Posted on by Ken Kremer

America’s Youth Christen NASA’s Twin New Lunar Craft – Ebb & Flow

Ebb and Flow - New Names for the GRAIL Twins in Lunar Orbit. 4th Grade Students from Montana win NASA’s contest to rename the GRAIL A and GRAIL B spacecraft. Artist concept of twin GRAIL spacecraft flying in tandem orbits around the Moon to measure its gravity field in unprecedented detail and unravel the hidden mysteries of the lunar interior’s composition. Credit: NASA/JPL Montage:Ken Kremer

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A classroom of America’s Youth from an elementary school in Bozeman, Montana submitted the stellar winning entry in NASA’s nationwide student essay contest to rename the twin GRAIL lunar probes that just achieved orbit around our Moon on New Year’s Eve and New Year’s Day 2012

“Ebb” & “Flow” – are the dynamic duo’s official new names and were selected because they clearly illuminate the science goals of the gravity mapping spacecraft and how the Moon’s influence mightily affects Earth every day in a manner that’s easy for everyone to understand.

“The 28 students of Nina DiMauro’s class at the Emily Dickinson Elementary School have really hit the nail on the head,” said GRAIL principal investigator Prof. Maria Zuber of the Massachusetts Institute of Technology in Cambridge, Mass.

“We asked the youth of America to assist us in getting better names.”

“We chose Ebb and Flow because it’s the daily example of how the Moon’s gravity is working on the Earth,” said Zuber during a media briefing held today (Jan. 17) at NASA Headquarters in Washington, D.C. The terms ebb and flow refer to the movement of the tides on Earth due to the gravitational pull from the Moon.

“We were really impressed that the students drew their inspiration by researching GRAIL and its goal of measuring gravity. Ebb and Flow truly capture the spirit and excitement of our mission.”

Leland Melvin, NASA Associate Administrator for Education, left, Maria Zuber, GRAIL Prinicipal Investigator at the Massachusetts Institute of Technology, and James Green, Director of the Planetary Science Division in the Science Mission Directorate at NASA Headquarters, right, applaud students from Emily Dickinson Elementary School in Bozeman, Mont. during a news conference, Tuesday, Jan. 17, 2012, at NASA Headquarters in Washington. Nine hundred classrooms and more than 11,000 students from 45 states, as well as Puerto Rico and the District of Columbia, participated in a contest that began in October 2011 to name the twin lunar probes. Credit: NASA/Paul E. Alers

Ebb and Flow are flying in tandem around Earth’s only natural satellite, the first time such a feat has ever been attempted.

As they fly over mountains, craters and basins on the Moon, the spaceships will move back and forth in orbit in an “ebb and flow” like response to the changing lunar gravity field and transmit radio signals to precisely measure the variations to within 1 micron, the width of a red blood cell.

The breakthrough science expected from the mirror image twins will provide unprecedented insight into what lurks mysteriously hidden beneath the surface of our nearest neighbor and deep into the interior.

The winning names from the 4th Graders of Emily Dickinson Elementary School were chosen from essays submitted by nearly 900 classrooms across America with over 11,000 students from 45 states, Puerto Rico and the District of Columbia, Zuber explained.

The students themselves announced “Ebb” and “Flow” in a dramaric live broadcast televised on NASA TV via Skype.

“We are so thrilled that our names were chosen and excited to share this with you. We can’t believe we won! We are so honored. Thank you!” said Ms. DiMauro as the very enthusiastic students spelled out the names by holding up the individual letters one-by-one on big placards from their classroom desks in Montana.

Watch the 4th Grade Kids spell the names in this video!

Until now the pair of probes went by the rather uninspiring monikers of GRAIL “A” and “B”. GRAIL stands for Gravity Recovery And Interior Laboratory.

The twin crafts’ new names were selected jointly by Prof. Zuber and Dr. Sally Ride, America’s first woman astronaut, and announced during today’s NASA briefing.


NASA’s naming competition was open to K-12 students who submitted pairs of names and a short essay to justified their suggestions.

“Ebb” and “Flow” (GRAIL A and GRAIL B) are the size of washing machines and were launched side by side atop a Delta II booster rocket on September 10, 2011 from Cape Canaveral, Florida.

