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...
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...
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...
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...
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 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...
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/ Volume...
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...
Homework Statement
Homework Equations
I guess kepler's law but most importantly conservation of angular momentum are key here.
The Attempt at a Solution
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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!
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 [Broken]
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...
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...
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...
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...
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...
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...