Dropping things can be fun. Dropping things in a vacuum is even cooler. You might think that dropping things in a giant vacuum chamber would be the ultimate in coolness. Well, it’s close. In fact, this is the best feather and heavy object dropping video. Yes, astronaut David Scott dropped a hammer and feather in a much larger vacuum chamber – the moon. Heavier Objects Don’t Hit the Ground First I’ve already covered the common ideas about dropping objects. In general, most people think that heavier objects should fall faster than lighter objects. Really, what they mean is that heavier objects should fall with a greater acceleration than light objects, but they like to say “faster”. Here is the short answer. If there is no air resistance, after you let go of an object the only force on it is the gravitational force. The gravitational force is proportional to the mass of the object. More massive objects have a greater gravitational force. The acceleration of an object is proportional to the net force on the object and inversely proportional to the mass of the object. Let me write this mathematically. See. The masses cancel. Mass doesn’t matter even though matter is made of mass (physics pun). Also, I wrote these equations as scalar instead of vectors just to make it look simpler. The Bowling Ball and Feather in Real Speed The bowling ball and feather drop in the BBC Human Universe video looks awesome. However, they ran the shot in slow motion to make it look more dramatic. Wouldn’t in be cool to see it in real time? I think I can make that happen. Normally, I would take a video like this and find the real frame rate. I’ve done this before with some of the MythBusters videos. The basic idea is to look at a falling object. Since you know the acceleration should be -9.8 m/s2, you can just find the correct frame rate to give you that acceleration. It’s pretty simple. However, that doesn’t work in this case. The problem here is that there are two things I don’t know. I don’t know the distance scale and I don’t know the frame rate. This means I need another strategy. Luckily, the video shows the same bowling ball and feather dropping with air and in real time. I can use that to find the scale of the video. In this case, I will use the close up shot that shows the bowling ball and I will find the diameter. If I use a bowling ball diameter of 21.59 cm, the falling ball seems to have the correct acceleration. Here is a plot of the vertical motion of that first fall. The term in front of 2 in the fitting equation would be 1/2 of the acceleration. So, a coefficient of -4.73 would give an acceleration of 9.46 m/s2. This isn’t 9.8 m/s2 like I would expect, but it’s close enough. I can also get the total falling time from the video with a value of 2.04 seconds. This means that I can solve for the drop height of the ball. However, I ignored the air resistance on the bowling ball during this drop. Is that ok? Let’s say the ball has a mass of 6 kg. If you then create a numerical calculation for a falling ball both with and without air resistance, you get a time difference of just 0.048 seconds. Yes, you can try this calculation for yourself (as a homework exercise). Moving on to the slow motion video (without air), I get the following plot for the vertical position of the bowling ball. This gives an acceleration of 0.018 m/s2 – but that’s not a real second, that’s a fake second (since the video isn’t in real time). If I call this time unit s’, I can set this acceleration equal to 9.8 m/s2 (real seconds here) and solve for the relationship between real and fake time. This means the slow motion video would have to be recorded at 580 frames per second instead of 25 frames per second. Perfect. Now I just need to increase the speed. Here’s what that would look like. Pretty cool, right? Ok. I admit that I cheated a little bit. I used iMovie to speed up the video and there is a default “20x” speed increase so I used that. Yes, it’s not 23 times faster but it still looks better.

]]>Does the moon have significantly different gravity depending on

]]>The test of any scientific law is our verification of its anticipations. A people, superstitious and ignorant of every scientific law, wondered to see Him do what He did. The scientific law of atavism is a guarantee of resurrection. In defining our problem, therefore, we find ourselves under the influence of a scientific law of development. An explanation by superior powers, by spirits, by occult virtues, seemed clearer to them than an explanation by scientific law. For, as he tells you, facts establish a scientific law—law in the mouths of scientific men, meaning an established order of facts. Nobody ever perceived a scientific law of nature by intuition, nor arrived at a general rule of duty or prudence by it. The enormous number of new facts brought to light by manipulating hypotheses could not but modify our view of scientific law. For the essence of a scientific law is the expression of a relation. It is essential, then, to the existence of a scientific law that there should be uniformity of phenomena.