They followed a circuitous 3.5 month low energy path to the Moon to minimize the fuel requirements and overall costs.

So far the probes have completed three burns of their main engines aimed at lowering and circularizing their initial highly elliptical orbits. The orbital period has also been reduced from 11.5 hours to just under 4 hours as of today.

“The science phase begins in early March,” said Zuber. At that time the twins will be flying in tandem at 55 kilometers (34 miles) altitude.

The GRAIL twins are also equipped with a very special camera dubbed MoonKAM (Moon Knowledge Acquired by Middle school students) whose purpose is to inspire kids to study science.

“GRAIL is NASA’s first planetary spacecraft mission carrying instruments entirely dedicated to education and public outreach,” explained Sally Ride. “Over 2100 classrooms have signed up so far to participate.”

Thousands of middle school students in grades five through eight will select target areas on the lunar surface and send requests for study to the GRAIL MoonKAM Mission Operations Center in San Diego which is managed by Dr. Ride in collaboration with undergraduate students at the University of California in San Diego.

By having their names selected, the 4th graders from Emily Dickinson Elementary have also won the prize to choose the first target on the Moon to photograph with the MoonKam cameras, said Ride.

Zuber notes that the first MoonKAM images will be snapped shortly after the 82 day science phase begins on March 8.

Ebb & Flow Achieve Lunar Orbit on New Year’s Weekend 2012
NASA’s twin GRAIL-A & GRAIL-B spacecraft are orbiting the Moon in this astrophoto taken on Jan. 2, 2012 shortly after successful Lunar Orbit Insertions on New Year’s Eve and New Year’s Day 2012.
Credit: Ken Kremer

Read continuing features about GRAIL and the Moon by Ken Kremer here:
Dazzling Photos of the International Space Station Crossing the Moon!
Two new Moons join the Moon – GRAIL Twins Achieve New Year’s Orbits
First GRAIL Twin Enters Lunar Orbit – NASA’s New Year’s Gift to Science
2011: Top Stories from the Best Year Ever for NASA Planetary Science!
NASA’s Unprecedented Science Twins are GO to Orbit our Moon on New Year’s Eve
Student Alert: GRAIL Naming Contest – Essay Deadline November 11
GRAIL Lunar Blastoff Gallery
GRAIL Twins Awesome Launch Videos – A Journey to the Center of the Moon
NASA launches Twin Lunar Probes to Unravel Moons Core
GRAIL Unveiled for Lunar Science Trek — Launch Reset to Sept. 10
Last Delta II Rocket to Launch Extraordinary Journey to the Center of the Moon on Sept. 8
NASAs Lunar Mapping Duo Encapsulated and Ready for Sept. 8 Liftoff
GRAIL Lunar Twins Mated to Delta Rocket at Launch Pad
GRAIL Twins ready for NASA Science Expedition to the Moon: Photo Gallery

Posted on by Tammy Plotner

Andromeda Dwarf Galaxies Help Unravel The Mysteries Of Dark Matter

The circled cluster of stars is the dwarf galaxy Andromeda 29, which University of Michigan astronomers have discovered. The bright star within the circle is a foreground star within our own Milky Way galaxy. This image was obtained with the Gemini Multi-Object Spectrograph at the Gemini North telescope in Hawaii. Credit: Gemini Observstory/AURA/Eric Bell

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Yep. It’s that time of year again. Time to enjoy the Andromeda Galaxy at almost every observing opportunity. But now, rather than just look at the nearest spiral to the Milky Way and sneaking a peak at satellites M32 and M110, we can think about something more when we peer M31’s way. There are two newly discovered dwarf galaxies that appear to be companions of Andromeda!

Eric Bell, an associate professor in astronomy, and Colin Slater, an astronomy Ph.D. student, found Andromeda 28 and Andromeda 29 by utilizing the Sloan Digital Sky Survey and a recently developed star counting technique. To back up their observations, the team employed data from the Gemini North Telescope in Hawaii. Located at 1.1 million and 600,000 light-years respectively, Andromeda XXVIII and Andromeda XXIX have the distinction of being the two furthest satellite galaxies ever detected away from the host – M31. Can they be spotted with amateur equipment? Not hardly. This pair comes in about 100,000 fainter than Andromeda itself and can barely be discerned with some of the world’s largest telescopes. They’re so faint, they haven’t even been classified yet.

