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...
Homework Statement
I have phase space coordinates (x0,y0,z0,vx,vy,vz)=(1,0,0,0,1,0). I need to analytically show that these phase space coordinates correspond to a circular orbit.
Homework Equations
r=sqrt(x^2+y^2+z^2) maybe?
The Attempt at a Solution
My core problem here is maybe that I...
A space vehicle enters the sensible atmosphere of the earth (300,000 ft) with a velocity of 25,000 ft/sec at a flight-path angle of -60 degrees. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent?
(Assuming no drag or perturbations, two body orbital...
Would the velocity of a body which is orbiting another body change due to its radius to the center of gravity? If so, why? A body which moves passed a planet and starts orbiting it should have the same velocity it had before ,regarding the fact that it is orbiting a planet. Also, gravity isn’t...
What If the velocity of particle moving in a circular orbit has increased , would the particle be no longer in circular orbit or it would go in an orbit with bigger radius?
This is a possible science-fiction scenario, and I'm wondering if it is scientifically plausible.
If someone wanted to take a one-way trip into future, say 1000 years from now, then SR gives you a possible way to do it without dying of old age: Just hop in a rocket ship, accelerate to nearly...
Homework Statement
The orbits of the planets remains extremely stable over long times however this not always true for comets. Can you explain why not? What hazards might they encounter during their travels?
Homework Equations
None
The Attempt at a Solution
I think that due to the comet's not...
1. The problem statement, all variables, and given/known data
Satellites orbiting the Earth are often put into orbit at different heights around the planet. What affect will this have on the motion of the satellite and how exactly would the motion of a very high orbit satellite differ from one...
1. The problem statement, all variables, and given/known data
Venus is sometimes described as either the “Morning Star” or the “Evening Star”, since it can only be seen near sunrise and sunset, very close to the Sun in the sky. Why does Venus always appear close to the Sun in the sky for an...
Hi! first time poster here.
I'm making an orbital simulation and I am having a problem with one minor detail.
The gravity is working great, and I've programmed it using this formula:
A force vector is applied = DirectionOfCentralBodyNormalized * ((GravConstant * centralbodymass *...
I have a satellite orbiting at a velocity of 3850Km/hr around planet earth in a circular orbit, please help me in calculating it's height of orbit. I do know that the closer a satellite is, the faster it's orbital velocity, and the farther it is the slower it would be, and help me with the formulas?
How does the adiabatic invariance of actions J imply that closed orbits remain closed when the potential is deformed adiabatically?
Is it because a closed orbit has commensurate angular frequencies $$\omega_i$$ defined by $$\omega_i = \frac{\partial H}{\partial J_i}$$ where H is the...
First off, I'd like to note that I am by no means a physics expert. I am merely a high school student and a physics/maths enthusiast, nothing more, so if my thoughts are completely dysfunctional and downright incorrect, which is more than a distinct possibility, please tell me.
I recently took...
Hi!
This is a textbook problem that I need help with (I want to practice as much as I can before the exams) and I hope that there is someone who can guide me. The question is:
You’re doing a first-order analysis on a new satellite in an elliptical (e = 0.2) orbit at 700 km altitude. Can you...
Homework Statement
A satellite moving in a highly elliptical orbit is given a retarded force concentrated at its perigee. This is modeled as an impulse I. By considering changes in energy and angular momentum, find the changes in a (semi major axis) and l (semi latus rectum). Show that \delta...
Homework Statement
Show that Kepler's third law, \tau = a^{3/2}, implies that the force on a planet is proportional to its mass.
Homework Equations
3. The Attempt at a Solution [/B]
I haven't really attempted anything. I'm not sure what the question is going for. What can we assume and use?
There have been many questions on this forum about celestial mechanics in general, and concerning position and velocity in an orbit in particular. So I offer this post as a summary and reference.
Here's a method for finding heliocentric position and sun-relative velocity in ecliptic coordinates...
Hello friends (I hope :biggrin:),
For a maths project I am working on, I need to be able to prove the equation for an elliptical orbit, related to Kepler's first law:
and p = a(1-e2) (or should be as p can be replaced by that value)
Where:
r = distance from sun to any point on the orbit
p =...
Homework Statement
A satellite is in a circular orbit of radius R from the planet's center of mass around a planet of mass M.
The angular momentum of the satellite in its orbit is:
I. directly proportional to R.
II. directly proportional to the square root of R
III. directly proportional to...
So let's say you are on an orbital satellite in an elliptical orbit around our planet Earth, meaning that the at one point in the orbit you are going faster, due to the gravitational pull of the planet. Would you feel the acceleration in space due to the shape of the orbit?
Would you guys agree with these websites on how orbits work?
http://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-orbit-58.html
http://www.qrg.northwestern.edu/projects/vss/docs/space-environment/1-what-causes-an-orbit.html
Hi! I am currently trying to write a code in C to simulate the orbit of planets around the Sun in the solar system.
I am using the velocity Verlet approach and finding that my code produces no acceleration in the ##y##-direction (aside from for ##t_n = 0##,) and that the planet just flies off...
Hi,
I've read that SOHO (SOlar and Heliospheric Observatory) is orbiting around the L1 point. I remember this point being unstable (that is, that something in orbit will diverge from stability). How are the corrections made for this orbit ? Does it really cost a tiny amount of fuel, or is the...
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...
Can someone please give a step by step explanation of an orbital rendezvous by a spacecraft for a target that is orbiting the body it launched from? And if possible, can you explain how mission control is involved and what part computers play? When the RCS is active is it changing the...
Hi there,
I was reading one of my textbooks and I had a thought. For a black hole, there is minimum orbiting radius of ##R_{min}=3R_s## where ##R_s## is the Schwarzschild Radius. This minimum orbit is created by the fact that in order to obtain an orbit of that radius around a black hole, you...
Firstly, apologies if this is in the wrong thread.
I'm currently writing a presentation on the physics of getting a spacecraft from Earth to Mars in the near future. In my research I've come up against Porkchop plots which seem to plot contours of equal characteristic energy so you can find out...
I was thinking about the motion of two stars in a binary star system, but there is something I cannot quite figure out. Suppose you have a binary star system with two stars masses m1 and m2 with m2>m1 so that m2 is closer to the centre of mass of the system. Then when the two stars are as far...
A satellite changes its orbit inclined 66° at 260.0 km altitude to a polar orbit at the same altitude. What Delta V was required?
... I am stuck.
do I figure it out using:
DeltaV1 = |V_transfer at orbit 1 - V_orbit 1|
and
DeltaV2 = |V_transfer at orbit 2 - V_orbit 2|
or is there another...
A satellite has been placed in a circular, sun-synchronous orbit at an altitude of 1300.0 km. The satellite has a mass of 5,000.0 kg. What is the K.E. of the satellite?
I know K=(1/2)mv^2 .... but I have no idea where to go from here. I Know I am over-thinking this. So any help would be greatly...