What is Planetary motion: Definition and 71 Discussions
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.
Hi,
I am writing a code for planetary motion using ODE with runge-kutta.
Currently it has only two body, however, I could not get the initial values to fit in properly, the bodies will not move in circular orbital motion. They are moving towards each other.
at the v=[10 0;-10 0]...
Homework Statement
OK so here goes.
I'm using an ODEsolver in java to plot the total energy over time of a planetary system. So I've been trying to calculate the rate of energy (per unit mass), \frac{E}{m}.
Homework Equations
The equation for total energy (per unit mass) of a planetary...
State Keplers laws of planetary motion.
The motion of a planet about the Sun, assumed to be fixed at the origin, may be approximated by
r''= -ur^(-3) r
for u=y ms, where y is the universal gravitational constant and ms is the mass of the Sun. Derive the energy equation for this system...
Can someone briefly explain to me how Kepler's law of planetary motion uses differential calculus?
I'm searching for a topic for a 7 page report on a mathematical concept that uses differential calculus. I thought about Kepler's law on planetary motion, but I have a very vague understanding on...
Hello,
Ive got a problem in MATLAB and have searched the internet a lot for help with this but nothing really addresses my issue specifically.\. I wish to use the ode45 solver to calculate and plot the orbits of all the planets in the solar system. I can manage just fine to get them to go...
Homework Statement
A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 2.50 hours. What is density of the planet? Assume that the planet has a constant density.
R= radius
G= gravational constant = 6.6742x10^-11
M = mass of
m =...
I just need an explanation of a formula, and I think part of it is wrong, so here is the formula:
(T_A/T_G)^2=(R_A/R_B)^3
so T is the period and T_A is the period of planet A
then below it is what I think is wrong, T_G G is the Kepler's constant, I'm not sure what that really is
=...
Homework Statement
"Yoda has just discovered planetary system consisting of star Dagobahr and its two planets: Rool and Krau. Planet Rool has average orbital radius 1.6 times as big as planet Krau. If planet Rool orbits Dagobahr in 2.9 Earth years, how long is a year for the resident of...
Consider a pair of binary stars with a separation of 3.60E12 m and an orbital period of 2.55E9s. Assuming the two stars are equally massive, determine the mass of each.
keplar's law...
so I rearranged the formula and set (2pi*r)/T=sqrt((GM)/r), and then I solved for M, which gave me the...
Compare the orbital speeds of satellites that orbit at the following altitudes.
(a) One Earth radius above the surface of the Earth (in km/s)
(b) Two and a half Earth radii above the surface of the Earth.
Here is the equation to be used,
orbital speed is v=(sqrt)(GM/r)
G is the...
Homework Statement
The sun rotates around the center of the milky way galaxy at a distance of about 30,000 light years (1ly= 9.5*10^15m). if it takes about 200 million years to make one rotation, estimate the mass of our galaxy. Assume that the mass distribution of galaxy is concentrated...
Homework Statement
Planets X & Y travel in circular orbits around the same star. The ratio of the radii of their orbits is 5:2. 5 years after the planets were aligned, planet x has rotated 92.6 degrees. how many degrees has y traveled in the same amount of time?
Homework Equations...
I've added short Fourier/Laplace analysis and planetary motion tutorials to my web page.
First, the planetary motion page - my thinking is that the three big steps in the intellectual history of the human race are -
1. when we came down out of the trees,
2. when Newton solved the two-body...
Homework Statement
The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh =...
Homework Statement
Derive the equation using Newton's Law of gravitation and the equation for circular motion.
Homework Equations
V = \sqrt{\stackrel{GM}{r}}
Where G is the universal gravitational constant, M is the mass of the central body and r is the radius...
Homework Statement
Two masses, m and M, are initially at rest at a great distance from each other. The gravitational force between them causes them to accelerate towards each other. Using conservation of energy and momentum, show that at any instant the speed of one of the particles relative...
The following question deals with planetary motion: energy totals and binding energy. I have solved the question to the best of my ability, but I cannot get the right answer! I don't know what I am doing wrong, and would greatly appreciate it if someone could point out my mistakes.
Homework...
The mean distance between the Earth and the moon is 3.84x10^8 m, and the moon has an orbital period of 27.3 days. Find the distance from Earth of an artificial satellite that has an orbital period of 8.5 days.
a. 1.76x10^8 m
b. 1.76x10^4 m
c. 1.76x10^10 m
d. 5.24x10^8 m
So far I got:
I...
hi i hv these 2 doubts...i tried using the elliptic equation:
r= a(1-e^2)/[1-e cos(theta)] however i can't really figure out how do i determine the answer,,i mean if i could know what exactly to do.
1) the orbit of venus is very near circular (e=0.0068).Assuming that the orbit is completely...
Help! Planetary motion
Please help!
Planet X rotates in the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs 946 N on the Earth weighs 920 N at the north pole of Planet X and only 854 N at its equator. The distance...