Tidal Forces and Black Holes

Tidal forces on Earth are caused by the uneven gravitational pull from the moon (and less from the sun) on opposite sides of the planet. But what are tidal forces like for objects near a black hole, a celestial object we are unable to see or explore?

The information scientists have collected on black holes is based on the influence black holes have on objects around them. The force of gravity within a black hole is so strong that not even light can escape. This is because they consist of such high amount of mass within such a small space. Visit Nasa’s website to read more about the science behind black holes.

An artist’s rendition of a Black Hole, courtesy of Curiosity

The Roche Limit is the minimum distance a satellite can keep from a center mass before the central body’s tidal forces overcome the orbiting body’s internal gravitational forces. Basically, this is how close you can get before you are ripped apart by tidal forces.

Many scientists have hypothesized about what would happen to a person if he or she were to approach a black hole. This hypothesis is called spaghettification: the person would be stretched and ultimately ripped apart, much like a piece of spaghetti. This process would happen again and again, creating successively smaller pieces of your body. Because the gravitational force is so strong within a black hole, the difference in the tug from the black hole on a person’s head and feet would be immense. According to SpaceMath, “the difference in acceleration between the head and feet could be thousands of Earth gravities.” The tidal forces caused by a black hole are much, much more significant than those of the moon. So stay clear of a black hole unless you like spaghetti so much you wish to become it.

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Gravity’s Effect On Everything

Gravitational Effects Around Earth

Gravity has an affect on nearly everything in the entire universe. From galaxies, to solar systems, to planets and their moons, and even on the planets themselves (like the tides), if there are objects with mass then gravity is present. Newton’s Universal Law of Gravitation explains the effect of gravity between objects. Newton’s Law says that all objects with mass attracts other objects with mass (called gravity), the gravitational force between two masses is directly proportional to their product (doubling one mass doubles force of gravity between the objects), and the force of gravity decreases with the square of the distance between the objects. Through this law we see that all objects with mass effect the force of gravity between other objects. Even though all objects attract each other with some force we do not always feel the effect (i.e. the force of us on a book) because these masses are so small that the force is not strong enough to move either object. However, with much larger objects with exponentially higher masses that our own bodies the force of gravity is than increased, for example the gravity between the sun and the earth. The sun is so massive that the force between it and the earth is so great that the sun pulls it (along with all the other objects in our solar system) into orbit. Even more impressive than this is that our entire solar system orbits around the center of the Milky Way Galaxy, meaning that there is an object with such an enormous mass in the center of our galaxy that it pulls our entire solar system in orbit even though there is an unfathomable distance from our solar system to the center our galaxy (26,000 light-years). It is incredible to see the different effects that the force of gravity can have on the large objects within our universe.

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Gravity-Assists in Reverse

Gravity assist maneuvers are incredibly useful for sending spacecraft far into space. The maneuver is like a skiing parent using a pole to give their kid a boost. The parent loses a bit of momentum, but leverage their larger size to quickly speed their kid up. The same is true for a gravity assist. There, instead of firing boosters to go directly to some far away place, the spacecraft flies towards a closer-by planet. Then, the spacecraft orbits around the planet, leveraging its gravity to launch it further into deep space. New Horizons was able to gain an additional 14,000 km/hr in velocity with a gravity assist around Jupiter.

But the laws of physics dictate that energy and momentum must be conserved. So, Jupiter slows down very slightly as the spacecraft speeds up. Effectively, the spacecraft is stealing some of Jupiter’s momentum and its energy. But this raises an interesting question: what would happen if you tried to do this in reverse? Gravity assists typically have the spacecraft and planet travel in the same direction (counter-clockwise). But if the spacecraft is orbiting in the opposite direction as the planet, can you send the spacecraft faster in one direction and the planet faster in the other? That would preserves momentum. But, if both increase their velocities, both would seem to have more energy, which would violate the laws of physics.

Unfortunately, there aren’t many good public-source orbital simulators that involve inter-planetary transfers. So I had to use the next best thing: Kerbal Space Program. KSP is a video game that uses a very basic model to simulate orbits. It assumes that every object is orbiting only one other object, and ignores the effect of other nearby planets. After all, in real life, the Moon’s distance from the Sun is very similar to the Earth’s distance from the Sun. So, you can get a good estimate of the Moon’s location by looking at its position relative to Earth as a function only of the Earth’s gravity, and then tracking the Sun’s effect on Earth separately.

