What is Kepler: Definition and 119 Discussions

Johannes Kepler (; German: [joˈhanəs ˈkɛplɐ, -nɛs -] (listen); 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, and astrologer. He is a key figure in the 17th-century scientific revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonices Mundi, and Epitome Astronomiae Copernicanae. These works also provided one of the foundations for Newton's theory of universal gravitation.
Kepler was a mathematics teacher at a seminary school in Graz, where he became an associate of Prince Hans Ulrich von Eggenberg. Later he became an assistant to the astronomer Tycho Brahe in Prague, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He also taught mathematics in Linz, and was an adviser to General Wallenstein.
Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting (or Keplerian) telescope, and was mentioned in the telescopic discoveries of his contemporary Galileo Galilei. He was a corresponding member of the Accademia dei Lincei in Rome.Kepler lived in an era when there was no clear distinction between astronomy and astrology, but there was a strong division between astronomy (a branch of mathematics within the liberal arts) and physics (a branch of natural philosophy). Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through the natural light of reason. Kepler described his new astronomy as "celestial physics", as "an excursion into Aristotle's Metaphysics", and as "a supplement to Aristotle's On the Heavens", transforming the ancient tradition of physical cosmology by treating astronomy as part of a universal mathematical physics.

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  1. vinicius0197

    Deducing Kepler's second law from Newton's laws?

    I've searched a little bit and found that I can derive kepler's third law from Newton's law of gravitation. That's okay. But I want to deduce kepler's second law too: "An imaginary line joining a planet and the sun sweeps out an equal area of space in equal amounts of time". I know it's possible...
  2. DaveC426913

    NASA New Earth-sister Kepler 452b announced by NASA

    http://www.nasa.gov/keplerbriefing0723 As I type this, NASA is announcing discovery of a new planet Kepler 452b that is - small and (probably) rocky like Earth - orbits a G2 star - is in the star's habitable zone This is the first candidate that meets all three criteria. (Most Earth-twins so...
  3. Hansa

    How did Kepler derive his laws WITHOUT law of gravitation?

    How did Kepler derive his laws of Planetary Motion without knowing about Newton's law of gravitation? Specifically, the first law of planetary motion which says that planets follow elliptical paths - how did he figure that out without the knowledge of the gravitational pull of the sun? Was it...
  4. S

    General differential equation solution for Kepler Problem

    To be honest, I don't know any physics. I am a high school student who has taken high school physics, but America's education system isn't known for teaching much more than Newton's laws. I have, however, taken Multivariable/Vector calculus, so I have a decent math background. I was wondering...
  5. S

    Proof to Kepler's first and second laws

    I am a 10th grade student, and I tried for a few weeks now to find a proof to Kepler first and second laws. Is there a simple proof to Kepler' s laws?
  6. T

    How can I improve my skills in finding general solutions in physics?

    Hello, few days ago I took an exam in my honors physics class and believe I did not do as well as I did on the other exam. Last exam had a few computational problems and the rest were general solution problems. This recent exam had 8 questions that were all general solution problems as opposed...
  7. A

    Travel time for apollo to the moon with Kepler's thirs law

    Hi everyone, For one of my project in school, i need to calculate the travel time to the moon. To do that, I thought to use Kepler's third law which is : (2(pi) / P )2 * a3 = GM where : P : period of travel a : major semiaxes (not sure in english, but it is the half the longest radius of the...
  8. M

    What is the significance of the foci in gravitational orbits?

    hey everyone, this is a qualitative question on gravitational orbits: I was going through questions in which the trajectory of the orbiting body is determined based upon the eccentricity of the orbit, e.g. 0<Ecc<1, ellipses, Ecc=1, parabola, Ecc>1, hyperbola. I did the math and found out what...
  9. K

    Path of a ball thrown radially from a satellite orbiting Earth

    Homework Statement A satellite has a circular orbit 500 km above earth. A ball is thrown directly downwards radially at 20 m/s. Find the path of the ball relative to the satellite. Homework Equations mv^2/r=GMm/r^2 The Attempt at a Solution From the height of the orbit you can easily solve...
  10. K

    Maple demonstration of kepler law

    Hello, I have been trying to do an assignment for one of my physics class. We are trying to demonstrate the planetary motion using Kepler's law. I have been trying to solve a integral. I was able to solve it using maple. I am trying to solve equation 29 in attached figure. I got equation 31...
  11. T

    Can I See Kepler 22 from Earth?

