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.
TL;DR Summary: orbital speed laws
I would appreciate a bit of explanation on how did we find e1 and e2 and if there are any useful references to learn about Kepler laws since I am lost for the most part, and would like to gain understanding and solving ability
,and if you can go into some...
I mean. For example, Earth in one month sweep the same area* than Jupiter in one month?
*The line joining the Earth with the Sun than the line joining Jupiter with the Sun.
I think yes, but is not what 2nd law says. I think in the fact that the aceleration just depends on the distance to the...
I was reading about the Tusi couple and read it "as a solution for the latitudinal motion of the inferior planets, and later used extensively as a substitute for the equant". Since the Tusi couple is related to plotting out an ellipse, did Nasir al-Din al-Tusi already discover the laws for...
When we use the third Kepler law to calculate the period, distance and velocity of the Earth, we consider that the Sun is fixed. We know this is not true, because the Sun is also attracted by the Earth. I was wondering, how could we use Kepler laws to calculate the period, distance and velocity...
I was wondering if the electrical force, which is a radial force that depends on the inverse of the distance squared, also respect the Three Kepler Laws?
If so, what will the constant for the third law be?
I have tried to solve the problem through the use of a rotating reference frame, since I should have as a solution an orbit given by the Kepler potential, but I haven't come up with anything. Any ideas ?
I solve (1).
But to solve (2), What should be the suitable separation constants?
I am so confused...
E=2/(m*(a+b)) * (a*(dWa/da)^2+b*(dWb/db)^2-k)+l^2/(2mab)
where l(constant) is pc since c is cyclic.
What should I do to solve the problem?
Let's consider the Hamiltonian $$H = \frac{1}{2m} p_r^2 + \frac{1}{2mr^2} p_{\phi}^2 - \frac{k}{r}$$where the generalised momenta are here ##p_r = m\dot{r}## and ##p_{\phi} = mr^2 \dot{\phi}## conjugate to the coordinates ##r## and ##\phi##. Since ##p_{\phi}## does not depend on ##\phi## it can...
On one hand:
wiki - Kepler Problem - There doesn't seem to be a clear statement of what the problem is. There is a section on the solution which is given as a function u(θ) where u = 1/r.
In Classical Dynamics, Thornton, et. al., the section on Planetary motion - Kepler's Problem - "The...
Hi everyone:) I have spend a couple of days trying to teach myself the math of orbital mechanics and have been able to generate a model of the orbital path of Haley's Comet, incorporating realistic distances and periods using Kepler's second law & ellipsoid functions.
This is a GIF of the motion...
I am confused because the question implies that I need to do some sort of calculation with Kepler's law. I got
##r+d = \sqrt[3]{\frac{T^2 GM}{4 \pi^2} } ##
But don't understand why I need this, since I already have the distance and the angular diameter should be ##\arctan (2R/d)## I think I...
Introduction: I am writing a Matlab program that solves the Kepler problem for any Elliptical, Hyperbolic, or Circular orbit. Given an initial position vector, velocity vector, find the position vector and velocity vector after some given time. I am not doing this for any class, I have been...
It is easy to find that the equation for an ellipse is:
$$1 = x^2/a^2 + y^2/b^2$$
Then according to Kepler's equation:
$$x = a(\cos(E)-e)$$
$$y = b\sin(E)$$
where E is the eccentric anomaly and e is the eccentricity.
If you plug the Kepler's equations' x and y into the equation for the ellipse...
I have a lot of questions as usually, but must begin with the difficult to understand moment which have started my explorations of the Kepler's second law. In the book of Steven Wainberg "To Explain The World", in the technical paragraph twenty one I have found the next formula which represents...
Below, I have already solved - I assume - correctly for question 1. Question 2, I am nearing to what I believe is the solution. Question 3, I simply have no idea where I should begin considering that it is interconnected with question 2.
With that said, below is the lengthy and somewhat tedious...
