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Dark Matter and Galaxy Rotation
Some of the strongest evidence that dark matter exists comes from measuring the speed of stars as they orbit around the center of their galaxy.

In a solar system, planets further out move more slowly in their orbit because they feel a weaker gravity force from their sun. It was expected that stars in a galaxy would behave the same way - those further away from the center would move more slowly. This is because most of the galaxy’s stars are in the core, making the core act somewhat like the sun in a solar system.

Instead, in almost all galaxies, the star orbit speed is is near constant out to very large distances. The only explanation seems to be that each galaxy is enveloped in a vast cloud of dark matter that interacts with ordinary matter only through gravity. The dark matter increases the gravity force on the outer stars, resulting in higher orbit speeds than they would have otherwise.

Calculations indicate that the dark matter has about 5 times the mass of all the stars in a galaxy.

#gravity #physics


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The Moon, Earth’s Protector
The Earth has a mass about 81 times that of the Moon. As a fraction of planet mass, this makes our moon by far the largest in the solar system. Jupiter, by comparison, is about 13,000 times the mass of its moon Ganymede.

Our moon’s size has given the Earth a good bit of protection from asteroids, some of which could have wiped out life had they hit the Earth.

The animation shows the Moon interacting with an actual object called J002E3, starting in April, 2002. By June, 2003, the moon had deflected the object away from the Earth. J002E3 was actually the upper stage of one of the Apollo Moon rockets, but it could just as well have been an asteroid.

The dinosaurs may wish to point out that this protection does not always work.

Animation source: JPL/NASA
#gravity #physics #moon

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The Orbit of a planet is an ellipse, with the Sun at one focus
This is Kepler’s First Law. It applies not just to planets, but to comets and asteroids, and to moons or satellites orbiting a planet.

The animation shows the general form of the law, as discovered by Newton: two bodies in orbit each move in an ellipse, with a focus of each ellipse at the center of mass of the two. The center of mass itself does not move.
With our solar system, the Sun is so much more massive than any planet that the center of mass is inside the Sun, and the only motion we see is the planet’s elliptical motion, with the Sun effectively at rest. In the animation, one mass is half the other, as might be the case with a binary star system.

When Johannes Kepler announced this law in 1609, he overturned 2,000 years of belief that all motion in the sky had to be circular. Kepler himself originally had a bias for circular motion, and Carl Sagan said that we could date the beginning of modern science with when Kepler overcame that bias. In Sagan’s words:

When he found that his long-cherished beliefs did not agree with the most precise observations, he accepted the uncomfortable facts. He preferred the hard truth to his dearest illusions. That is the heart of science.

#astronomy #gravity

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Orbit Precession
The elliptical orbit of a satellite or moon does not stay fixed at the same place in space. Instead, the orbit shifts, or precesses, as shown in the animation.

The precession of the orbit would not happen if the planet were a perfect sphere. For a sphere, the gravitational force on the satellite decreases as the square of the distance from the planet’s center, and Newton’s laws require that the satellite’s orbit is a simple, stationary, ellipse.

However, no planet is perfectly spherical. The Earth, for example, is slightly flattened at the poles because of the centrifugal force of its rotation. For a non-spherical planet, the gravity force has additional term, one that decreases as the cube of the distance.

This additional term becomes significant when the satellite’s orbit brings it close to the planet (that is, when R is small). Then, the extra term adds a bit to the inverse square force, which makes the orbit “bend” more than for a pure elliptical shape. The effect is that the next orbit is turned counter clockwise relative to the preceding orbit.

#gravity #physics

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The Hodograph
An object in an elliptical orbit moves faster as it gets closer to the parent body, then slows down as it gets further away (Kepler’s Second Law). The effect is shown in the left side of the animation for two different elliptical orbits. Note that the velocity vectors are longer (higher speed) as the orbit becomes lower.

One quite surprising property of these velocity vectors is shown on the right side. If the vectors are placed so that they have a common starting point, their tips always form a circle.

In general, when any object is in motion, and we arrange its velocity vectors in this way, the result is called the velocity space diagram of the motion. It’s a good way to show how the object’s speed and direction changes over time. The tips of the velocity vectors trace out a curve that is called the hodograph of the motion. Only elliptical motion in a gravity field produces a circular hodograph.

#gravity #physics

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Gravity Waves and Software
When the discovery of gravity waves was announced recently, I happened to have just read the book The Perfect Theory by Pedro Ferreira. It was published two years ago, and is a popular history of the General Theory of Relativity.