]]>Fg = force due to gravity between the two objects (N) G = the Gravitational Constant m1 and m2 = the two masses (kg) r = the distance between the two objects’ centres (m) This formula shows that any objects with mass will pull towards each other with a gravitational force. You might have heard the phrase in a Social Studies class. It usually refers to one country having a political or military influence over another. We usually say that an object has a gravitational field around it. Any field is just a sphere of influence around the object. The closer you get, the more you are affected by it. In the case of gravity, the bigger the mass of the object, the bigger the field. The formula also shows that the closer the objects are, the greater the effect of the gravitational field. This is the first formula that you'll see from a family of formulas called the "inverse square formulas". They all look pretty much the same, and lead physicists to believe that there are many common connections and relationships throughout all of physics. Newton then turned his attention to trying to find the value for the Gravitational Constant, “G”. Nope, it isn’t the acceleration due to gravity on Earth, 9.81m/s2. Newton looked for a way of calculating the value for G from the formula above. If we solve that formula for G we get: Let’s look at how we will substitute numbers into this formula. Newton realized that the only thing he could measure a Fg for would be an object on Earth’s surface. An example would be you. We could calculate the force due to gravity on your body easily using Fg = mg. We need to know the distance from the centre of the Earth to your centre… which we do have: 6.38e6 m. And yup, they even had a pretty good estimate of this in Newton's time! We need to know your mass, which would be m1… that’s no problem. The last thing we need, m2, is the mass of the Earth. Oh, oh. That one is a problem. In Newton’s time no one had any idea how heavy the Earth really was. If we knew G, then we could calculate the mass of the Earth, but that’s what we are trying to calculate here! Newton continued to look for some way to calculate G indirectly, but never found a way. Cavendish's Torsion Balance He attached a really heavy pair of metal balls to the ends of a long metal rod, and then hung the rod from a wire. He then brought another pair of really heavy metal balls near the balls on the rod. Cavendish knew that because they had mass they should pull on each other, but very weakly. To measure this weak pull, he carefully measured how much the wire was twisting (torque) whenever he brought the other masses near by. This is why the device he used is called a torsion balance. After a lot of very careful, very tedious tries, he found that G was 6.67e-11Nm2/kg2. Cavendish realized that because he knew the value for G, he could now calculate the mass of the Earth. That’s why he titled the paper that he published “Weighing the Earth.” Example 1: Using values that you now know, Determine the mass of the Earth. We know that the force exerted on my body by the Earth is Fg = mg, where little “m” is my mass. I also know that the force could be found using Newton's big Universal Gravitation Formula, where one mass is a little “m” (my mass), and the other mass is a big “Me” (the mass of the Earth). Fg = Fg Me= 5.99e24 kg Notice that we were able to combine a couple of formulas to get the new formula . Me does not always have to be the mass of the Earth. It could be the mass of the moon, Mars, an asteroid, whatever! It let’s you calculate the acceleration due to gravity on that object if you know the other values. Example 2: The planet Mars has a mass of 6.42e23 kg and a radius (from its centre to the surface) of 3.38e6 m. How much would a 60 kg person weigh on Mars compared to their weight on Earth? Determine How heavy he would “feel” he weighed in kilograms on Mars. On Earth the person has a weight of… Fg = mg = (60kg) (9.81m/s2) Fg = 5.9e2 N Gravity on Mars can be found using the formula shown above. Note: On an exam you need to show how you got this formula. g = 3.75m/s2 So that person’s weight on Mars will be… = (60kg) (3.75m/s2) Fg = 2.3e2 N Remember, mass never truly changes... it's a constant. This is just how much you would feel like, in measurements you can better understand. To figure out how much he would feel like he weighed on Mars in kilograms, remember that we spend our lives here on Earth and our body thinks that 9.81m/s2 is what gravity should always be. Therefore, this person will feel like his mass is… m = Fg / g = (2.3e2 N) / (9.81m/s2) m = 23 kg Example 3: Determine the force of attraction between a 15.0kg box and a 63.0 kg person if they are 3.45m apart. I have to assume that the distance I have been given is the distance between the two centres of the objects.