I have yet to decide on values for the mass of the fixed object, M, the mass of the moving celestial body, m, the initial velocity, v, and the distance between the two objects, r. I will most definitely decide on a larger mass M because I would like the celestial body to spiral in towards the...
Here were my assumptions: Energy and angular momentum are both conserved because the only force acting here is a central force. The initial angular momentum of this particle is ##L = mv_0b## and we can treat E as a constant in the homework equation given above. I solved for the KE (1/2 mv^2) in...
Homework Statement
Homework Equations
1/r = a/b2 * (1+e cosθ)
The Attempt at a Solution
How do you derive 7.27?
I tried to substitute r in the orbit equation by (acosψ - ae) / cosθ and got
(cos ψ - e)/cosθ*(1+e cosθ)=b^2/a^2 I don't know what to do next. Please help, thank you.
Homework Statement
Find the period of a low Earth orbiting satellite using Kepler Laws
earth radius = 6.38E6 meters
T^2/R^3 for Earth = 2.97E-19 (sec^2/m^3)
Homework Equations
2.97E-19 = T^2/(6.38E6)^3
T^2 = (2.97E-19)(6.38^6)^3 = 77.1
T = 8.72 sec
The Attempt at a Solution
This is not...
I am in the process of making a program that visually shows an elliptical orbit over time. I wish to find the tangential velocity of the satellite in the elliptical orbit based on the variables that I know.
Here is what I know:
a) The angle relative to the right focus with 0 radians being the...
Homework Statement
I am working on the derivation of Kepler's Second Law based on torque and angular momentum. I understand that the vector "L" is equal to the mass (m) times the cross product of the vector "r" and the vector "v." The source I am following then states that
L = mrvtheta. I do...
Hello,
I am completing a research project for differential equations class. I am to derive Kepler's three laws and then compare the results of the derivation with real-world data. For Kepler's second law (a planet sweeps out an equal area in an equal time), I was hoping to find orbital data for...
Announcement
Vanderburg works on various stuff, with a focus on more recent data (K2 mission).
Jessie Dotson works on K2 data and seems to be a contact person for external users working with Kepler data.
Christopher Shallue https://www.linkedin.com/in/cshallue/.
Based on the panel, I have no...
How much more refined are the various variables of the Drake Equation in view of the recent findings by the Kepler Telescope?
I imagine fp and ne would surely be better estimates.
Is there a study on this anywhere?
I was wondering if it is possible to use only a stopwatch and a telescope to find the mass of a planet, such as Saturn. I've experimented with a couple of things but I keep running into problems. I previously asked this question in the homework section, but it does not involve numbers, is not...
I am confused about the units used in Kepler's 3rd law. Is T supposed to be in years or days? Is R supposed to be in kilometers or meters? Is there ever an instance where one combination of units is preferable over another (for example, if you want to use the answers from Kepler's third law to...
hello everyone anyone knows if this research is made? imagine you have available the data from the kepler telescope to search exoplanet, create a training set of data based on the concept of find exo planet , calculate their orbit and try to design the virtual exo solar sistem , understand the...
Homework Statement
A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 × 104 m/s, and the radius of the orbit is 5.25 × 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of...
Hello, quick question here
I am studying mathematical astronomy / the history of , and I have noted that by raising the average sidereal period of any planet in our solar system, to the power .666666, that you are left with the average distance of that planet from the Sun, in AU
I was told...
We were asked to do an experiment where we had to prove the equation:
T2=(4π2m)/Mgr
Where M is the mass of the mass stack in kg (0.3kg), m is the mass of the rubber bung in kg (0.0226kg), T is the time taken for one rotation in seconds, r is the horizontal radius of rotation in meters, and g is...
Hello I'm wondering, what is difference in trajectory or period or...something if I try to compare solution of Kepler problem for point bodies and "rigid" bodies with spins. More precisely is some easy way how to include a spin of bodies to this problem? Or this procedure for describing of such...
Kepler problem explains closed elliptic trajectories for planetary systems or in Bohr's classical atomic model - let say two approximately point objects, the central one has practically fixed position, they attract through 1/r^2 Newton's or Coulomb force.