So, using KSP, I did my best to plan a maneuver to do a reverse-gravity assist. Here are a series of pictures showing the gravity-assist I attempted:

This was the beginning orbit, on course to be intercepted by the Moon (or, in KSP, the “Mun”). Important to note are its velocity and altitude: 2799.2m/s at an altitude of 243,190m. Source: KSP
This is the spacecraft in its orbit, about to enter the Moon’s sphere of influence. Source: KSP
This was the orbital trajectory of the spacecraft as its was captured by the Moon. Source: KSP
This is the final orbit. Notably, the velocity increased (∆v = 6.9m/s) even at the higher altitude (∆d = 158m). Source: KSP

The maneuver did, technically, work. The spacecraft went faster despite its higher altitude. But it wasn’t close to the magnitude of effect from a traditional gravity-assist. And with a change in velocity of only 6.9m/s, KSP’s physics engine may have just shown something that a more accurate engine would show couldn’t happen. But it is worth noting that the spacecraft is further from the planet than the Moon when it enters the Moon’s sphere of influence. This yields a possibility: that the spacecraft accelerated towards the planet and the Moon accelerated away from the planet. This would decrease the Moon’s orbital velocity, conserving energy and momentum.

Fundamentally, though, I wanted to answer a simple question: could you do the sort of gravitational assist that’s typically possible if the spacecraft and planet orbit in opposite directions? And I got an answer: basically, no.

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Light is Everything

I watched a Crash Course video on light that proved to be really helpful and informative.

After watching this video, I realized the importance of spectroscopy and understood what light actually is. The scientific term for light is actually electromagnetic radiation, and even humans emit them. Once again, the video touched upon the wavelength spectrum. I always thought that the difference in wavelengths between radio and gamma rays would be relatively small. However, the wavelengths of radio waves are actually the size of buildings, while the wavelengths of gamma rays are around the size of atomic nuclei. Later, I learned that since different atoms emit different colors of light, we can measure what an object is made of with instruments, even if we can’t touch that object. This allows us to know that Jupiter has methane in its atmosphere, while Venus has carbon dioxide. We can also use light to measure distances. Similar to the Doppler effect for sound, If objects are moving towards you, then the light wavelengths get compressed. If they are moving away from you, the light wavelengths get longer. We can use this principle to determine whether celestial objects are moving towards or away from us. By doing so, we have discovered that the universe is expanding, as well as other pertinent information such as the fact that other galaxies are on collision courses.

Since almost all the information we get from our universe comes in the form of light, I have now realized the significance of spectroscopy in astronomy. Without it, we would not know much of what we now know today about the universe.

A better representation of the differences in wavelength
Picture from NASA

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Telescopes and Space

I don’t know about you, but without my glasses, I literally cannot see anything, even if it’s right in front me. Whether I’m sitting in the classroom trying to take notes from the professor’s lecture or trying to watch my favorite Netflix show, my ability to actually see anything with my naked eye is severely impaired. Now, when I’m able to actually use my glasses, I can actually see things. It doesn’t matter whether it’s the board in class or the TV screen — using the lenses to bend the light around my eyes, my glasses are able to change the light rays entering my eye in such a way that allows me better sight than I would have without them.What’s crazy is how the concepts used to create glasses can be applied on a much larger scale to allow us to view objects much further away than a TV screen or a whiteboard.

Telescopes, or optical devices that magnify distant objects through the use of particularly-arranged curved lenses and mirrors, allow astronomers to peer through Space and observe all that it has to offer. More specifically, telescopes can be typified by their two most fundamental characteristics — light-collecting area (how much light the telescope can collect at a given time) and angular resolution (the smallest angle we can differentiate two distinct dots. Additionally, the different types of lenses and mirrors used in specifically different arrangements allow experts to create fundamentally different types of telescopes. From the textbook, we know about both refracting telescopes (glass lens collects and focuses light) and reflecting telescopes (precisely curved mirror gathering light, secondary mirror reflects the collected light). A graphic demonstrating how they actually work in shown below.

reflect
This picture represents the differences between reflection and refraction. It can be found (and explained) at the following link.

And, it gets even more interesting when we throw the telescopes into space (Earth’s orbit) — this allows the telescope to avoid electromagnetic radiation, it reduces other atmospheric influences / side effects, and it mitigates light pollution from around Earth. Even though they’re more expensive and difficult to maintain, space telescopes allow astronomers to see beyond our Solar System into the Observable Universe.