]]>Where G if Newton's gravitational constant, is the mass of the object being pulled on by the Moon, MMoon is the mass of the Moon, and rMoon is the distance between the Moon and the object. A similar force acts between the Earth and various objects, except that we use the distance to the Earth, rEarth, and the mass of the Earth, MEarth, in place of the lunar values. Since the Earth's force on something is the object's weight, W, we can write MMoon / MEarth is about 1/80, and for an object at the surface of the Earth rEarth is about 4000 miles, while rMoon is about 240, 000 miles, or 60 times greater; so at the surface of the Earth the pull of the Moon is 80 times smaller than the object's weight because of its lesser mass, and another 3600 (= 60 squared) times smaller because of its greater distance. Combining these two effects, the Moon's pull on objects near the Earth is only 1/300, 000th of their Earth weight . So if something weighs 150 pounds due to the pull of the Earth, the pull of the Moon on that object would be about 150/300000, or 1/2000th of a pound. This is a very small force but it produces a number of interesting effects because it acts on every object near the Earth, including the Earth itself. What does this force do? (most of what follows will be considerably revised, being too incomplete to leave as-is) (2) Tidal Effects (incomplete first draft) Gravitational Interactions of the Earth and Moon: Barycentric Motion describes the effect of the Moon's gravity on the Earth as a whole. But there is a second effect, due to the fact that if you are on the "front" side of the Earth (the side where the Moon is up), you are closer to the Moon than if you are on the "back" side of the Earth (the side where the Moon is down), and given the inverse square nature of the Law of Gravity, this means that you are pulled on harder when the Moon is up than when it is down. This produces what are referred to as differential forces, or because of their observable effect, tidal forces. On the side of the Earth facing the Moon you are as much as 1/60th closer to the Moon than if you were in the middle of the Earth, producing a force which is 1/30th larger than average. On the side of the Earth facing away from the Moon, you are as much as 1/60th further away from the Moon than if you were in the middle of the Earth, producing a force which is 1/30th smaller than average. So on the near side, you are pulled by a force which is 1/300, 000th of your weight, which moves you around the barycenter every month, AND by an additional force equal to 1/30th of this, or 1/10, 000, 000th of your weight, which tends to pull you away from the rest of the Earth. And on the far side, you are pulled on this much less than the rest of the Earth, which tends to pull the rest of the Earth away from you. KEEP IN MIND that at the Equator, where things seem to weigh 1/3% less than at the Poles because of the Coriolis effect of the Earth's rotation, the Earth bulges out by about 1/3%. In other words, it bulges out by a fraction of its radius approximately equal to the apparent reduction in weight. IF THE SAME THING happened with the differential force = tidal force of the Moon, the 1/10, 000, 000th difference in force on different parts of the Earth would make various parts of the Earth deviate from their normal position by 1/10, 000, 000th of the radius of the Earth, which is about half a meter, or 1 1/2 feet. And on the average, that is exactly what happens in some places; but the actual tides involve a number of other factors, so they can differ from this simple result by a considerable amount.