    Kepler 22 has generated some hype because it was the first star to have a planet in the habitable "goldilocks" zone to be found by the Kepler Space Telescope. I also know it is somewhere in the constellation of Cygnus. I have done many a Google search on this, yet returned nothing. My question...
  12. T

    Exploring Kepler 22b: Could Life Exist?

    People are saying that Kepler 22b looks like it may harbour life. How could we ever know? I was just wandering, but what would the delta v be to do a Hoffmann transfer (if this works on an interstellar scale) to Kepler 22b?
  13. AntSC

    What are the Recommended Texts for Understanding Kepler's Laws?

    I am after a text that takes one through the derivation of Keplers Laws and related material. I'm sure i knew of one in my undergraduate days but can't remember. Any suggestions?
  14. I

    How does this relate to the size and mass of gas giants like Kepler 7b?

    Or, just how big can a gas giant get? I read this article recently: http://www.bbc.co.uk/news/science-environment-24348024 In it, Kepler 7b's clouds are 'directly' mapped for the first time. The planet itself is said to have an overall mass roughly that of polystyrene. Bearing in mind...
  15. E

    How Do You Derive the Axes of a Kepler Orbit from Its Equation?

    Homework Statement I am trying to see if I am on the right track with this. The problem: A kepler orbit (an ellipse) in Cartesian coordinates is: $$(1−\epsilon^2)x^2 + 2\alpha \epsilon x + y^2 = \alpha^2$$. The task is to show that the major and minor axes are: $$a =...
  16. Philosophaie

    Lagrangian for the Kepler Problem

    In a two-body solution ( Kepler Problem) how do you find the Lagrangian, L, if the position vector is: x = (v_x * t + x_0, v_y * t + y_0, v_z * t + z_0) Action from Wikipedia is: S = \int_{t_1}^{t_2} L * dt
  17. Philosophaie

    Solving Kepler Problem for 2-Body System: Velocity & Position

    How do you solve the Kepler Problem for a 2-body system where m1<<m2 with a given velocity and position vector resulting in a new velocity and position for a certain time interval?
  18. jaumzaum

    Second Kepler law for hyperbolas

    A body can describe 3 types of orbits around another (considering only the gravitational force), a elipse, a hyperbole or a parabola. Does the second kepler law (area law) work for hyperboles or parabolas too?
  19. R

    Angular Momentum in a Kepler Orbit

    I got myself here a satellite rotating at a large distance around planet X. Distance from center of planet X = 100, mass of the satellite = 1 gram (really small), mass of planet X = 1.0 kg velocity of my satellite 10 m/sec and in this oddball universe the gravitational constant = 10**4...
  20. marcus

    Kepler mission announces possibly habitable planets found (18 April)

    http://cosmiclog.nbcnews.com/_news/2013/04/18/17811465-kepler-mission-makes-big-splash-with-possibly-habitable-super-Earth's Just announced 18 April. "Kepler-mission-makes-big-splash-with-possibly-habitable-super-Earth's". These are in constellation Lyra. I can't evaluate how definite or...
  21. S

    A question about a moving satellite (Kepler)

    Homework Statement Hi I have a question about a satellite moving in an elliptic motion. It begins its motion on the x axis, when x=2Re, and with a velocity: Vx=0, Vy=v0, Vz=-0.5V0. Re is radius of the earth. Solving this I arrived at: r0 = 10Re/4. e=1/4. Rmin = 2Re. Rmax = 10Re/3. Given all...
  22. B

    Are there any habitable binary star systems in the Kepler catalog?

    Hi, this is my first post, and it is sort of a complicated question (I think. Perhaps it is easy and I don't know how to solve it). In the Kepler catalog, are there any binary star systems, where the secondary star orbits the central star that have something close to the following...
  23. C

    Kepler problem: flows generated by constants of motion

    Consider the Hamiltonian of Kepler problem H(\boldsymbol{r},\boldsymbol{p})= \frac{|\boldsymbol{p}^2|}{2\mu} +\frac{\alpha}{|\boldsymbol{r}|}, \qquad \mu>0>\alpha, where \boldsymbol{r}\in M=\mathbb{R}^3\setminus\{ 0 \}, \ (\boldsymbol{r},\boldsymbol{p})\in T^*M and...
  24. C