It would be remiss not to mention the most known and relevant telescope to this article post — the Hubble Space Telescope. The first major optical telescope put into space, Hubble represents one of the biggest pieces of innovatory machinery in modern astronomy. Not only has it made more than 1.3 million observations since it was deployed to Earth’s orbit — it generates roughly 10 terabytes of Science-related data per year, it is the length of a full school bus, and it is stupidly powerful and accurate (according to NASA, it can see in a way akin to “seeing a pair of fireflies in Tokyo that are less than 10 feet apart from Washington, DC”). And, as a reflecting telescope, it uses mirrors larger and heavier than any human being that ever existed.

hubblespacetelescope
This is a picture of the Hubble Space Telescope. This picture and more information about the Hubble Space Telescope can be found at the following link.

A picture of the Hubble Space Telescope can be seen above. At the end of the day, it really is just mirrors, solar panels, communications hardware, and lots of very finely tuned pieces of metal!

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Telescopes

Digital Trends

Telescopes have been an essential instrument in the history of astronomy. So much has been learned and will be learned through the use of them. Although, they all have the same general function, telescopes can come in many shapes, sizes, and types. The two main types of telescopes are the refractor and reflecting telescopes. In a refactor telescope, a piece of glass known as the objective lens gathers light and focuses it onto the eyepiece lens, which enlarges the image for our eye to see. Galileo used this type of telescope to see the moons of Jupiter and the phases of Venus. On the other hand, a reflector telescope has two mirrors rather than the refractor’s two lens. One curved mirror reflects the incoming light from a distant object onto a tiny, flat mirror which in turn reflects the light to the eyepiece. Isaac Newton is credited for inventing the reflecting telescope. Reflecting telescopes are the most popular telescopes used for research purposes.

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Thom & Stone Circles

Alexander Thom was a Scottish engineer who, later in his life, became curious about megalithic monuments, specifically the stone circles of the British Isles and France. He was interested in the prehistoric peoples that built them, and any astronomical meaning behind their construction.  His first interpretation of the sites suggested that megalithic yards were used as a standardized prehistoric measurement. He visited over five hundred megalithic sites throughout his researching years and developed ways to classify sites of varying shapes and sizes. Thom’s studies eventually lead to theories about the sites being used to predict eclipses and model solar and stellar alignments. This research actually provided a foundation for Archaeoastronomy.  He published several works detailing specific observations and results from his years of research. One important conclusion he made was that the prehistoric man’s calendar derived declinations fairly close to information known at the time of research.  Although his research was met with resistance and conflict, Thom ended up forming the standards for fieldwork in Archaeoastronomy, and his practices are still used in the field today.

Long Meg and Her Daughters, an example of a megalithic site

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Apparent Retrograde Motion: what it is, and what it isn’t

One thing that must be said right away: retrograde motion is not the same thing as apparent retrograde motion. Retrograde motion generally denotes ‘backwards’ motion, and the specifics depend on how the term is being used. A retrograde orbit refers to an object orbiting in the opposite direction that the thing it orbits around is spinning (see image below).

An animation depicting retrograde orbit. Author/Source: Anynobody, user on Wikipedia

Retrograde rotation refers to an object rotating on its axis in a direction opposite to the motion of its own orbit. For example, when visualizing the orbit of the planets as seen from above the North Pole of the Sun, the planets all orbit the Sun counterclockwise, and most also rotate on their axes counterclockwise; however, Venus rotates on its axis in a clockwise direction, and thus exhibits retrograde rotation.

Apparent retrograde motion refers to the phenomenon that a planet begins moving backwards (e.g. from east to west, rather than west to east) across the sky, as seen from the surface of Earth.

Apparent Retrograde motion of Mars in 2003.
Author/Source: Eugene Alvin Vilar, via Wikipedia

This occurs because, simply put, the Earth is catching up to and ‘lapping’ the other planet during their orbits. As Earth passes the other planet in its orbit, the other planet appears to move backwards. Retrograde motion is something that is observed over the course of weeks or months, as a planet changes place in the sky in relation to the stars, constellations, and other objects in the night sky (that is to say, it is not at all observable overnight). An important thing to keep in mind is that apparent retrograde motion is only apparent. The planet in the sky is not actually moving ‘backwards’ at any point, it simply appears to be in relation to how Earth itself is moving.

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Retrograde motion probably isn’t ruining your life

It seems that anytime Mercury enters its period of retrograde motion, the Internet starts freaking out because according to astrologers, Mercury retrograde is bad for communication. Although this is a nice scapegoat for any misfortune one might encounter, there is no scientific evidence that this phenomenon has an effect on your day-to-day life. So what is retrograde motion?