Kind of the best motivated expansion we...
Hello! I am a bit confused about Kepler 3rd law for circular orbits. So assume you have 2 bodies of masses M>m orbiting in circles around their center of mass. As the center of mass passes through the line connecting them, they must have the same period. But according to Kepler's 3rd law, this...
This isn't exactly homework, but something which you'd get as an assignment, so I'll still post it here in order to reach the right people..
I'm attempting to freshen up my knowledge on Hamiltonian systems, so I've tried to formulate the Kepler problem in Hamiltonian dynamics...
Astronomers are viewing a single point in space (.1 arcseconds), using the Kepler space telescope but to view a planet 4.2 light years from the Earth that would require a planet with a diameter of more than ten times the diameter of our solar system.
Homework Statement
A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 2.53 hours. What is the density of the planet? Assume that the planet has a uniform density.
Homework Equations
T^2=(4pi^2r^3)/GM
V=4/3piR^3
Density= Mass/...
Homework Statement
Attached.
Homework Equations
I am assuming the coordinate transformation is \vec{x}' = \vec{x} + \alpha\vec{\gamma} ?
Then you have \vec{v}' = \vec{v} + \alpha\frac{d\vec{\gamma}}{dt}
And r is the magnitude of the x vector.
The Attempt at a Solution
Part A.
So to get the...
Homework Statement
Say I have some planet in a circular orbit around a star, and I give it a small radial push (directly toward or directly away from the star). How would I describe the new orbit? I.e. how would I determine the equations of motion? h
Homework Equations
Kepler orbital radius...
@Evo is this your blog (evonomics)? ;-P
Economists Discover Quasi-Equlibriated Economic Sub-Particle
The problem economists have explaining the financial crash
By Steve Keen
CERN has just announced the discovery of a new particle, called the “FERIR”.
This is not a fundamental particle of...
Source: NASA to Announce Latest Kepler Discoveries During Media Teleconference
Livestream
Time conversion reference: this post was posted at 7:45 pm EDT.
My guess: various roughly Earth-sized exoplanets around dwarf stars, probably at least one in the habitable zone.
Edit: More than 1000...
Just noticed the Kepler telescope is running in "safe mode" burning precious fuel very quickly. Could be the end of the show for K-2 if they don't come up with a workaround soon.
If anyone hears of progress regarding the problem could they please mention it here? Thanks:smile...
Homework Statement
Homework Equations
I guess kepler's law but most importantly conservation of angular momentum are key here.
The Attempt at a Solution
[/B]
I put down E as the answer, but the solutions have D as the correct answer. Why is this the case?
Thanks in advance for the help!
In my Kepler Bb story, some of the humanoids that go to school, in fact a lot of them, have some kind of morphing power.
Here is an example of what a typical grade in Wilderness Survival class(which is weighted especially on females since when they are looking for a husband they either stay...
Homework Statement
How far would be a planet from the earth, when its period would be 2 years?
T = 2 years/730 days
a = 150*106km
Homework Equations
a3/T2 = C
(C is the Kepler-Constant)
The Attempt at a Solution
I tried inserting T in days and years, but I always get a wrong solution, since C...
Homework Statement
http://[url=http://postimg.org/image/f7e6kp0xv/][PLAIN]http://s21.postimg.org/f7e6kp0xv/image.jpg
Homework Equations
Kepler's laws
The Attempt at a Solution
I thought the answer will be C : I and II
But the solution written (it was my friends book) is B, which is correct?
Solar system:
Double binary star(2 binary stars in a quadruple star system)
Kepler A:
A big blue star. It is bigger than all the other stars in the double binary system. It will however last longer than our sun just like the other 3 stars will.
Kepler B:
This is a green star(The green star...
Hi.
I'm writing a simulation of (an approximation of) the solar system. So far I've been able to translate the Wikipedia article on Kepler's laws to a function that uses a description of an elliptical orbit (eccentricity, periapsis, known position in time) to return a position when passed an...