    Kepler problem: flows generated by constants of motion

    Consider the Hamiltonian of Kepler problem H(\boldsymbol{r},\boldsymbol{p})= \frac{|\boldsymbol{p}^2|}{2\mu} +\frac{\alpha}{|\boldsymbol{r}|}, \qquad \mu>0>\alpha, where \boldsymbol{r}\in M=\mathbb{R}^3\setminus\{ 0 \}, \ (\boldsymbol{r},\boldsymbol{p})\in T^*M and...
  25. B

    Inscribed sphere - Kepler Conjecture

    Newbie to the forum here. Hoping y'all can help with something that's been bugging me for a while now. I would like to know the relationship between two characteristic radii in a close packing of equal spheres. The first radius of interest is that of the equal sphere's themselves (r1). The...
  26. A

    The Kepler Orbits (algebra manipulation)

    Homework Statement We have proved that any Kepler orbit can be written in the form of r(\phi) = \frac{c}{1+\epsilon*cos(\phi)} where c>0 \epsilon\geq 0. for the case that 0 \leq \epsilon < 1, rewrite this equation in rectangular coordinates (x,y) and prove that the equation can be cast in...
  27. Gliese123

    Stargazing How many percent does the kepler telescope investigate of the sky?

    As the title. How many precent of the entire sky is investigated by the kepler telescope? I'm aware of that it's very little, but does anyone find a good page of this? I've looked, without results. I'm very thankful for help! :biggrin:
  28. E

    Kepler Exoplanet findings and galactic plane question

    Noob here, be gentle… I am of the understanding that the solar system formed by means of an accretion disk that made its plane normal to the sun rotation. I suppose that the Galactic plane formed by the same basic gravitational and centripetal means. Question: Does our Solar System’s...
  29. A

    Kepler 16-b: first circumbinary planet?

    NASA says that the case of Kepler 16-b is "the first unambiguous detection of a circumbinary planet." But Wikipedia lists at most five circumbinary systems: PSR B1620-26, HW Virginis, Kepler-16, DP Leonis, and NN Serpentis. If so, why is Kepler's discovery the FIRST if four systems were already...
  30. G

    Ptolemy reduces to Kepler as Epicycles → ∞?

    Does Ptolemy's theory of epicycles mathematically reduce to Kepler's 3 Laws in the limit of the number of epicycles tending to infinity? Thanks
  31. fluidistic

    Solving the Kepler problem with the Hamiltonian

    Homework Statement Write down the Hamiltonian and its corresponding Hamilton equations for a particle in a central potential. Find the solution to the Kepler problem in this description.Homework Equations Hamiltonian. The Hamilton equations or motion equations are \dot q _i = \frac{\partial...
  32. M

    Kepler's Questions: Saturn's Orbit & Satellite Radius Calculations

    Question 1: Homework Statement https://www.physicsforums.com/showthread.php?t=44239 except the planet is Saturn. Homework Equations r = (t / (2pi)) ^ {2 / 3} * (G * M) ^ {1 / 3} The Attempt at a Solution I tried many things, so I thought I would give tony873004's solution...
  33. A

    How did Kepler know that the time of Mars' orbit was 687 days ?

    How did Kepler knew that the time of Mars' orbit was 687 days ? It doesn't seem to me a simple task to determine that timing because after 687 days, Earth is at a different place in the solar system and Mars seems to be also in a different place in the solar system. How was that 687 days...
  34. H

    Finding mass of Earth using the Moon and Kepler

    When calculating the mass of the Earth using the moon as a reference and Kepler's 3rd Law, is it correct to subtract the moon's mass after completing the sum: me = (4*(pi)2*r3) / (G*t2) me = (4*(pi)2*3850000003) / (G*23587202) me = 6.07E+24 Should I be subtracting the moons mass to get: me...
  35. P

    How Kepler derived that T^2 is proportional to r^3

    How did Kepler exactly prove that the period squared is proportional to the radius cubed? If he didn't prove it. Then how is it proven?
  36. N

    Kepler problem with Runge-Kutta

    Homework Statement Solve the Kepler problem by Runge-Kutta method, where initial conditions x(0)=x0, y(0)=y0, vx(0)=vx0, vy(0)=vy0 Homework Equations dvx/dt = -GMx/(x2+y2)3/2 (1) dvy/dt = -GMy/(x2+y2)3/2 (2) dx/dt = vx...
  37. alemsalem

    How did Kepler arrive at his equation without calculus?

