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        The early development of radar was driven primarily by military imperatives, and the targets that were to be detected were mainly aircraft and ships. It was no surprise that echoes were also received from terrain and from rainstorms, but the discovery, during World War II, that birds were often detectable was less expected. As the technology developed, and specially after transmission at the shorter ‘microwave’ wavelengths became commonplace, echoes from insects were also identified. In the late 1940’s and the 1950’s, radar technology was adapted rapidly to the needs of meteorologists, while ornithologists pioneered the use of defence and air-traffic control radars to study bird migration.

    Radar observations of insects, however, were relatively sparse until the early 1960’s, when radar meteorologists became rather intensely interested in a type of warm-weather echo that appeared, puzzlingly from their perspective, when there was not a cloud in sight. Perhaps spurred by the meteorologists’ observations, entomologists began their own exploitation of the technology in 1968, when a rather modest radar, built by G.W. Schaefer specifically for insect observation and operated in West Africa just south of the Sahara, proved to be very effective.

Fonte: DRAKE, V.A. and REYNOLDS, D.R. Radar Entomology: Observing Insect Flight and Mi gration. CAB Internacional, 2012.

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What links Sir Isaac Newton, alien solar systems, and a new multi-million dollar TV show? The answer is “the three-body problem”: a conundrum in astronomy and mathematics that describes why it’s often difficult to predict the long-term trajectory of planets, moons and stars. So, what exactly is the problem? And how did it end up becoming the title of a TV series?

To understand, you first need to know a bit about the background to the TV show and its premise. The story is based on Liu Cixin’s epic sci-fi trilogy, The Remembrance of Earth’s Past, of which The Three-Body Problem is the first book. The original trilogy is characterised by the author’s attention to scientific detail. The adaptation is less so, but still crammed with scientific ideas.

The TV series focuses on the “Oxford Five”, who all studied under the same professor at the University of Oxford. Some have gone on to become scientists themselves (a postdoctoral physics researcher, a founder and chief scientific officer of a nano-tech company, and a theoretical physics academic), one has become a school physics teacher, while the fifth is now a snack-food entrepreneur. Scientific credentials abound.

The crux of the story is that an alien race — called the Trisolarans or San-Ti Ren — is headed to Earth to colonise it. Through intergalactic communication, these travellers attempt to intimidate human scientists into slowing down our rapid technological advancement, making Earth easier to conquer. But why are these aliens so hell-bent on taking over our planet in the first place? This is where the three-body problem comes in.

Bodies, in this context, is a scientific byword for planets, moons, suns or any other massive astronomical object. The extraterrestrials’ home planet is situated in a solar system with three suns, hence their name in the English translation of the book — the Trisolarans. This three-sun system can be highly unstable, making conditions difficult for life, hence the desire to travel across the Universe in order to inhabit our relatively stable Solar System. We only have one Sun, so Earth’s future is relatively predictable — at least for the next few million years.

Fonte: YATES, Kit. What is the three-body problem? The chaotic, cosmic mathematics behind the Netflix TV show. BBC, 2024. Disponível em: https://www.bbc.com/future/article/20240328-the-science-astronomy-and-mathematics-of-netflixs-3-body-problem-tv-show. Adaptado.

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What links Sir Isaac Newton, alien solar systems, and a new multi-million dollar TV show? The answer is “the three-body problem”: a conundrum in astronomy and mathematics that describes why it’s often difficult to predict the long-term trajectory of planets, moons and stars. So, what exactly is the problem? And how did it end up becoming the title of a TV series?

To understand, you first need to know a bit about the background to the TV show and its premise. The story is based on Liu Cixin’s epic sci-fi trilogy, The Remembrance of Earth’s Past, of which The Three-Body Problem is the first book. The original trilogy is characterised by the author’s attention to scientific detail. The adaptation is less so, but still crammed with scientific ideas.

The TV series focuses on the “Oxford Five”, who all studied under the same professor at the University of Oxford. Some have gone on to become scientists themselves (a postdoctoral physics researcher, a founder and chief scientific officer of a nano-tech company, and a theoretical physics academic), one has become a school physics teacher, while the fifth is now a snack-food entrepreneur. Scientific credentials abound.

The crux of the story is that an alien race — called the Trisolarans or San-Ti Ren — is headed to Earth to colonise it. Through intergalactic communication, these travellers attempt to intimidate human scientists into slowing down our rapid technological advancement, making Earth easier to conquer. But why are these aliens so hell-bent on taking over our planet in the first place? This is where the three-body problem comes in.

Bodies, in this context, is a scientific byword for planets, moons, suns or any other massive astronomical object. The extraterrestrials’ home planet is situated in a solar system with three suns, hence their name in the English translation of the book — the Trisolarans. This three-sun system can be highly unstable, making conditions difficult for life, hence the desire to travel across the Universe in order to inhabit our relatively stable Solar System. We only have one Sun, so Earth’s future is relatively predictable — at least for the next few million years.

Fonte: YATES, Kit. What is the three-body problem? The chaotic, cosmic mathematics behind the Netflix TV show. BBC, 2024. Disponível em: https://www.bbc.com/future/article/20240328-the-science-astronomy-and-mathematics-of-netflixs-3-body-problem-tv-show. Adaptado.

Convenções: Considere o sistema de coordenadas cartesiano, a menos que haja indicação contrária. Os eixos horizontal e vertical são indicados respectivamente por Ox e Oy, e o centro do sistema, por O.

N = {1; 2 ;3; .  .  .}: denota o conjunto dos números naturais.

R                         : denota o conjunto dos números reais.

i                           : denota a unidade imaginária, i2 = -1:

$\overline{AB}$                       : denota o segmento de reta de extremidades nos pontos A e B.

AB                       : denota a reta que passa pelos pontos A e B.

Convenções: Considere o sistema de coordenadas cartesiano, a menos que haja indicação contrária. Os eixos horizontal e vertical são indicados respectivamente por Ox e Oy, e o centro do sistema, por O.

N = {1; 2 ;3; .  .  .}: denota o conjunto dos números naturais.

R                         : denota o conjunto dos números reais.

i                           : denota a unidade imaginária, i2 = -1:

$\overline{AB}$                       : denota o segmento de reta de extremidades nos pontos A e B.

AB                       : denota a reta que passa pelos pontos A e B.

Convenções: Considere o sistema de coordenadas cartesiano, a menos que haja indicação contrária. Os eixos horizontal e vertical são indicados respectivamente por Ox e Oy, e o centro do sistema, por O.

N = {1; 2 ;3; .  .  .}: denota o conjunto dos números naturais.

R                         : denota o conjunto dos números reais.

i                           : denota a unidade imaginária, i2 = -1:

$\overline{AB}$                       : denota o segmento de reta de extremidades nos pontos A e B.

AB                       : denota a reta que passa pelos pontos A e B.

Convenções: Considere o sistema de coordenadas cartesiano, a menos que haja indicação contrária. Os eixos horizontal e vertical são indicados respectivamente por Ox e Oy, e o centro do sistema, por O.

N = {1; 2 ;3; .  .  .}: denota o conjunto dos números naturais.

R                         : denota o conjunto dos números reais.

i                           : denota a unidade imaginária, i2 = -1:

$\overline{AB}$                       : denota o segmento de reta de extremidades nos pontos A e B.

AB                       : denota a reta que passa pelos pontos A e B.