Predicting Satellites’ Visibility

The orbital parameters of most satellites (the TLE data) are freely available, and we can use them to predict the visibility of the satellites. The following is a very simple Python script to predict the visibility of the ISS for the next few weeks.

Flat-Earthers invented many “explanations” about the visibility of satellites. By studying the satellites’ orbital parameters and how they can be used to predict the visibility of the satellites, we know that flat-Earthers’ claims are just nonsense.

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Ancient Greeks and Spherical Earth

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Ancient Greeks have known spherical Earth since at least the 3rd century B.C. According to historian Otto E. Neugebauer, the Greeks discovered Earth is a sphere from the drastic variation in the stars’ positions & motions between Greek settlements of different latitudes.

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Sweden Solar System

The Sweden Solar System is the largest scale model of the Solar System in the world. We can use it to get a better sense of the sizes and distances in the Solar System.

Flat-Earthers claim there is no scale model of the Solar System and use the fact to “prove” the failure of science to explain the world. The Sweden Solar System proves them wrong and gives us an idea about the problem of making a scale model of the Solar System.

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Moonlight and Inverse Square Law

Light intensity is inversely proportional to the square of its distance. The light we receive from the Moon increases 50000× if we land there. But so does the Moon’s apparent size, spreading the increase in intensity over a larger area.

Flat-Earthers incorrectly claim the inverse square law means the Moon would be too bright if we land there, and they use the argument to “prove” it is impossible to go to the Moon. In reality, the inverse square law applies to a point source. For a large light source, its change in apparent size must also be considered.

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Sundial

A sundial tells the time of day from the position of the shadow of its gnomon as cast by the sun. The gnomon is usually raised parallel to Earth’s axis of rotation, so its shadow will always fall to the same line despite the sun’s annual apparent motion.

Aligning the gnomon to the Earth’s axis of rotation allows the sundial to be accurate throughout the year. All of this happens because Earth is a rotating sphere orbiting the sun with a tilted axis.

Flat-Earthers incorrectly claim that sundial works because Earth is flat. In reality, sundials are designed with the knowledge Earth is a sphere. Real-world sundials cannot possibly work if Earth were flat. If Earth were flat, we would have constructed sundials in a very different design.

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Sunrays are Practically Parallel, but not Perfectly Parallel

The sun emits sunrays in every direction. But as the sun is very far, the sun rays that reach us are practically parallel. From Earth, any two sun rays form a maximum angle of ~0.53°. Sun rays are practically parallel, but not perfectly  parallel.

For most practical purposes, we can assume sun rays are parallel for  simplification. But in other cases, the small angle is critical to the problem & we need to take it into account.

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Earthshine Shows the Moon Obscuring the Sun During a Total Solar Eclipse

During a total solar eclipse, the Moon’s side facing Earth does not receive sunlight but still receives light reflected from Earth’s surface. The phenomenon is called Earthshine and can be captured using a camera with a long exposure.

Flat-Earthers demand visual evidence of the Moon blocking the Sun during a solar eclipse. Earthshine provides this visual evidence & shows that the Moon is blocking the Sun.

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Galilean Moons: First Objects Observed to Orbit Another Object

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Jupiter has four moons (Io, Europa, Ganymede, & Callisto) that we can easily observe using a binocular or telescope. They are the first objects found to orbit another, proving it is possible for a satellite to orbit planets other than Earth.

Flat-Earthers like to demand evidence of an object orbiting another. All they have to do is use a telescope to observe Jupiter. Its moons have short orbital periods (1.8 to 16.7 days), & thus, it is not hard to observe the orbiting motion.

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Analemma

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An analemma is an image or diagram showing the change in the position of the Sun in the sky, seen from a fixed location on Earth, at the same time every day, over the course of a year.

The north-south component of an analemma results from the change in the Sun’s declination due to the tilt of Earth’s axis of rotation. The east-west component results from the non-uniform rate of change of the Sun’s right ascension, governed by the combined effects of Earth’s axial tilt and orbital eccentricity.

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Polaris Distance and How It Does Not Appear to Move

In a very casual observation, Polaris appears stationary in the sky because it is very far & we do not live nearly long enough.

Flat-Earthers use that Polaris always appears in the exact location as “evidence” of a stationary Earth. In reality, it does not appear in motion the same way mountains do not appear to move if we move less than an inch.

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Satellite Tracking Apps and the Two-Line Element Set Data (TLE)

The orbit of an Earth-orbiting satellite is often described using two-line element set (TLE) data. From the TLE data of a specific satellite, we can determine its position at a certain time.

