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Key concepts and summary

Calculating the gravitational interaction of more than two objects is complicated and requires large computers. If one object (like the Sun in our solar system) dominates gravitationally, it is possible to calculate the effects of a second object in terms of small perturbations. This approach was used by John Couch Adams and Urbain Le Verrier to predict the position of Neptune from its perturbations of the orbit of Uranus and thus discover a new planet mathematically.

For further exploration

Articles

Brahe and Kepler

Christianson, G. “The Celestial Palace of Tycho Brahe.” Scientific American (February 1961): 118.

Gingerich, O. “Johannes Kepler and the Rudolphine Tables.” Sky&Telescope (December 1971): 328. Brief article on Kepler’s work.

Wilson, C. “How Did Kepler Discover His First Two Laws?” Scientific American (March 1972): 92.

Newton

Christianson, G. “Newton’s Principia : A Retrospective.” Sky&Telescope (July 1987): 18.

Cohen, I. “Newton’s Discovery of Gravity.” Scientific American (March 1981): 166.

Gingerich, O. “Newton, Halley, and the Comet.” Sky&Telescope (March 1986): 230.

Sullivant, R. “When the Apple Falls.” Astronomy (April 1998): 55. Brief overview.

The Discovery of Neptune

Sheehan, W., et al. “The Case of the Pilfered Planet: Did the British Steal Neptune?” Scientific American (December 2004): 92.

Websites

Brahe and Kepler

Johannes Kepler: His Life, His Laws, and Time: http://kepler.nasa.gov/Mission/JohannesKepler/. From NASA’s Kepler mission.

Johannes Kepler: http://www.britannica.com/biography/Johannes-Kepler. Encyclopedia Britannica article.

Johannes Kepler: http://www-history.mcs.st-andrews.ac.uk/Biographies/Kepler.html. MacTutor article with additional links.

Noble Dane: Images of Tycho Brahe: http://www.mhs.ox.ac.uk/tycho/index.htm. A virtual museum exhibit from Oxford.

Newton

Sir Isaac Newton: http://www-groups.dcs.st-and.ac.uk/~history//Biographies/Newton.html. MacTutor article with additional links.

Sir Isaac Newton: http://www.luminarium.org/sevenlit/newton/newtonbio.htm. Newton Biography at the Luminarium.

The Discovery of Neptune

Adams, Airy, and the Discovery of Neptune: http://www.mikeoates.org/lassell/adams-airy.htm. A defense of Airy’s role by historian Alan Chapman.

Mathematical Discovery of Planets: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Neptune_and_Pluto.html. MacTutor article.

Videos

Brahe and Kepler

“Harmony of the Worlds.” This third episode of Carl Sagan’s TV series Cosmos focuses on Kepler and his life and work.

Tycho Brahe, Johannes Kepler, and Planetary Motion: https://www.youtube.com/watch?v=x3ALuycrCwI. German-produced video, in English (14:27).

Newton

Beyond the Big Bang: Sir Isaac Newton’s Law of Gravity: http://www.history.com/topics/enlightenment/videos/beyond-the-big-bang-sir-isaac-newtons-law-of-gravity. From the History Channel (4:35).

Sir Isaac Newton versus Bill Nye: Epic Rap Battles of History: https://www.youtube.com/watch?v=8yis7GzlXNM. (2:47).

The Discovery of Neptune

Richard Feynman: On the Discovery of Neptune: https://www.youtube.com/watch?v=FgXQffVgZRs. A brief black-and-white Caltech lecture (4:33).