“With presently available imaging we are unable to determine whether there is ongoing or recent star formation, which prevents us from classifying it as a dwarf spheroidal or a dwarf irregular.” explains Bell.

The dwarf galaxy Andromeda 29, which University of Michigan astronomers have discovered, is clustered toward the middle of this image, obtained with the Gemini North telescope in Hawaii. Credit: Gemini Observstory/AURA/Eric Bell

In their work – published in a recent edition of the edition of the Astrophysical Journal Letters – the team of Bell and Slater explains how they were searching for dwarf galaxies around Andromeda to help them understand how physical matter relates to theoretical dark matter. While we can’t see it, hear it, touch it or smell it, we know it’s there because of its gravitational influence. And when it comes to gravity, many astronomers are convinced that dark matter plays a role in organizing galaxy structure.

“These faint, dwarf, relatively nearby galaxies are a real battleground in trying to understand how dark matter acts at small scales,” Bell said. “The stakes are high.”

Right now, current consensus has all galaxies embedded in surrounding dark matter… and each “bed” of dark matter should have a galaxy. Considering the volume of the Universe, these predictions are pretty much spot on – if we take only large galaxies into account.

“But it seems to break down when we get to smaller galaxies,” Slater said. “The models predict far more dark matter halos than we observe galaxies. We don’t know if it’s because we’re not seeing all of the galaxies or because our predictions are wrong.”

“The exciting answer,” Bell said, “would be that there just aren’t that many dark matter halos.” Bell said. “This is part of the grand effort to test that paradigm.”

Right or wrong… pondering dark matter and dwarf galaxies while observing Andromeda will add a whole new dimension to your observations!

For Further Reading: Andromeda XXVIII: A Dwarf Galaxy more than 350 kpc from Andromeda and Andromeda XXIX: A New Dwarf Spheroidal Galaxy 200 kpc from Andromeda.

Posted on by Jerry Coffey

What did Isaac Newton Invent?

Classical Mechanics
Isaac Newton, Father of Classical Mechanics

Sir Issac Newton is best know for his laws of motion. Many people’s knowledge of his scientific contributions stops there. Issac Newtons inventions contributed a great deal to our current understanding of subjects from optics to theology and how early scientists were able to view their world.

In mathematics Isaac Newton inventions included laying the ground work for differential and integral calculus. His work was based on his insight that the integration of a function is merely the inverse procedure to differentiating it. Taking differentiation as the basic operation, he produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions.

Issac Newton inventions in mechanics and gravitation were summarized the Principia. His discoveries in terrestrial and celestial mechanics showed how universal gravitation provided an explanation of falling bodies on Earth and of the motions of planets, comets, and other bodies in the heavens. He explained a wide range of then unrelated phenomena: the eccentric orbits of comets, the tides and their variations, the precession of the Earth’s axis, and motion of the Moon as perturbed by the gravity of the Sun. This work includes Newton’s three famous laws of motion, fluid motion, and an explanation of Kepler’s laws of planetary motion.

Isaac Newton inventions in optics included his observation that white light could be separated by a prism into a spectrum of different colors, each characterized by a unique refractivity. He proposed the corpuscular theory of light. He was the first person to understand the rainbow. He was the first person to use a curved mirror in a telescope to prevent light form being broken up into unwanted colors.

Isaac Newton inventions and contributions to science were many and varied. They covered revolutionary ideas and practical inventions. His works in physics, mathematics and astronomy are still important today. His contributions in any one of these fields would have made him famous; taken as a whole, they make him truly outstanding.

We have written many articles about Isaac Newton’s inventions for Universe Today. Here’s an article about celestial mechanics, and here’s an article about Newton’s laws of motion.

If you’d like more info on Isaac Newton’s inventions, check out How Stuff Works for an interesting article about Isaac Newton’s inventions, and here’s a link to Isaac Newton’s Biography.

We’ve also recorded an entire episode of Astronomy Cast all about Gravity. Listen here, Episode 102: Gravity.