The book includes a dramatic back story to the discovery of gravity waves. As the detector was being planned and built, the physicists knew that the easiest gravity waves to detect would be those that came from the merger of two black holes. However, to separate the signal from the background noise, they needed to know exactly what the gravity wave signal should look like. This required that Einstein’s equations be applied to the merger of black holes, and the task proved to be extremely difficult. For 30 years, teams of programmers and physicists tried to solve the problem. Millions of dollars were spent on supercomputers, with little result. One physicist said there seemed to be only two possible outcomes – the programmer would kill himself, or the computer would blow up.

Finally, in 2005, a lone South African physicist named Frans Pretorius succeeded. To simulate the last half second of the event, his computer model ran for three months on a supercomputer. The end result was the red line shown in the graphic - the signature of the gravity waves. The gray line shows the wave that was actually detected, in nearly perfect agreement with theory. Pretorius’ model even allows the mass of the black holes to be inferred from slight variations in the signal.

Without the Pretorius work, the 1.1 billion dollar experiment could have been in some jeopardy. Perhaps he will be remembered when the Nobel Prize is awarded.

#physics #gravitywaves


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Black Holes and Hypervelocity Stars
Beginning in 2005, a few stars have been discovered which are moving at extraordinary velocities – 1000 km per second or so. At this speed, they will easily escape the Milky Way’s gravity, and continue into the space between galaxies.

No ordinary mechanism could accelerate something as massive as a star up to these speeds, but there is a plausible way this could happen. It involves the supermassive black hole at the center of the galaxy.
The animation shows the sequence:

1. An ordinary binary star system (two stars in orbit around each other) happen to wander near the supermassive black hole.
2. The pair falls inward toward the black hole. As they approach the black hole, the pair is moving at very high velocity.
3. Near the black hole, the intense gravity causes a “tidal disruption”, separating the pair, with one going into orbit around the black hole.
4. By the conservation of energy principle, the pair’s total energy before the encounter must equal their total energy after. Because the captured star (red) is now moving slower (lower energy), the blue star gains energy, and flys away at high speed.

This scenario is called the Hills Mechanism, after physicist Jack Hills, who worked out the mathematics in 1988, and predicted that they would be discovered eventually. And now they have.

Note that some hypervelocity stars could even be from an other galaxy – a sort of intergalactic bullet fired by the other galaxy’s black hole, and the star happens to be passing through our Milky Way. A planet on such a star could even spread life between galaxies.

Animation source:

#physics #gravity #hypervelocitystars

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Jupiter and the Asteroids
Most asteroids orbit peacefully between Mars and Jupiter. However, many asteroids have orbits that have been determined by Jupiter’s massive gravity.

The Trojans (green) share Jupiter’s orbit, and are always about 60 degrees ahead of, or behind, Jupiter. These are the Lagrangian points L4 and L5. At these points, the gravity of Jupiter and the Sun balance out, forming a sort of gravity island. L4 and L5 are stable, meaning that an asteroid that strays from the precise balance point will tend to return to that point.

The Hildas (red) are in a 3:2 resonance with Jupiter – they complete 3 orbits for every 2 orbits of Jupiter.
Their orbits are eccentric, and arranged so that when they overtake Jupiter, they are closest to the Sun (and therefore furthest from Jupiter). The helps to prevent Jupiter’s gravity from disrupting their orbits.
The effect is that Jupiter “herds” them around the Sun, while they stay in a roughly triangular shape.

Near Earth Asteroids (not shown) have orbits that bring them close to the Earth. Almost all of these have been tossed out of the asteroid belt because of gravity interactions with Jupiter. One such asteroid caused the dinosaurs to have a very bad day.

#physics #gravity #asteroid

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A Possible Triple Star System

This is a computer simulation of three stars orbiting in a figure 8 pattern.

No system like this has actually been discovered, though some astronomers believe that there may be one or more of these per galaxy.

A planet around one of the stars would experience some  very strange daylight and dark patterns.

#gravity #stars
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This simulation of the Milky Way - Andromeda collision is, I believe, the one used in episode 3 of the Cosmos TV series. Presumably, it is from a supercomputer simulation, but I could not track down the source.
Andromeda vs. Milky way galaxy collision

The Milky Way and Andromeda galaxy are on a collision course! In about 3 billion years, the two galaxies will collide. Then over a span of 1 billion years or so after a very complex gravitational dance, they will merge to form an elliptical galaxy.
Video link: Galaxy Collision- The Milky Way vs Andromeda!
Original source:

#Galaxy   #Collision  
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