Newton’s cannonball was a thought experiment Isaac Newton used to explain the principle of orbital motion. It was the first explanation of an orbit and still the easiest to understand.
Newton visualizes a cannon on top of a very tall mountain where the air resistance is no longer a factor. As more charge is used with each cannon shot, the speed of the cannonball will be greater, and the cannonball will hit the ground farther and farther. Finally, at a certain speed, it will not hit the ground at all. It will fall toward the spherical Earth just as fast as the Earth curves away from it. In the absence of drag from the atmosphere, it will continue forever in orbit around the Earth.
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The Sun and the Moon appear about the same size in the sky, but they are not perfectly the same size, and their sizes are not constant because their orbits are not perfectly circular.
Flat-Earthers claim it is too much of a coincidence that the Sun is perfectly 400× larger than the Moon and perfectly 400× farther, making them appear perfectly the same size. In reality, the Sun and the Moon are not perfectly the same size in the sky.
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The distances to the Sun and the Moon are 149,600,000 km and 384,400 km. These figures are average values, and the actual values are around these averages. In a solar eclipse, the actual distances determine whether a total or annular solar eclipse occurs.
Flat-Earthers calculated the geometry of a solar eclipse using these average distances and discovered the umbra does not reach Earth’s surface. They wrongly concluded that an eclipse should not occur. In reality, the numbers are only averages, not the real values. And if the umbra does not reach Earth’s surface, it will still produce an annular solar eclipse.
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In orbit, objects are weightless because both the objects and the spacecraft have the same speed and direction, and both are affected by the same gravitational influence. We use the spacecraft as the frame of reference. Because the objects are not in motion relative to the spacecraft, they appear to float.
In Earth orbit, the objects are still affected by Earth’s gravity, but yet they float. Flat-Earthers use it to disprove spaceflight. In reality, the objects float because we are using the spacecraft as the frame of reference, which is also moving by the same amount and is affected by the same gravity as the objects themselves.
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Rocket launches have a curved trajectory because their objective is not only to reach space but also to enter Earth orbit. To achieve it, a spacecraft needs to gain a sufficient horizontal speed, parallel to Earth’s surface.
Flat-Earthers claim the curved appearance of a rocket launch trajectory “proves” rockets never reach space. In reality, it is caused by the motion of the rocket parallel to Earth’s surface, perspective effect, and the curvature of the Earth.
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If a satellite is placed in an orbit 35786 km above the equator, it will be in motion at the same speed as the Earth’s rotation. As a result, the satellite will appear practically motionless from an observer on Earth’s surface. Many communication satellites are in this orbit so that a satellite receiver does not need to track the satellite continuously.
Flat-Earthers often take the fact that satellites are in motion, and most satellite dishes have a fixed direction as ‘proof’ the receivers cannot be pointing to satellites. In reality, it is possible to place a satellite in a geostationary orbit to make it appear in a fixed position in the sky relative to an observer on Earth.
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A frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements. Speed or velocity is relative to a frame of reference. It is possible that two speeds/velocities are measured relative to a different frame of reference and thus cannot be directly compared.
Flat-Earthers would often compare two different speed measurements like an airplane moving at 900 km/h (560 mph) and Earth’s surface near the equator at 1674 km/h (1040 mph). They would conclude the airplane should not be able to catch up with Earth’s surface and would not be able to land if the Earth is rotating. They are wrong. The speeds are measured relative to the different frame of reference, and therefore, cannot be compared directly.
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The Moon is tidally locked. Half of the Moon is always facing the Earth. However, due to libration, we can take a glimpse of areas of the moon that are not always visible.
Flat-Earthers invented many “scenarios” to “explain” how the so many lunar-related phenomena can happen on the flat Earth model. Some of these “explanations” include “transparent Moon”, “hemisphere-shaped Moon”, “flat circular Moon”, etc. Lunar libration rules out the majority, if not all, of these “explanations.”
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A satellite in a high enough orbit can remain operational for a very long time because in space there is practically no air resistance. This is a situation that never occurs in our everyday life. A car requires a constant consumption of fuel to keep running, but a satellite can remain in motion without consuming any fuel because there’s practically no force stopping it.
Flat-Earthers claim that satellites cannot stay up there for such a very long time because ‘we never refuel any satellites.’ They are wrong. In space, there is practically no drag, and satellites only need to consume fuel to adjust their speed periodically.
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The orbit of the Earth and that of the Moon are not perfectly aligned in the same plane. The orbital plane of the Moon is inclined 5.145° from the Earth’s orbital plane. This is the reason an eclipse does not happen every month.
Sometimes we see flat-Earthers claim that an eclipse should happen every month. But it does not, and they take that as ‘evidence’ of the failure of modern science to explain the occurrence of an eclipse. Their mistake is that they don’t account for the orbital inclination.
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Jupiter possesses four large moons: Io, Europa, Ganymede, and Callisto. These are called the Galilean Moons. They are easy to observe and the first objects found to orbit a planet other than the Earth.
Flat-Earthers are often seen demanding proof that an object can orbit another object. All they have to do is to use a telescope to observe Jupiter and its Galilean moons.
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The directions of up and down are determined from the direction of the Earth’s gravitational acceleration. Up is in the opposite direction, and down is in the same direction as the Earth’s gravitational acceleration.
Flat-Earthers are often seen making fun of this fact. They show us ‘upside down’ pictures taken in the southern hemisphere. They are wrong. To anyone in the southern hemisphere, down is in the same direction as the Earth ‘s gravitational acceleration, the same as anyone in the northern hemisphere.
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If Earth’s gravity pulls everything towards the Earth, then how can satellites stay up there and are not falling towards the Earth?
The answer is that satellites orbit the Earth. They have the correct velocity with respect to Earth’s position and gravitational pull.
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A human eye can only visually perceive the curvature of the Earth if we are at a considerable altitude from the surface, which is still beyond the reach of most humans today. A commercial jet airliner is the highest position realistically attainable by most humans today. At such altitude, we can only perceive very slight curvature, and only in an ideal condition.
The basis of flat-Earthers’ belief is that the horizon appears flat. They would say if we cannot see the curvature, then there’s no curvature, and thus, the Earth is flat. They are wrong. Most of us these days cannot travel high enough to see the curve. The best we can do these days is going on board a commercial jet airliner, which can only go about 11-15 km up, only a fraction of the radius of the Earth.
Continue reading “So, Where’s the Curvature?”