Sources:
How Stuff Works
University of Virginia
NASA

Posted on by Jon Voisey

Gravitational Redshifts: Main Sequence vs. Giants

Pleiades
The Pleiades, Anglo-Australian Observatory/Royal Observatory

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One of the consequences of Einsteins theories of relativity is that everything will be affected by gravitational potentials, regardless of their mass. The effect of this is observed in experiments demonstrating the potential for gravity to bend light. But a more subtle realization is that light escaping such a gravitational well must lose energy, and since energy for light is related to wavelength, this will cause the light to increase in wavelength through a process known as gravitational redshifting.

Since the amount of redshift is dependent on just how deeply inside a gravitational well a photon is when it starts its journey, predictions have shown that photons being emitted from the photosphere of a main sequence star should be more redshifted than those coming from puffed out giants. With resolution having reached the threshold to detect this difference, a new paper has attempted to observationally detect this difference between the two.

Historically, gravitational redshifts have been detected on even more dense objects such as white dwarfs. By examining the average amount of redshifts for white dwarfs against main sequence stars in clusters such as the Hyades and Pleiades, teams have reported finding gravitational redshifts on the order of 30-40 km/s (NOTE: the redshift is expressed in units as if it were a recessional Doppler velocity, although it’s not. It’s just expressed this way for convenience). Even larger observations have been made for neutron stars.

For stars like the Sun, the expected amount of redshift (if the photon were to escape to infinity) is small, a mere 0.636 km/s. But because Earth also lies in the Sun’s gravitational well the amount of redshift if the photon were to escape from the distance of our orbit would only be 0.633 km/s leaving a distance of only ~0.003 km/s, a change swamped by other sources.

Thus, if astronomers wish to study the effects of gravitational redshift on stars of more normal density, other sources will be required. Thus, the team behind the new paper, led by Luca Pasquini from the European Southern Observatory, compared the shift among stars of the middling density of main sequence stars against that of giants. To eliminate effects of varying Doppler velocities, the team chose to study clusters, which have consistent velocities as a whole, but random internal velocities of individual stars. To negate the latter of these, they averaged the results of numerous stars of each type.

The team expected to find a discrepancy of ~0.6 km/s, yet when their results were processed, no such difference was detected. The two populations both showed the recessional velocity of the cluster, centered on 33.75 km/s. So where was the predicted shift?

To explain this, the team turned to models of stars and determined that main sequence stars had a mechanism which could potentially offset the redshift with a blueshift. Namely, convection in the atmosphere of the stars would blueshift material. The team states that low mass stars made up the bulk of the survey due to their number and such stars are thought to undergo greater amounts of convection than most other types of stars. Yet, it is still somewhat suspect that this offset could so precisely counter the gravitational redshift.

Ultimately, the team concludes that, regardless of the effect, the oddities observed here point to a limitation in the methodology. Trying to tease out such small effects with such a diverse population of stars may simply not work. As such, they recommend future investigations target only specific sub-classes for comparison in order to limit such effects.

Posted on by Matt Williams

Precession of the Equinoxes

Semi Major Axis
Solstice and Equinox - Credit: NASA

When he was first compiling his famous star catalogue in the year 129 BCE the Greek astronomer Hipparchus noticed that the positions of the stars did not match up with the Babylonian measurements that he was consulting. According to these Chaldean records, the stars had shifted in a rather systematic way, which indicated to Hipparchus that it was not the stars themselves that had moved but the frame of reference – i.e. the Earth itself.

Such a motion is called precession and consists of a cyclic wobbling in the orientation of Earth’s axis of rotation. Currently, this annual motion is about 50.3 seconds of arc per year or 1 degree every 71.6 years. The process is slow, but cumulative, and takes 25,772 years for a full precession to occur. This has historically been referred to as the Precession of the Equinoxes.

The name arises from the fact that during a precession, the equinoxes could be seen moving westward along the ecliptic relative to the stars that were believed to be “fixed” in place – that is, motionless from the perspective of astronomers – and opposite to the motion of the Sun along the ecliptic.

This precession is often referred to as a Platonic Year in astrological circles because of Plato’s recorded remark in the dialogue of Timaeus that a perfect year could be defined as the return of the celestial bodies (planets) and the fixed stars to their original positions in the night sky. However, it was Hipparchus who is first credited with observing this phenomenon, according to Greek astronomer Ptolemy whose own work was in part attributed to him.

