The Most Amazing Space Photos This Week!


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The Most Amazing Space Photos This Week!

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CALCULATE THE DISTANCE TO THE HORIZON USING DIFFERENTIATION — PRACTICE QUESTION


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CALCULATE THE DISTANCE TO THE HORIZON USING DIFFERENTIATION — PRACTICE QUESTION

By Mark Ryan

http://www.dummies.com/education/math/calculus/calculate-the-distance-to-the-horizon-using-differentiation-practice-question/

Have you ever looked at a distant horizon and wondered just how far away it was? Wonder no more! Now, you can use differentiation to solve this age-old problem.

Before you get started, though, take a moment to refresh your memory on tangents and normals:

  • At its point of tangency, a tangent line has the same slope as the curve it’s tangent to. In calculus, whenever a problem involves slope, you should immediately think derivative. The derivative is the key to all tangent line problems.

  • At its point of intersection to a curve, a normal line is perpendicular to the tangent line drawn at that same point. When any problem involves perpendicular lines, you use the rule that perpendicular lines have slopes that are opposite reciprocals. So all you do is use the derivative to get the slope of the tangent line, and then the opposite reciprocal of that gives you the slope of the normal line.

PRACTICE QUESTION

  1. The Earth has a radius of 4,000 miles. Say you’re standing on the shore and your eyes are 5 feet, 3.36 inches above the surface of the water. How far out can you see to the horizon before the Earth’s curvature makes the water dip below the horizon? (Refer to the following figure.)

    image0.png

ANSWER AND EXPLANATION

  1. The horizon is about 2.83 miles away.

    How do you get that? First, write the equation of the Earth’s circumference as a function of y.

    image1.png

    You can disregard the negative half of this circle because your line of sight will obviously be tangent to the upper half of the Earth.

    Now, express a point on the circle in terms of x:

    image2.png

    Take the derivative of the circle.

    image3.png

    Using the slope formula, set the slope of the tangent line from your eyes to

    image4.png

    equal to the derivative and then solve for x.

    Your eyes are

    image5.png

    above the top of the Earth at the point (0, 4,000) on the circle. Convert your height to miles; that’s exactly 0.001 miles (what an amazing coincidence!). So the coordinates of your eyes are (0, 4,000.001).

    image6.png

    Many people are surprised that the horizon is so close. What do you think?

‘Hand of God’ Spotted by NASA Space Telescope (Photo)


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‘Hand of God’ Spotted by NASA Space Telescope (Photo)

 http://www.space.com/24225-hand-of-god-photo-nasa-telescope.html
'Hand of God' Spotted by NASA Space Telescope (Photo)

The hand might look like an X-ray from the doctor’s office, but it is actually a cloud of material ejected from a star that exploded. NASA’s NuSTAR spacecraft has imaged the structure in high-energy X-rays for the first time, shown in blue. Lower-energy X-ray light previously detected by NASA’s Chandra X-ray Observatory is shown in green and red.

Credit: NASA/JPL-Caltech/McGill

Religion and astronomy may not overlap often, but a new NASA X-ray image captures a celestial object that resembles the “Hand of God.”

The cosmic “hand of God” photo was produced when a star exploded and ejected an enormous cloud of material, which NASA’s Nuclear Spectroscopic Telescope Array, or NuSTAR, glimpsed in high-energy X-rays, shown in blue in the photo. NASA’s Chandra X-ray Observatory had imaged the green and red parts previously, using lower-energy X-rays.

“NuSTAR’s unique viewpoint, in seeing the highest-energy X-rays, is showing us well-studied objects and regions in a whole new light,” NuSTAR telescopeprincipal investigator Fiona Harrison, of the California Institute of Technology in Pasadena, said in a statement.

The new image depicts a pulsar wind nebula, produced by the dense remnant of a star that exploded in a supernova. What’s left behind is a pulsar, called PSR B1509-58 (B1509 for short), which spins around 7 times per second blowing a wind of particles into material ejected during the star’s death throes.

As these particles interact with nearby magnetic fields, they produce an X-ray glow in the shape of a hand. (The pulsar is located near the bright white spot in the image but cannot be seen itself, NASA officials said.)

Scientists aren’t sure whether the ejected material actually assumes the shape of a hand, or whether its interaction with the pulsar’s particles is just making it appear that way.

“We don’t know if the hand shape is an optical illusion,” Hongjun An, of McGill University in Montreal, said in a statement. “With NuSTAR, the hand looks more like a fist, which is giving us some clues.”

The red cloud appearing at the fingertips is a separate structure called RCW 89. The pulsar’s wind may be heating the cloud to produce the low-energy X-ray glow, astronomers believe.

The X-ray energies seen by NuSTAR range from 7 to 25 kiloelectron volts, or keV, whereas the energies seen by Chandra range from 0.5 to 2 keV.

The Hand of God is an example of pareidolia, the psychological phenomenon of perceiving familiar shapes in random or vague images. Other common forms of pareidolia include seeing animals or faces in clouds, or the man in the moon. Despite its supernatural appearance, the Hand of God was produced by natural astrophysical phenomena.

