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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

may i ask a question
Raluca Reply
yes why not you don't need to ask anyone for permission
Tanmay
-Why there are moons in every planet but there's note in mercure ?
Amal Reply
Well with mercury Venus also does not have moon.The reason that Mercury is not having moons is since it is too close to sun and thus if it would have any moon orbiting it ,then the moon will eventually attracted by sun due to it's high gravitational force whereas mercury has the lowest gravity
Anjali
The gravitational force of mercury is lowest in solar system and it won't be able to hold a moon in it's orbit
Anjali
Nice explanation
Asim
Thank you brother
Anjali
Did general theory of relativity leads us to singularity?
Asim
yes the general theory of relativity leads us to singularity
Anjali
But Einstein was not a believer of big bang. And singularity lead us to big bang?
Asim
yes Einstein was really astonished by his mathmatical answers that came fron his equations (this is what almost every one says)
Tanmay
and there are many theories stating how our universe came in which one is big bang
Tanmay
Einstein was against the fact that anything can come from nothing that our big bang says and he also thought that singularity (infinite mass in zero volume) can not be real(also what most people say)
Tanmay
also what most people say means that there is no evidence that he was against all these things
Tanmay
Okay
Asim
Tanmay
Asim
anything else
Tanmay
Do you believe that grand unified theory can be complete in future?
Asim
Do you believe that grand unified theory will be complete in future?
Asim
yes I do believe in it as I also believe big bang
Tanmay
Well i don't believe in big bang like Einstein didn't.
Asim
do you believe in wormholes are real?
Amit
@Asim then what do you think our universe came from or how it started
Tanmay
Well it's a myth.
Asim
@Amit I believe wormholes are real
Tanmay
It came from nothing Tanmay.
Asim
Even I believe in wormholes
Anjali
So Tanmay you must believe in baby universes.?
Asim
I believe that they are many things we can't explain or give prove but they are theories,imaginations and they are the basics for new discoveries
Anjali
So ,it is useless to argue over them
Anjali
But we should try to find new possibilities if we don't believe in old ones
Anjali
you are right @anjali
Amit
what is dark matter?
Amit
can a star turn into planet?
Amit
I have doubt on how Stephen hawking posses ideas of black hole by himself?
Enceladus
why do people believe in God and how are humans made
ilyes
No amit star can't turn into planet.
Asim
you are wrong asim
Amit
also Asim, please tell me why you think the big bang is a myth?
ben
what is the model about the earth being the center of the universe called?
Lordgy Reply
geocentric model
SCIENCE
I hope you got your answer.
SCIENCE
heliocentric universe
Jason
you are wrong Jason skerbinc
SCIENCE
in heliocentric model sun is at the center of the universe
Tanmay
what is black hole and stellar black hole
azeb Reply
does Millikan consider electron axial spin in his discovery of electrons mass using q/m ratio ? If No how it is possible that he found rest mass of electron (9×10^31 Kg) ?
Anurag Reply
how did light from up
Sourav Reply
Before there stars , there was matter and radiation . Before there were neutral atoms ,there was an ionized plasma ,and when that plasma froms neutral atoms , those allow the Universe to deliver the earliest light we see today .......
Apsara
how to know the distance of a star
Sourav Reply
What is time
Sourav
Technical Infinite Measurement of Evolution
Doc
not by the book but the simplicity of word play ....
Doc
to calculate the distance of a star we use parallax method (as far as my school has taught me).
Tanmay
in this method we see the star from one point and then after traveling some distance perpendicular to the distance of star we see it again. With this we can make a triangle and then it's median will give our distance
Tanmay
And time is just a way of defining when an event happened
Tanmay
oh and we will know the distance of all the 3 sides of triangle formed above if we multiply the time taken by light with speed of light and the third side will be known to us as it is dependent on our will
Tanmay
what are wormholes?
facty Reply
Holes made by worms
Neil
What is the difference between black hole and white hole ?
Apsara
black hole is the place where the massive body makes a large disturbance in space time fabric causing large gravity even light can't escape from it and all the bodies enter into on reaching a specific distance.
SCIENCE
A white hole is a hypothetical region of spacetime and singularity which cannot be entered from the outside, although energy-matter and light can escape from it. In this sense, it is the reverse of a black hole, which can be entered only from the outside and from which energy-matter and light can
SCIENCE
White holes appear in the theory of eternal black holes
SCIENCE
worm holes join 2 distant region of spacetime through which you can travel, covering large distance in short time
Tanmay
for example if you need to travel from A to B on a plane of paper then you can travel in a straight line joining those points but a worm hole will join those points using 3rd dimention which will make you travel that distance in short time
Tanmay
Hi,Do you known Kyaw Nyein Chan Hein!
zin Reply
No
Astrophysicist
Hello : I'm Kyaw Nyein Chan
zin
Hi I'm Kyaw Nyein Chan
zin Reply
Hello : good moring, I'm Kyaw Nyein Chan
zin Reply
hello good morning
Astrophysicist
good morning bro
Tanmay
how do you do?
Astrophysicist
I am fine what about you?
Tanmay
same as you
Astrophysicist
cool
Tanmay
How the Big Bang is made .
Apsara Reply
Kyaw Nyein Chan
zin
What is heliocentric
Apsara Reply
helio is from the greek god helios or ilios and means sun. Centric is from central. So heliocentric means with the sun in the middle
Robin
Usually in the context of astronomy its about the moment the world goes from the idea of 'earth in the middle of the solar system' to the idea that the sun is in the center of the solar system
Robin
so from a geocentric (geo meaning earth) to a heliocentric idea
Robin
yes correct this theory states that sun is in the middle of the solar system rather than earth
Tanmay
oh you have already said this
Tanmay
Hello: good afternoon
zin
hello
Tanmay
Thankyou to all to solve my doubt . I don't know more about the solar system beacause i am a small little girl my old is 9 and i love science but i am trying to learn more about science .
Apsara
that's great you should definitely check science in a nutshell YouTube channel it will provide you with good information
Tanmay
that's great you should definitely check science in a nutshell YouTube channel it will provide you with good information
Tanmay
that's great you should definitely check science in a nutshell YouTube channel it will provide you with good information
Tanmay
here is the link ***youtube.com/c/inanutshell
Tanmay
You not alone Apsara I'm 14 but know little about the universe
Swazi
what is solar system
Himanshi
what do you mean by astronomy
Himanshi
astronomy is a study of planetary science.
Enceladus
Astronomy is a branch of Physics that deals with the study of celestial bodies.
Satyam
An astronomy is a scientist in the field of astronomy who focuses their studies on a specific questions or field outside the scope of Earth 🌍🌎🌏 . They observe astronomical objects such as star's , planets , moon , comets and galaxies - in either observational (by analyzing the data)
Apsara
what is the difference between astronomy and cosmology
Astrophysicist
The collection of eight planets and their moon's in orbit around the Sun , together with smaller bodies in the form of asteroids , meteoroids and comets . The planet of the solar system are ( in order of distance from the sun ) Mercury , Venues , Earth ,Mass , Jupiter , Sartune ,Uranus , Neptune .
Apsara
In Astronomy, we study about celestial objects but in cosmology we study the origin and the formation of universe.
Satyam
how much temperature were can find on neptune
Ayyan Reply
the temperature is between -200 to -218 degree Celsius
Tanmay
how can I apply online astronomy course ? if you have link send it.
Dawit Reply
what is astronomy
Khanyisa

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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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