]]>NIST has taken part in a new push to address a persistent and growing problem in physics: the value of G. The Newtonian constant of gravitation, used to calculate the attractive force of gravity between objects, is more than 300 years old. But although scientists have been trying to measure its value for centuries, G is still only known to 3 significant figures. By contrast, other constants have been measured with much greater precision; the mass of the electron in kilograms, for example, is known to about 8 digits.i On October 9-10, 2014, several dozen scientists from around the world gathered at NIST to consider their options. "We're all here because we have a problem with G – and I mean, boy, do we have a problem with G, " said Carl Williams, Chief of PML's Quantum Measurement Division, to the assembled group on the first morning of the meeting. "This has become one of the serious issues that physics needs to address." The gravitational constant is familiarly known as "big G" to distinguish it from "little g, " the acceleration due to the Earth's gravity.ii Despite its name, big G is tiny – about 6.67 x 10-11 m3 kg-1 s-2 – and comparatively feeble, roughly a trillion trillion trillion times weaker than the electromagnetic force responsible for affixing souvenir magnets to refrigerators. And its weakness makes it difficult to measure. Experimentalists have used a variety of approaches – swinging pendulums, masses in freefall, balance beams, and torsion balances that measure the torque or rotation of wires supporting masses that are attracted to other masses. But a plot of all the results from the past 15 years reveals a relatively wide spread in values ranging from about 6.67 x 10-11 m3 kg-1 s-2. Furthermore, CODATA – the International Council for Science Committee on Data for Science and Technology, which analyzes the results of individual experiments and provides an internationally accepted sets of values for fundamental physical constants – has had to increase the uncertainty on its latest recommendation for a value of G due to the divergence of the experiments.iii At the NIST workshop, the 53 participants agreed unanimously that something should be done. They recommended that one or more organizations establish annual or biannual meetings focused specifically on the campaign to determine big G's value with greater accuracy, and they supported the idea of focusing on new approaches to the measurement, such as the atomic interferometry setup used in a recent experiment involving laser-cooled rubidium atoms.iv The main culprit in these discrepancies is suspected to be systematic uncertainties in the measurements, and much of the discussion focused on reducing noise. One way to address this problem, participants felt, is for different teams to conduct independent experiments using the same set of apparatus. Two groups with particularly deviant results offered their equipment during the meeting, pending discussions with the teams that will reuse the resources. Workshop attendees expressed moderate interest in forming a consortium, an organization that would centralize the process of finding consensus. A potential benefit of a consortium would be providing NIST and other National Measurement Institutes (NMIs) with a means of contributing support, for example in the form of precision length metrology services, to members. "Clearly, there is no right answer for how to move forward, " Williams said. "But there is international support around resolving the big G controversy, and so it's a great time for us in that regard." Explore further: NIST 'noise thermometry' system measures Boltzmann constant More information: i The mass of an electron is 9.109 382 91(40) x 10-31 kg, where the number in parentheses indicates uncertainty in the final two digits. ii Calculating the gravitational attraction between two objects requires taking the product of two masses and dividing by the square of the distance between them, then multiplying that value by . The equation is = Gm 12/2. iii CODATA's latest set, released in 2010, recommended a value for of 6.673 84(80) x 10-11 m3 kg-1 s-2 compared to its previous result from 2006 of 6.674 28(67) x 10-11 m3 kg-1 s-2. The values in parentheses indicate standard uncertainty (based on standard deviation), in this case plus or minus 0.000 80 x 10-11 m3 kg-1 s-2 and plus or minus 0.000 67 x 10-11 m3 kg-1 s-2 respectively. iv In this experiment, researchers pushed two clouds of cold rubidium atoms into a vacuum chamber with laser light. The atoms accelerated differently depending on the placement of high-density masses (tungsten weights totaling about 500 kg) arranged in various configurations. Differences in acceleration due to the atoms' gravitational attraction to the tungsten masses could be picked up in the clouds' interference pattern. G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli and G.M. Tino. Precision measurement of the Newtonian gravitational constant using cold atoms. Nature . Vol. 510. 518–521. June 26, 2014. DOI: 10.1038/nature13433

]]>In this lesson, you will learn what gravitational potential is, the equation we use to calculate it, and how to use that equation. We'll look at some real life examples so you can see how it works. A short quiz will follow. Click "next lesson" whenever you finish a lesson and quiz. Got It You now have full access to our lessons and courses. Watch the lesson now or keep exploring. Got It You're 25% of the way through this course! Keep going at this rate, and you'll be done before you know it. Way to go! If you watch at least 30 minutes of lessons each day you'll master your goals before you know it. Go to Next Lesson Take Quiz Congratulations on earning a badge for watching 10 videos but you've only scratched the surface. Keep it up! Go to Next Lesson Take Quiz You've just earned a badge for watching 50 different lessons. Keep it up, you're making great progress! Go to Next Lesson Take Quiz You have earned a badge for watching 20 minutes of lessons. You have earned a badge for watching 50 minutes of lessons. You have earned a badge for watching 100 minutes of lessons. You have earned a badge for watching 250 minutes of lessons. You have earned a badge for watching 500 minutes of lessons.