Collaborative group activities

  1. An eccentric, but very rich, alumnus of your college makes a bet with the dean that if you drop a baseball and a bowling ball from the tallest building on campus, the bowling ball would hit the ground first. Have your group discuss whether you would make a side bet that the alumnus is right. How would you decide who is right?
  2. Suppose someone in your astronomy class was unhappy about his or her weight. Where could a person go to weigh one-fourth as much as he or she does now? Would changing the unhappy person’s weight have any effect on his or her mass?
  3. When the Apollo astronauts landed on the Moon, some commentators commented that it ruined the mystery and “poetry” of the Moon forever (and that lovers could never gaze at the full moon in the same way again). Others felt that knowing more about the Moon could only enhance its interest to us as we see it from Earth. How do the various members of your group feel? Why?
  4. [link] shows a swarm of satellites in orbit around Earth. What do you think all these satellites do? How many categories of functions for Earth satellites can your group come up with?
  5. The Making Connections feature box Astronomy and the Poets discusses how poets included the most recent astronomical knowledge in their poetry. Is this still happening today? Can your group members come up with any poems or songs that you know that deal with astronomy or outer space? If not, perhaps you could find some online, or by asking friends or roommates who are into poetry or music.

Thought questions

Is it possible to escape the force of gravity by going into orbit around Earth? How does the force of gravity in the International Space Station (orbiting an average of 400 km above Earth’s surface) compare with that on the ground?

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What is the momentum of an object whose velocity is zero? How does Newton’s first law of motion include the case of an object at rest?

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Evil space aliens drop you and your fellow astronomy student 1 km apart out in space, very far from any star or planet. Discuss the effects of gravity on each of you.

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A body moves in a perfectly circular path at constant speed. Are there forces acting in such a system? How do you know?

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As friction with our atmosphere causes a satellite to spiral inward, closer to Earth, its orbital speed increases. Why?

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Use a history book, an encyclopedia, or the internet to find out what else was happening in England during Newton’s lifetime and discuss what trends of the time might have contributed to his accomplishments and the rapid acceptance of his work.

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Two asteroids begin to gravitationally attract one another. If one asteroid has twice the mass of the other, which one experiences the greater force? Which one experiences the greater acceleration?

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How does the mass of an astronaut change when she travels from Earth to the Moon? How does her weight change?

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If there is gravity where the International Space Station (ISS) is located above Earth, why doesn’t the space station get pulled back down to Earth?

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Compare the density, weight, mass, and volume of a pound of gold to a pound of iron on the surface of Earth.

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If identical spacecraft were orbiting Mars and Earth at identical radii (distances), which spacecraft would be moving faster? Why?

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Figuring for yourself

By what factor would a person’s weight be increased if Earth had 10 times its present mass, but the same volume?

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Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth’s). What must be the mass of this planet such that the gravitational force ( F gravity ) at the surface would be identical to Earth’s?

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What is the semimajor axis of a circle of diameter 24 cm? What is its eccentricity?

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If 24 g of material fills a cube 2 cm on a side, what is the density of the material?

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If 128 g of material is in the shape of a brick 2 cm wide, 4 cm high, and 8 cm long, what is the density of the material?

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If the major axis of an ellipse is 16 cm, what is the semimajor axis? If the eccentricity is 0.8, would this ellipse be best described as mostly circular or very elongated?

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What is the average distance from the Sun (in astronomical units) of an asteroid with an orbital period of 8 years?

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What is the average distance from the Sun (in astronomical units) of a planet with an orbital period of 45.66 years?

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In 1996, astronomers discovered an icy object beyond Pluto that was given the designation 1996 TL 66. It has a semimajor axis of 84 AU. What is its orbital period according to Kepler’s third law?