While the planets we see in the sky usually appear to move eastward through the stars, sometimes they reverse course (as shown by Mars in the figure below), moving westward for a period before continuing along their eastward path. These periods can span from weeks to months, depending on the planet. For early astronomers who believed that the Earth was the center of the universe, retrograde motion was a difficult issue to explain. But now that we know that the planets in our solar system orbit around the Sun, retrograde motion has a simple explanation! As the Earth moves along its orbit around the Sun and passes planets with slower orbits, those slower planets (like Mars) appear to move backwards relative to Earth. Picture this: you’re driving down the highway and passing the slower cars on your right. As you’re catching up to and passing the slower cars, they appear to move backwards. So, like the slower moving cars on a highway, the planets that undergo this apparent change in direction aren’t actually moving backwards. This apparent motion is caused by our vantage point on Earth as we pass these planets. Thus, retrograde motion is just an optical phenomenon caused by the different speeds of the planets as they complete their orbits around the Sun. And probably isn’t the reason for any of the bad things in your life.

By Eugene Alvin Villar (seav) – Own work, CC BY-SA 4.0


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Blog 2: When is the Best Time to Surf?

When’s the right time grab your surfboard and hit the beach? High tides cause closeouts, which blocks a surfer’s path, and low tides cause slow-rolling waves, which are low frequency and high amplitude waves. Ideally, you want to surf during mid tide conditions. But first, what causes these changes in tide?

Tides are caused by the “differences in gravitational pulls of the Moon and Sun between near and far sides of the Earth,” (Pogge, 2007). However, the effect of the Sun’s gravitational pull on Earth’s tides are approximately 46% of the Moon’s effect on tides. This is because the Sun is 390 times further from the Earth than the Moon. Therefore, the difference of gravitational pull of the Moon from the near side to far side of the Earth impacts the tides the most. The effect is a “bulge” in Earth’s waters being pulled toward the Moon on the side in line with the Moon, or pushed away from the Moon on the far side of Earth. This causes high tide. High tide occurs every 12 hours as the Earth rotates 360-degrees in a single day. Additionally, since the Moon is orbiting the Earth, the times for high tides and low tides in a given location will change by 50 minutes every day.

During a New Moon or Full Moon, the tides are 20% higher in high tide regions and 20% lower in low tide regions. This is caused by the perfect alignment between the Moon, Earth, and Sun, causing extreme tides. Using “Rule of Twelfths” you can find the perfect time to go surfing.

In order to understand the “Rule of Twelfths,” we first need to understand the tempo of the tides. When the tide reaches the highest point, it slows down before changing directions into low tide. At its halfway point, the tides have reached its maximum speed. This maximum speed occurs two times a day as there are two high tides and two low tides in a day, approximately 6 hours apart from each other. In the first hour, the “water level rises by 1/12th of the total range,” (Carey, 2013) then rises by 2/12ths of the total tide in the second hour, then rises by 3/12th in the third and fourth hours, then 2/12ths the fifth hour, and lastly rises by 1/12th the sixth hour. The pattern is 1, 2, 3, 3, 2, 1. Clearly, during mid tide the rise is the fastest at 3/12ths in the third and fourth hours, which is how you can determine this is the best time to surf, avoiding closeouts from high tides and slow-rolling waves during low tides. Note that the “Rule of Twelfths” only applies to the semi-diurnal tide, a “tide having two high waters and two low waters during a tidal day,” which occurs in most locations.

To conclude, understanding the effect the Moon has on Earth’s tides during the day can allow someone to plan their perfect surf session. By applying the “Rule of Twelfths” to your understanding of the difference gravitational pull on Earth by the Moon, you can surf during ideal mid tide conditions.

References:

Pogge, Richard. “Lecture 20: Tides.” GPS and Relativity, The Ohio State University, 14 Oct. 2007, http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html.

“How Do the Moon and Sun Affect Tides and Surfing?” SurferToday, SurferToday, http://www.surfertoday.com/surfing/how-do-the-moon-and-sun-affect-tides-and-surfing.

“How Do the Moon and Sun Affect Tides and Surfing?” IndoSurfLife.com, 30 Sept. 2011, indosurflife.com/2011/09/how-do-the-moon-and-sun-affect-tides-and-surfing/.

Carey, Teresa. “Understanding the Rule of Twelfths for Tide Prediction.” Sail Magazine, 12 Apr. 2013, http://www.sailmagazine.com/cruising/understanding-the-rule-of-twelfths-for-tide-prediction.

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