The precession of the Earth’s axis has a number of noticeable effects. First of all , the positions of the south and north celestial poles appear to move in circles against the backdrop of stars, completing one cycle every 25, 772 years. Thus, while today the star Polaris lies approximately at the north celestial pole, this will change over time, and other stars will become the “north star”. Second, the position of the Earth in its orbit around the Sun during the solstices, equinoxes, or other seasonal times slowly changes.

The cause of this was first discussed by Sir Isaac Newton in his Philosophiae Naturalis Principia Mathematica where he described it as a consequence of gravitation. Though his equations were not exact, they have since been revised by scientists and his original theory proven correct.

It is now known that precessions are caused by the gravitational source of the Sun and Moon, in addition to the fact that the Earth is a spheroid and not a perfect sphere, meaning that when tilted, the Sun’s gravitational pull is stronger on the portion that is tilted towards it, thus creating a torque effect on the planet. If the Earth were a perfect sphere, there would be no precession.

Today, the term is still widely used, but generally in astrological circles and not within scientific contexts.

We have written many articles about the equinox for Universe Today. Here’s an article about the astronomical perspective of climate change, and here’s an article about the Vernal Equinox.

If you’d like more info on Earth, check out NASA’s Solar System Exploration Guide on Earth. And here’s a link to NASA’s Earth Observatory.

We’ve also recorded an episode of Astronomy Cast all about Gravity. Listen here, Episode 102: Gravity.

Sources:
http://en.wikipedia.org/wiki/Axial_precession_%28astronomy%29
http://en.wikipedia.org/wiki/Chaldea
http://en.wikipedia.org/wiki/Ecliptic
http://en.wikipedia.org/wiki/Great_year
http://www.crystalinks.com/precession.html
http://en.wikipedia.org/wiki/Isaac_Newton

Reference:
NASA: Precession

Posted on by Jerry Coffey

What is Gravitational Force?

Why Do Planets Orbit the Sun
The Solar System

Newton’s Law of Universal Gravitation is used to explain gravitational force. This law states that every massive particle in the universe attracts every other massive particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This general, physical law was derived from observations made by induction. Another way, more modern, way to state the law is: ‘every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses’.

Gravitational force surrounds us. It is what decides how much we weigh and how far a basketball will travel when thrown before it returns to the surface. The gravitational force on Earth is equal to the force the Earth exerts on you. At rest, on or near the surface of the Earth, the gravitational force equals your weight. On a different astronomical body like Venus or the Moon, the acceleration of gravity is different than on Earth, so if you were to stand on a scale, it would show you that you weigh a different amount than on Earth.

When two objects are gravitational locked, their gravitational force is centered in an area that is not at the center of either object, but at the barycenter of the system. The principle is similar to that of a see-saw. If two people of very different weights sit on opposite sides of the balance point, the heavier one must sit closer to the balance point so that they can equalize each others mass. For instance, if the heavier person weighs twice as much as the lighter one, they must sit at only half the distance from the fulcrum. The balance point is the center of mass of the see-saw, just as the barycenter is the balance point of the Earth-Moon system. This point that actually moves around the Sun in the orbit of the Earth, while the Earth and Moon each move around the barycenter, in their orbits.

Each system in the galaxy, and presumably, the universe, has a barycenter. The push and pull of the gravitational force of the objects is what keeps everything in space from crashing into one another.

We have written many articles about gravitational force for Universe Today. Here’s an article about gravity in space, and here’s an article about the discovery of gravity.

If you’d like more info on Gravity, check out The Constant Pull of Gravity: How Does It Work?, and here’s a link to Gravity on Earth Versus Gravity in Space: What’s the Difference?.

We’ve also recorded an entire episode of Astronomy Cast all about Gravity. Listen here, Episode 102: Gravity.

Posted on by Fraser Cain

Ballistic Trajectory

The flight trajectory for the HEAT rocket. Credit: Copenhagen Suborbitals.

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Imagine you throw a ball as hard as you can. The ball flies through the air and lands some distance away. The harder you’re able to throw the ball, the further away it will land. When you throw the ball, it follows a ballistic trajectory, from where it takes off, to where it lands; its path is defined by the speed of its launch and the force of gravity pulling it down (and a little bit of atmospheric drag).