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Questions & Answers

Where is a moon HOW MANY KILLOMETER FAR FROM EARTH
Guddi Reply
On Average 383,000 Kilometers, Between Perigee And Apogee.....
Adam
how many stars are there in the world
ZERO Reply
we can't count them because there are infinity no. of Star
YOG
but in night sky there are approximately 100 thousand million stars
YOG
Visually speaking, there's only one in the day and a few thousand in my Tellurian corner of the world at night. And some of those stars may even be galaxies, too far to properly discern as billions points of light. The longer you gaze into the skies the more they manifest themselves. Keep watching!
Jocofranc
why people go to other planet
Rehan Reply
to explore mysteries and also for some new resources and life form
YOG
Presumably to find an alternative for our earth, since our population has been increasing at a crazy rate and we'd slowly be running out of space here, if we'd continue. Another point would be the scientific value. Apart from testing our knowledge we always hope to find a new form of life.
creative
and in future when life from earth will vanished then to maintain our existance we need a new planet.
YOG
History shows our insatiable appetite for energy. The mass tends to congregate around developed communities where energy is readily accessible. It's inevitable we will be become exo-tellurians. Necessity fuels our explorations.
Jocofranc
👏 Well said! @jocofranc knight
Jennifer
what was before big bang
Manish Reply
The creator and their empire
Mahesh
Like ur answer but submitting a light-hearted suggestion of my own : Our universe a galactic-verse of many other billions that are clustered tightly together in a super-constellate. The Big Bang was the result of a magnetic wave originating from inside the constellate desrupting our serene corner.
Jocofranc
nice to here jocofranc, please explain what is before big bang
Mahesh
This increasingly hypothetical scenario suggest that the Big Bang was created when a superwave from this so-call Super-Constellate destabilized our dormant singularity. The wave was the catalyst. When this wave stops buckling our galactic-verse, it will recede back to a singularity. Ok it was God.
Jocofranc
how fast light travel around the earth
Starbuck Reply
lol
Videos
If you could travel at the speed of light, you could go around the planet 7.5 times in one second
Greg
how was moon formed
Kosi Reply
what is steral evolution (star evolution
meron Reply
hi
Nisha
when a star's mass changes over time
Joe
hi
Joe
hi
Lisette
Hii
Asim
hi
Nisha
what big bang
Nisha
yes joe over time chang star mass
Nisha
star prouduce nucluer fusion first stag ( hydroge fusion helium- carbon-neon-oxygen-silicon- last fusion iron hevy star mass not handle iron blast super nova
Nisha
what is the worm hole theory
Nisha Reply
it states that you can travel back through time by this. It's like folding a paper into half and making two points, and there states that you can bend spacetime but according to Einstein's equation that it can break easily and only really small particles can pass through it.
Dark
dark dream what is dark matter
Nisha
what is the great filter theory
Nisha
the great filter theory it's just like the literally filtering it says that when once a civilization achieved its highest state or let's say the highest technology for instance their civilization will end.
Dark
what is radio burst
Nisha
please answer
Nisha
what is the simulatin hypothies
Nisha
smart obsevatin
Nisha
In radio astronomy, a fast radio burst (FRB) is a transient radiopulse of length ranging from a fraction of a millisecond to a few milliseconds, caused by some high-energy astrophysical process not yet identified. We can say that this can be they way to at least know if there's other civilizations~
Dark
~out there
Dark
Simulation hypothesis it proposes that the earth, the universe and the reality you are in is just an artificial simulation or like you are living in a computer simulation.
Dark
sir possible time travel
Nisha
?
Nisha
Yes. Everything is possible.
Dark
replay
Nisha
thanks
Nisha
sir how to make neutron star
Nisha
replay
Nisha
?
Nisha
sir what is the white hole?
Nisha
hi good morning
Nisha
why does the matter of an objects density change the fabric of space time rather than the objects volume..? (hopefully I have expressed that question properly) thanks
Daijahrel Reply
because an objects density consists of it's energy & momentum. an objects volume, for example a photon can have no density (hopefully I expressed that answer properly)
