage every pass and look like a fixed sea level offset (aliasing).

Why is ECOSTRESS on the ISS instead of a sun-synchronous satellite?

The ISS orbit precesses, so ECOSTRESS sees the same place at different times of day, revealing daily cycles of plant water stress and heat.

A day of satellite data shows nearly north-south swaths that converge toward the poles. What orbit made it?

A polar (typically sun-synchronous) LEO orbit, such as Aqua's.

What is the difference between orbital period and revisit period?

Orbital period is the time for one trip around Earth. Revisit period is how long until the sensor can image the same spot again, which can be days even with a 99-minute orbit.

A day of polar-orbiter data shows black diamond-shaped gaps between swaths near the equator but none at high latitudes. What causes them?

The swath is narrower than the ~2,750 km spacing between successive ground tracks at the equator, while the tracks converge toward the poles.

For a polar-orbiting satellite, which latitudes get the most frequent revisits?

High latitudes, where swaths overlap. The equator gets the fewest looks.

Why does MODIS revisit a spot every 1 to 2 days while a 30 m imager like Landsat needs 16 days?

MODIS's swath is about 2,330 km, Landsat's only about 185 km.

What kind of image does a nadir-only (profiling) instrument produce, and which listed instruments are like this?

A narrow 2-D curtain or line along the ground track, not a wide map. Examples: CALIPSO's lidar, CloudSat's radar, Jason's altimeter.

In a CALIPSO or CloudSat curtain image, how can you tell which way the satellite was moving?

The x-axis runs in time order, left to right. If latitude increases to the right, the satellite was moving north (ascending, the A-Train's daytime pass).

Why do geostationary satellites have better temporal but worse spatial resolution than sun-synchronous LEO satellites?

GEO stares at one region and images it every few minutes, but it is ~50 times farther away, so the same IFOV covers far more ground per pixel.

What is the basic tradeoff between MODIS and GOES?

MODIS: finer resolution and consistent lighting but only 1 to 2 looks a day. GOES: coarser pixels but images every few minutes.

What is the general rule connecting altitude, coverage and resolution?

Higher altitude gives wider coverage but coarser spatial resolution.

What is a multispectral sensor?

One that records a few to a few dozen separate, fairly broad bands (MODIS 36, GOES ABI 16, ASTER 14).

What is a hyperspectral sensor?

One that records hundreds of narrow, contiguous bands, giving a nearly continuous spectrum for every pixel.

How is GSD related to altitude and IFOV?

GSD = altitude × IFOV (IFOV in radians, small-angle approximation).

How does diffraction-limited ground resolution depend on wavelength, aperture and altitude?

Ground resolution ≈ 1.22 λH / D: ∝ λ, ∝ altitude, ∝ 1/D.

For the same antenna or telescope size, why are microwave footprints hundreds to thousands of times wider than thermal IR footprints?

Diffraction angle ∝ λ, and microwave wavelengths (about 1 mm to several cm) are roughly 100 to 3,000 times longer than thermal IR (~10 µm).

How does a whiskbroom (across-track) scanner build an image?

A rotating or oscillating mirror sweeps the view side to side across the swath while the satellite moves forward.

How does a pushbroom (along-track) scanner build an image?

A linear array of detectors images a whole cross-track line at once, with no scan mirror. The satellite's forward motion adds each new line.

Why does a pushbroom scanner get better signal-to-noise than a whiskbroom?

Each detector stares at its own ground pixel for the whole time the satellite takes to advance one pixel, a much longer dwell time.

What image artifact comes from poorly cross-calibrated detectors in a pushbroom array?

Striping: lines running parallel to the flight direction.

Is pixel size (GSD) the same thing as spatial resolution?

Not always. Pixel size is the sampling grid, while true resolution can be coarser because of optical blur, diffraction or motion.

Can resampling a 1 km image onto 250 m pixels improve its spatial resolution?

No. Resampled smaller pixels add no new detail.

Rules of thumb: what is the smallest kind of object you can make out at about 30 m, 10 m and 1 m resolution?

30 m: fields and city blocks. 10 m: large buildings. 1 m: cars.

What is a mixed pixel?

A pixel containing several surface types, so it records a blend of their signals.

How many brightness levels does an n-bit sensor record?

2ⁿ levels: 8-bit = 256, 12-bit = 4,096, 14-bit = 16,384.

What does a contrast stretch do to an image?

It remaps the narrow range of recorded brightness values onto the full display range (e.g. 0 to 255), so features stand out more.

Which filter best removes salt-and-pepper (random black and white dot) noise?

A median filte