Now take this analogy further. Imagine you could throw the ball so hard that it flew all the way around the Earth and hit you on the back of the head. If you could throw the ball a little harder, it would go into orbit, continuously falling back to Earth, but with enough velocity to continue going around the planet. This speed is about 28,000 km/hour – it’s pretty hard to throw a ball that hard.

The first spacecraft were launched in a ballistic, or sub-orbital trajectory. They reached space, 100 km above the surface of the Earth, but they didn’t have enough energy to go into a true orbital trajectory. For example, the recently built SpaceShipOne doesn’t have any horizontal velocity. It travels straight up at a speed of about 1 km/s. Compare this to a low-Earth orbit escape velocity of 7.7 km/s. If a spacecraft is going to cover some horizontal distance, it needs have a maximum speed somewhere in between.

Spacecraft with a higher speed will travel along a ballistic trajectory. For example, the V2 rockets launched by Germany during World War II reached space and traveled about 330 km. Their maximum speed was 1.6 km/s. In intercontinental ballistic missile travels much faster, reaching a speed of 7 km/s and an altitude of 1200 km. Future intercontinental passenger flights might follow a similar trajectory.

We have written many articles about trajectory for Universe Today. Here’s an article about the Bolide, and here’s an article about the lunar orbit.

If you’d like more info on Trajectory, check out an article about Trajectories and Orbit, and here’s a link to Reduced Gravity Trajectory Page.

We’ve also recorded an entire episode of Astronomy Cast all about Gravity. Listen here, Episode 102: Gravity.

Posted on by Fraser Cain

What Is Terminal Velocity?

Skydiving
Skydiving

The higher you are when you jump, the more it hurts when you hit the ground. That’s because the Earth’s gravity is constantly accelerating you towards its center. But there’s actually a maximum speed you reach, where the acceleration of the Earth’s gravity is balanced by the air resistance of the atmosphere. The maximum speed is called terminal velocity.

The terminal velocity speed changes depending on the weight of the object falling, its surface area and what it’s falling through. For example, a feather doesn’t weigh much and presents a very large surface area to the air as it falls. So its terminal velocity speed is much slower than a rock with the same weight. This is why an ant can fall off a tall building and land unharmed, while a similar fall would kill you. Keep in mind that this process happens in any gas or fluid. So terminal velocity defines the speed that a rock sinks when you drop it in the water.

So, let’s say you’re a skydiver jumping out of an airplane. What’s the fastest speed you’ll go? The terminal velocity of a skydiver in a free-fall position, where they’re falling with their belly towards the Earth is about 195 km/h (122 mph). But they can increase their speed tremendously by orienting their head towards the Earth – diving towards the ground. In this position, the skydiver’s velocity increases to more than 400 km/h.

The world skydiving speed record is held by Joseph Kittinger, who was able to fall at a speed of 988 km/h by orienting his body properly and jumping at high altitude, where there’s less wind resistance.

The gravity of the Earth pulls at you with a constant acceleration of 9.81 meters/second. Without any wind resistance, you’ll fall 9.81 meters/second faster every second. 9.81 meters/second the first second, 19.62 meters/ second in the next second, etc.

The opposing force of the atmosphere is called drag. And the amount of drag force increases approximately proportional to the square of the speed. So if you double your speed, you experience a squaring of the drag force. Since the drag force is going up much more quickly than the constant acceleration, you eventually reach a perfect balance between the force of gravity and the drag force of whatever you’re moving through.

Outside the Earth’s atmosphere, though, there’s no terminal velocity. You’ll just keep on accelerating until you smash into whatever’s pulling on you.

We have written many articles about the terminal velocity for Universe Today. Here’s an article featuring the definition of velocity, and here’s an article about the X-Prize Entrant completing the Drop Test

If you’d like more info on the Terminal Velocity, check out a Lecture on Terminal Velocity, and here’s a link to a NASA article entitled, The Way Things Fall.

We’ve also recorded an entire episode of Astronomy Cast all about Gravity. Listen here, Episode 102: Gravity.

Sources:
NASA
Wikipedia
GSU Hyperphysics

Posted on by Jean Tate

Eccentricity

The eccentricity in Mars' orbit means that it is . Credit: NASA

When it comes to space, the word eccentricity nearly always refers to orbital eccentricity, or the eccentricity of the orbit of an astronomical body, like a planet, star, or moon. In turn, this relies on a mathematical description, or summary, of the body’s orbit, assuming Newtonian gravity (or something very close to it). Such orbits are approximately elliptical in shape, and a key parameter describing the ellipse is its eccentricity.