Joe
I suppose each Individual has his or hers different laws and assumptions, so it can be difficult to ask and answer physics questions, but discussions are always positive
Joe
how
Melaku
which matter use rocket
Nisha
Does their is any procedure of star making
Asim Reply
Hope That Helps.....
Adam
how to produce star and how to dead star?
Nisha
waad mahad santnihiin dhamaan waxaan doonayaa inaan wax ka barto astronomyga waa maxay xidigis?
Abdicaroog Reply
understanding astronomy
ricardo Reply
What About Understanding Astronomy?
Adam
yap
Janmarc
what is astronomy?
Janmarc
define..
Janmarc
Currently, I'm studying in 10th grade. What should I do after my 10th so that I can get an astronomy career?
Chaya Reply
try jee exam and achieve a good score in jee advance to join in IIST(Space research institute)
Sri
okay.. thanks
Chaya
Hey there I want to be an astrophysicist... and I'm grade 9... what should I do to be an astrophysicist
Aymen
Know more about space,watch movies related to space ,and to become an astrophysicist u should be very good in physics,train urself to think everything logically. Start to focus on JEE Exam ,train urself or join any institute which is good in coaching for JEE ,then if u score high ,u can join IIST
Sri
Which is the best university for Astronomy
Asim
Probably Massachusetts Institute Of Technology.....
Adam
Math Math Math, Get Familiar With All Types Of Math.....
Adam
Which subject is most important for Astronomy
Asim
Geometry, Algebra, Calculus, Trigonometry, Do Alot Of It And Often.....
Adam
I Can't Say It Enough, Math Is The Language Of The Cosmos.....
Adam
Adam you are in which university?
Asim
I Went To University But Never Finished My Degree..... Had To Work And Couldn't Afford School.....
Adam
MaryMount University..... Philosophy Of Science Major.....
Adam
It ia a cathloic University. Am i write
Asim
And its main campas is in Arlington country
Asim
No, It's In New York City.....
Adam
It's Not A Catholic University.....
Adam
Ohh sorry
Asim
Are you interested in Astronomy
Asim
IIT ain't so good for Pure Astronomy. If you want to know how the universe works,go for pure science. If you want to make spacecraft,go for Aerospace Engineering
priyanshu
Your are in which university brother
Asim
I Love Astronomy, I'm An Active Amateur Astronomer.....
Adam
I also love Astronomy very much
Asim
And to help me to solve some puzzling questions
Asim
this famous person was the first to recognise earthshine on the moin
Rajan Reply
Leonardo Da Vinci.....
Adam
what is string theory?
sakshi Reply
A Cosmological Theory Based On The Exsistence Of Cosmic Vibrating Strings.....
Adam
Good Morning Asim Ali.....
Adam
I Can't Do That, You Can Ask Me What Ever You Want.....
Adam
If you don't mind can i ask why?
Asim
Do You Understand The Millions Of People Have Access To This Site, I Wouldn't Put My Information Out There, Knowing What People With Bad Intent Can Do With Personal Information.....
Adam
Ohh sorry
Asim
My question is that, there are many collision of stars in a day So that cause black hole. But is there any procedure of star making? Hopefully i ask my question properly.
Asim
No Need To Apologize, I Will Answer Anything You Need Answered And If I Can't Answer It I Will Guide You To The Answer.....
Adam
Thier Is Only One Way Stars Are Made, Gravity Makes Matter Come Together, And When The Amount Of Matter Gets Massive Enough Nuclear Fusion Starts Up And A Star Is Born.....
Adam
What is white drawft?
Asim
A White Dwarf Is A Low Mass Star That Has Exhausted All It's Central Nuclear Fuel And Lost It's Outer Layers As A Planetary Nebula.....
Adam
what is the great filter theory
Nisha
hi adam what is great filter theory
Nisha
Well First It's Not A Theory, It's A Hypothesis, The Great Filter Hypothesis States That What Ever Causes Dead Matter To Under Go Abiogenesis(Start Of Life) Must Be Very Hard And Very Rare In Our Universe, Because So Far We Only See 1 Civilisation That Made Through All The Requirements For.....
Adam
Intelligent Life, So Far Only Our Planet Has Intelligent Life, That We Know Of, And Again This Is Only A Hypothesis, No Evidence Exist To Back This Up.....
Adam
hi adam sir
Nisha
Good Day.....
Adam
Good to see you sir
Asim
hi
Nisha
good day
Nisha
hi
Nisha
Same Here.....
Adam
What's The Good Word For The Day?
Adam

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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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