Flat-Earthers discovered that changing their device’s time will cause satellites’ positions to change in some satellite tracking apps, and they use it as “evidence” of wrongdoing. In reality, these apps work by getting the TLE data from the Internet periodically and then using the data to calculate the satellites’ positions in the app itself. Therefore, these apps depend on the accuracy of the devices’ time.

Unlike what these flat-Earthers imagine, these apps do not work by receiving telemetry data from the satellites in real-time.

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How Satellites Can Orbit and Stay Up There

Earth’s gravity pulls things toward Earth. Satellites can stay up there because they are orbiting. They are moving at the right speed and right direction to counter the pull of gravity.

Flat-Earthers claim that satellites should fall down if gravity pulls toward Earth. In reality, we do not just launch satellites to space. We also give them the correct speed & direction, so they neither fall toward Earth nor keep going farther away.

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Milky Way Visibility

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Because Earth is a sphere moving around the Sun, we can easily see the Milky Way’s center only in certain months. In other months, the Milky Way will be too close to the Sun in the sky, where sunlight will overwhelm and obscure it from view.

Flat-Earthers claim that the Milky Way is visible every night “proves” a flat Earth. In reality, we are inside the Milky Way, and some parts will be visible. However, a specific part of it, like its brighter center, will not be visible every night.

Astrolabe

An astrolabe is a device historically used to determine the date and time of day from the positions of the sun or stars. Astrolabe was used from classical antiquity, about the 2nd century BC,  until the age of discovery. It was superseded by the more accurate sextant, star charts, and time-keeping devices.

Flat-Earthers claim an astrolabe can work because Earth is flat. In reality, astrolabes are designed using the spherical Earth model. They could not possibly work if Earth is flat.

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Geocentric Coordinate System Does not Imply Geocentrism

In astronomy, we use a celestial coordinate system to specify the position of celestial objects, like satellites, planets, stars, etc. Each of the coordinate systems has an origin, which can be the observer (topocentric), Earth (geocentric), the Sun (heliocentric), the Moon (selenocentric), or any other location. We choose a specific coordinate origin according to convenience and suitability for the problem at hand.

Some coordinate systems are described as “geocentric,” and flat-Earthers use it as “proof” of geocentrism, or that Earth is stationary and the center of the universe. In reality, it is just the origin of the coordinate. “Geocentric” here means Earth is the origin of the coordinate system. As we live on Earth, a geocentric coordinate is useful for many purposes.

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Alignment of Planets

Planets are in motion around the Sun. Sometimes the planets’ positions are aligned that they appear close to each other in the sky, and less frequently, involving more than two planets.

One such alignment of planets occurred in May 2011 where Mercury, Venus, Mars, and Jupiter are all appeared close together. Mercury and Venus are closer to the Sun than Earth, while Mars and Jupiter are farther. Flat-Earthers cannot understand how all of these planets can appear close to each other in the sky, and they use it to discredit science. In reality, this diagram can easily explain the general positions of the planets during the phenomenon.

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Observing Mercury and Venus

Mercury and Venus are inferior planets. Their orbits are closer to the Sun than Earth. We can see these planets if they are above the horizon, and it will be easier if the Sun is below the horizon. Generally, both planets can be seen early or late in the night.

Flat-Earthers claim we should not be able to see Mercury and Venus as they are closer to the sun, and at night we are facing away from the sun. In reality, early and late in the night, we can look toward the general direction of the Sun & observe both planets.

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Sky

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The sky appears practically identical to all observers on Earth, except that the Earth obstructs the view to a different part of the sky to a different observer on Earth, and daylight obscures the view to most objects in the sky.

The fact that the sky appears identical everywhere on Earth can only be adequately explained if all the astronomical objects are very far from us and that the Earth is a sphere.

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Visual Albedo of the Moon and the Earth

Visual albedo is the measure of the reflection of sunlight out of the total solar radiation received by an astronomical body, taking into account only the visible light. The visual albedo of the Earth is 0.37, and the Moon’s is 0.12.

The Moon appears dark if the Earth also appears in the same photograph. Flat Earthers use the fact to dismiss such photos as fake. In reality, the Moon’s brightness in a photo is just a matter of choosing the correct camera exposure. But if Earth is also present, increasing the exposure will make the Earth appear too bright.

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Georgia Guidestones

The Georgia Guidestones is a granite monument in Georgia, United States. In one of the stones, a hole is drilled through that points to the north celestial pole. And consequently, by looking through the hole, the star Polaris is visible at night.

Polaris is visible through the Georgia Guidestones’ hole every night, and flat-Earthers use the fact as “evidence” that Earth is stationary. In reality, due to Earth’s axial precession, in a few hundred years, Polaris will have moved far enough away from the north celestial pole and will no longer be visible through the hole.

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