    The Kepler equation is: M = E - e Sin(E); where M is the mean anomaly and E the eccentric anomaly and e is the eccentricity. we get it from integrating dr/r' and changing variables to E, how did Kepler get it without calculus and using only his laws. Another thing how did he see his second...
  38. nismaratwork

    Kepler Discovers Small Exoplanet

    http://www.cnn.com/2011/US/01/10/nasa.planet.discovery/index.html?hpt=C1 This is a portion of the article, but it's quite optimistic. I hope that I'm not posting old news, and if I am please just delete this mentors. If not, I'm impressed, and this new era of finding exoplanets... what are...
  39. S

    How Did Kepler Discover the Sun's Position in Planetary Orbits?

    I know that kepler looked at Tacho Bradhe's work and knew the equations related to ellipses but the question is as simple as: how did kepler knew the sun was at one of the foci of the ellipse?
  40. D

    Was Galileo, Kepler, or Newton more important?

    Hi, I have to pick one of these great scientists to write a middterm item on, so basically I'm curious about what you personally think would be the easiest answer to argue to this question: Which out of Galileo, Kepler or Newton was of the greatest significance in changing the scientific...
  41. U

    Understanding Buoyancy: Why Do We Float in Water?

    I have a very interesting question and is curious to know why: Why do you float 2 m above the bottom of a pool, when you do not float 2m above the ground in air?
  42. P

    Doubt about the polar equation of a Kepler orbit

    Good morning, I have a doubt about the differentiation of the polar equation of an orbit: r=\frac{p}{1+e\cos\nu} It represents the relative position of a planet with respect to the central body. Here, p is the parameter, e is the eccentricity and r is the radius of the planet measured from...
  43. H

    A simple algorithm, with no use of the mass, to reproduce the 3 laws of Kepler

    Hello, I was drawing some curves on my computer when something appeared : it is possible to build trajectories that agree with all Kepler's laws with a very simple iterative process and very simple conditions. I wrote a paper to describe this fact and I built an online demonstrator to...
  44. J

    Understanding the Physical Significance of 'a' in Kepler Orbit Equation

    Sorry if this is in the wrong forum. I have the equation r = \frac{a(1-e^2)}{1+e \cos \theta} , and I'm wondering what the physical significance of the numerator is. More specifically, what is 'a' (since e is what it usually is)? I've seen various other representations with terms like...
  45. H

    First law of Kepler explained without mass ?

    Hello, I have a question : is it possible to explain the first law of Kepler without any concept of mass ? Kepler's first law states that satellites are moving on an ellipse and the object around which they are orbiting is localized at the focus of this ellipse. As far as I know Newton and...
  46. N

    Kepler, Newton, Gravity, error

    Looking at the gravitational equation F=G*(M*m)/r^2 and centripetal force F = ((V^2)/r)*m If you set the two equal and solve for G you get: G = ((V^2)*r)/M Substituting (4*pi^2*r^2)/T^2 for V^2 you now have G = (4*pi^2*r^3)/(M*T^2) With solution for G, look at Kepler's...
  47. L

    Projectiles and the Kepler problem

    Homework Statement Within the gravitational field produced by a celestial body of mass M we want to send a projectile of mass m from (x1,y1) to (x2,y2). The M mass is placed at the origin of coordinates. If the flight time is T, what is the initial velocity vector that we have to give to the...
  48. P

    NASA Nasa's Kepler mission and planet X / Nibiru

    I was just searching the net to find something to read about 2012 (doom's day) :-) ... And i got to know about nibiru , south pole telescope and black patches in google sky etc...suddenly one thought struck my mind..i knew that NASA was going to launch a new satellite to find Earth like...
  49. I

    Plotting Two Masses' Orbit Using Ellipse Equation and Initial Conditions

    Homework Statement plot the orbit of two masses using the equation for an ellipse and coordinate system at one of the foci Masses Initial Positions Initial Velocities i mi x1 x2 x3 v_1 v_ 2 v_ 3 1 1 0.651 0.585 -0.238 -0.755 -0.828...
  50. P

    Stargazing Kepler Telescope is so productive?

    Arccording to Nasa, the Kepler telescope will be working for 3.5 years in orbit and during that time it will observe about 100000 stars looking for exoplanets. Howcome it can finish for that workload?
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