In simple terms, a circular orbit has an eccentricity of zero, and a parabolic or radial orbit an eccentricity of 1 (if the orbit is hyperbolic, its eccentricity is greater than 1); of course, if the eccentricity is 1 or greater, the ‘orbit’ is a bit of a misnomer!

In a planetary system with more than one planet (or for a planet with more than one moon, or a multiple star system other than a binary), orbits are only approximately elliptical, because each planet has a gravitational pull on every other one, and these accelerations produce non-elliptical orbits. And modeling orbits assuming the theory of general relativity describes gravity also leads to orbits which are only approximately elliptical (this is particular so for binary pulsars).

Nonetheless, orbits are nearly always summarized as ellipses, with eccentricity as one of the key orbital parameters. Why? Because this is very convenient, and because deviations from ellipses can be easily described by small perturbations.

The formula for eccentricity, in a two-body system under Newtonian gravity, is relatively easy to write, but, unfortunately, beyond the capabilities of the HTML coding of this webpage.

However, if you know the maximum distance of a body, from the center of mass – the apoapsis (apohelion, for solar system planets), ra – and the minimum such distance – the periapsis (perihelion), rp – then the eccentricity, e, of the orbit is just:

E = (ra – rp)/( ra+ rp)

Eccentricity of an Orbit (UCAR), Eccentricity of Earth’s Orbit (National Solar Observatory), and Equation of Time (University of Illinois) are websites with more on eccentricity.

Universe Today articles on eccentricity? Sure! For example: Measuring the Moon’s Eccentricity at Home, Buffy the Kuiper Belt Object, and Lake Asymmetry on Titan Explained.

Two Astronomy Cast episodes in which eccentricity is important are Neptune, and Earth; well worth listening to.

Posted on by Jean Tate

Gravity Formula

The gravity formula that most people remember, or think of, is the equation which captures Newton’s law of universal gravitation, which says that the gravitational force between two objects is proportional to the mass of each, and inversely proportional to the distance between them. It is usually written like this (G is the gravitational constant):

F = Gm1m2/r2

Another, common, gravity formula is the one you learned in school: the acceleration due to the gravity of the Earth, on a test mass. This is, by convention, written as g, and is easily derived from the gravity formula above (M is the mass of the Earth, and r its radius):

g = GM/r2

In 1915, Einstein published his general theory of relativity, which not only solved a many-decades-long mystery concerning the observed motion of the planet Mercury (the mystery of why Uranus’ orbit did not match that predicted from applying Newton’s law was solved by the discovery of Neptune, but no hypothetical planet could explain why Mercury’s orbit didn’t), but also made a prediction that was tested just a few years’ later (deflection of light near the Sun). Einstein’s theory contains many gravity formulae, most of which are difficult to write down using only simple HTML scripts (so I’m not going to try).

The Earth is not a perfect sphere – the distance from surface to center is smaller at the poles than the equator, for example – and it is rotating (which means that the force on an object includes the centripetal acceleration due to this rotation). For people who need accurate formulae for gravity, both on the Earth’s surface and above it, there is a set of international gravity formulae which define what is called theoretical gravity, or normal gravity, g0. This corrects for the variation in g due to latitude (and so both the force due to the Earth’s rotation, and its non-spherical shape).

Here are some links that you can follow to learn more about gravity formulae (or gravity formulas): Newton’s theory of “Universal Gravitation” (NASA), International Gravity Formula(e) (University of Oklahoma), and Newton’s Law of Gravity (University of Oregon).

Many aspects of gravity, including a gravity formula or three, are covered in various Universe Today articles. For example, New Research Confirms Einstein, Milky Way Dwarf Galaxies Thwart Newtonian Gravity?, and Modifying Gravity to Account for Dark Matter. Here’s some information on 0 gravity.

Astronomy Cast’s episode Gravity gives you much more on not just one gravity formula, but several; and Gravitational Waves is good too. Be sure to check them out!

Sources:
University of Nebraska-Lincoln
NASA
UT-Knoxville