Follow Tanya Lewis on Twitter and Google+Follow us @Spacedotcom, Facebook and Google+. Original article on SPACE.com.

THIS WOMAN GIVING BIRTH IN A STREAM HAS BEEN WATCHED OVER 54 MILLION TIMES (NSFW)


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THIS WOMAN GIVING BIRTH IN A STREAM HAS BEEN WATCHED OVER 54 MILLION TIMES (NSFW)

 http://decider.com/2016/07/21/watch-this-woman-give-birth-in-a-stream/

Typically, the miracle of birth is a very private affair, involving only the mother, father, and maybe a handful of doctors. Simone Thurbur is not a very typical person. Thurbur is a therapist and mother of four, but she’s probably best known for having more people than the entire population of California and New York City combined watch her give birth.

In an interview conducted by Haley Goldberg for SELF, Thurbur explained the reasoning behind the odd birthing choice. In 2012, Thurbur gave birth to her fourth child in a stream, completely unassisted. According to the interview, she had felt inspired by a video of Russian women giving birth in the Black Sea. Here’s the explanation in Thurbur’s own words:

“I just saw this footage and it was like my whole body responded and just went, ‘Oh my goodness … That feeling of connection to all of life is probably what hit me the most. We forget that we’re primal creatures and we can’t survive without the plants, and oxygen and trees and the water and sunshine…something spoke to me and I just wanted my child’s first experience when they came into life to see nature.”

Of course, the experience was slightly less crazy than it sounds. A week before Thurbur’s due date, she and her husband staked out the perfect stream in the Daintree Rainforest, and prior to going into labor, the couple contacted a local midwife and helicopter pilot in the area should anything go wrong. Eight hours of labor were filmed, and Thurber’s daughter, Perouze, was born healthy.

But we know what you’re interested in: What’s with this video and why has it been seen millions of times? Thurbur edited the birth down to a 22 minute video and posted it on YouTube in 2013. According to Thurbur, the video was posted to show what a normal and natural birth looks like. Currently, the video has over 54 million views and over 40,000 comments. The video comes with an inappropriate content warning, and it’s warranted. You see all parts of the mother. However, the exposing nature of the video doesn’t bother Thurbur. “There’s kind of this strange anonymity even though everyone’s seen me naked and it’s like, ‘Wow, that many people have seen my vagina and my butt hole,’ but it’s so removed from me,” she said.

Thurbur believes that people are drawn to the humanity and experience of the video. If this is an experience you want to have for yourself, then we’re not stopping you. Just make sure your boss isn’t watching before you press play.

Cops rescue naked lady perched on air conditioner


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Cops rescue naked lady perched on air conditioner

 http://nypost.com/2016/08/20/cops-rescue-nude-woman-perched-on-air-conditioner/

A nude and suicidal woman leaped from her fifth-story window in northern Manhattan on Saturday morning — but her life was saved when she landed two stories down onto an air conditioner.

Emergency Service Unit cops were able to coax the woman out of killing herself and pull her back into the building.

Modal Trigger
Photo: Tomas E. Gaston

“I think God just did this thing,” one witness said of the woman’s survival.

The late-morning drama unfolded along the brick side of an apartment building on Marble Hill Avenue in Marble Hill.

At first, “She wanted to jump out, but she didn’t,” the witness, neighbor Dahiana Rosario, 31, told The Post.

“At the beginning, her mom was holding her,” and trying to pull her inside, Rosario said.

“And she lost her hold,” Rosario said of the mother.

The unclothed woman then fell on top of an air conditioner jutting from a third-floor window above the building’s courtyard.

“She was sitting there,” Rosario said. “That’s where she stayed, thank God.”

Perched on the air conditioner, the woman began shouting in English and Spanish, Rosario said.

“She was saying that God is coming and everybody has to be better people, and we have to love each other,” Rosario said. “She was saying God loves us . . . and God loves everybody . . . and clean your house of bad things, bad energy.”

Neighbors called the police. They also put pillows and sofas outside beneath the air conditioner to cushion the woman’s fall in case she jumped.

The woman attempted to fight her rescuers, but they managed to pull her back in through the window.

Rescuers clothed the woman and then carried her from the building on a stretcher.

Modal Trigger
Photo: J.C. Rice

She was taken to North Central Bronx Hospital, where she will undergo a psychiatric evaluation, according to police.

The woman, whose name was not released, is not expected to be charged with a crime, law-enforcement sources said.

Earlier Saturday, an emotionally disturbed 36-year-old woman was pulled from the East River by firefighters after another apparent suicide attempt.

The woman had leapt into the waters from Grand Ferry Park near Grand Street in Williamsburg at about 6:45 a.m., cops said.

The FDNY’s Marine Unit No. 6 patrol boat spotted her, and its crew soon scooped her from the water.

But once she was on the boat, the woman broke free and jumped back into the water, witnesses said.

Pulled back on board a second time, she jumped right back in.

The woman was taken to Woodhull Hospital for observation.

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