]]>How does the universe work? Understanding the universe's birth and its ultimate fate are essential first steps to unveil the mechanisms of how it works. This, in turn, requires knowledge of its history, which started with the Big Bang. Previous NASA investigations with the Cosmic Microwave Background Explorer (COBE) and the Wilkinson Microwave Anisotropy Probe (WMAP) have measured the radiation from the universe when it was only 300, 000 years old, confirming theoretical models of its early evolution. With its improved sensitivity and resolution, ESA's Planck observatory probed the long wavelength sky to new depths during its 2-year survey, providing stringent new constraints on the physics of the first few moments of the universe. Moreover, the possible detection and investigation of the so-called B-mode polarization pattern on the Cosmic Microwave Background (CMB) impressed by gravitational waves during those initial instants will provide clues for how the large-scale structures we observe today came to be. Observations with the Hubble Space Telescope and other observatories showed that the universe is expanding at an ever-increasing rate, implying that some day - in the very distant future - anyone looking at the night sky would see only our Galaxy and its stars. The billions of other galaxies will have receded beyond detection by these future observers. The origin of the force that is pushing the universe apart is a mystery, and astronomers refer to it simply as "dark energy". This new, unknown component, which comprises ~68% of the matter-energy content of the universe, will determine the ultimate fate of all. Determining the nature of dark energy, its possible history over cosmic time, is perhaps the most important quest of astronomy for the next decade and lies at the intersection of cosmology, astrophysics, and fundamental physics. Knowing how the laws of physics behave at the extremes of space and time, near a black hole or a neutron star, is also an important piece of the puzzle we must obtain if we are to understand how the universe works. Current observatories operating at X-ray and gamma-ray energies, such as the Chandra X-ray Observatory, NuSTAR, Fermi Gamma-ray Space Telescope, and ESA's XMM-Newton, are producing a wealth of information on the conditions of matter near compact sources, in extreme gravity fields unattainable on Earth.

]]>In 1998, two teams of astronomers discovered that, instead of slowing down, the universe is expanding faster today than it was in earlier epochs Adam Riess Adam Riess thought there must have been a mistake. In late 1997, he was analyzing observations of exploding stars to help determine whether the universe would expand forever, or would someday reverse course and collapse in on itself. His observations seemed to show that not only would the universe continue to expand, but also that it was expanding faster as it got older — something that no one expected. Riess, who is now an astronomer at Johns Hopkins, double-checked his figures, and found there was no mistake. Something was pushing down on the universe's gas pedal, making it expand faster. For want of a better name, that 'something' was identified as dark energy. Riess was a member of one of two teams that made the same basic discovery. The other was headed by Saul Perlmutter of the University of California, Berkeley. Their discovery stunned scientists because it indicated that their understanding of the universe was far from complete — that some unknown force was counteracting gravity and pushing galaxies away from each other. Astronomers, physicists, and others continue to try to identify the cause of the accelerating universe. "The universe is not slowing down enough to come to a halt, and in fact it's not slowing at all, but it's speeding up, and that was obviously the big surprise at the end of '97, when we saw these results." — Saul Perlmutter Looking for Exploding Stars Both teams were examining a class of exploding stars known as Type Ia supernovae. These stars are white dwarfs — the hot, dense, dead cores of stars that were once similar to the Sun — with close stellar companions. The white dwarf 'steals' hot gas from its companion. The gas piles up, forming a superhot layer atop the white dwarf. When the gas pushes the star past a critical mass, it sets off a runaway nuclear explosion that blasts the star to bits. For a while, the supernova can outshine an entire galaxy of normal stars, so it's easy to see these exploding stars even in distant galaxies. The ability to see Type Ia supernovae far across the universe makes them good "standard candles" — a way to measure distances to other galaxies. All Type Ia supernovae brighten and fade in a predictable way. Measuring how long it takes a supernova to brighten and then fade reveals its true brightness. By comparing a star's true brightness to how bright it looks in our sky, astronomers can find its distance. One more step completes the picture. Astronomers measure how fast the star is moving away from Earth by measuring its redshift — a stretching of its light waves by the expansion of the universe itself. Hubble Space Telescope images show supernovae (arrows) in three distant galaxies. [P. Garnavich (CfA)/High-z Supernova Search Team/NASA] Pedal to the Metal By putting together the distances and speeds of many supernovae, the two teams hoped to show how the expansion of the universe had changed over the eons. Most astronomers expected one of two outcomes. If the universe contained enough stars, gas, planets, and other matter, and this material were packed tightly enough, then gravity would slow the expansion and eventually reverse it. In that case, the universe would end with a Big Crunch — the opposite of the Big Bang in which it was born. If, on the other hand, the universe contained less matter, then the universe would continue to expand forever, although the expansion would grow slower with time. Riess was analyzing observations made by the High-z Supernova Search Team, while Perlmutter led the Supernova Cosmology Project. Both teams observed several supernovae over several years. They used small telescopes to look at large patches of sky at different times, then compared the pictures to see if a supernova had appeared in any of the galaxies in their field of view. When a supernova appeared, they used larger telescopes to study the explosions in detail. Improved technology yielded supernovae that were up to 9 billion light-years away, which is much farther than earlier searches. Key Discoveries About the Expanding Universe After collecting their data, Riess ran a computer program that calculated how much mass was required to account for how quickly the universe was slowing down. The computer's answer was a negative number — in other words, negative mass. There's no such thing as negative mass, though, so Riess basically flipped the answer over. He realized that the computer was telling him that the expansion of the universe wasn't slowing down, but instead was getting faster. Perlmutter's team reached the same conclusion, and the teams published their findings in 1998. Science magazine named their discovery the 'Breakthrough of the Year' for 1998, and hundreds of other scientists jumped into the fray — beginning the effort to understand dark energy.

]]>Physics is based on the assumption that certain fundamental features of nature are constant. Some constants are considered to be more fundamental than others, including the velocity of light c and the Universal Gravitational Constant, known to physicists as Big G. Unlike the constants of mathematics, such as p, the values of the constants of nature cannot be calculated from first principles: they depend on laboratory measurements. As the name implies, the physical constants are supposed to be changeless. They are believed to reflect an underlying constancy of nature, part of the standard assumption of physics that the laws and constants of nature are fixed forever. Are the constants really constant? The measured values continually change, as I show in my book ( in the UK). They are regularly adjusted by international committees of experts know as metrologists. Old values are replaced by new "best values", based on the recent data from laboratories around the world. Within their laboratories, metrologists strive for ever-greater precision. In so doing, they reject unexpected data on the grounds they must be errors. Then, after deviant measurements have been weeded out, they average the values obtained at different times, and subject the final value to a series of corrections. Finally, in arriving at the latest "best values", international committees of experts then select, adjust and average the data from an international selection of laboratories. Despite these variations, most scientists take it for granted that the constants themselves are really constant; the variations in their values are simply the result of experimental errors. The oldest of the constants, Newton's Universal Gravitational Constant, known to physicists as Big G, shows the largest variations. As methods of measurement became more precise, the disparity in measurements of G by different laboratories increased, rather than decreased. Between 1973 and 2010, the lowest average value of G was 6.6659, and the highest 6.734, a 1.1 percent difference. These published values are given to at least 3 places of decimals, and sometimes to 5, with estimated errors of a few parts per million. Either this appearance of precision is illusory, or G really does change. The difference between recent high and low values is more than 40 times greater than the estimated errors (expressed as standard deviations). What if G really does change? Maybe its measured value is affected by changes in the earth's astronomical environment, as the earth moves around the sun and as the solar system moves within the galaxy. Or maybe there are inherent fluctuations in G. Such changes would never be noticed as long as measurements are averaged over time and averaged across laboratories. In 1998, the US National Institute of Standards and Technology published values of G taken on different days, revealing a remarkable range. On one day the value was 6.73, a few months later it was 6.64, 1.3% lower. (The references for all the data cited in this blog are given in Science Set Free / The Science Delusion .)

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