# Orbital mecahnics Definition and 13 Discussions

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1. ### I Change in orbit when mass is doubled

A satellite is orbiting a planet in a circular orbit. The planet's mass doubles instantly. What happens to the orbit of the satellite? I think it would move to an elliptical orbit with major axis equal to the old radius and a minor axis equal to either 1/2 or sqrt(2)/2 times the old radius. I'm...
2. ### Change of ellipse while accelerating the rocket

When the rocket accelerates in space does its trajectory which is an ellipse change in size and not the focal points because the Earth is still in one of two and also the current height doesn't increase, right?
3. ### Maximum safe mass of an asteroid in geostationary orbit

Summary:: What is the maximum safe mass of an asteroid in geostationary orbit before it causes problems? Hello everyone, If there was an asteroid in geostationary orbit around the Earth, over the Pacific Ocean, what would be the highest mass it could have before it would start having...
4. ### I If Jupiter had a 5th large moon until "recently", would we know?

Hi! I'm fascinated by the apparent "concentration" of the four large Galilean moons in a barely 1.5 million km "strip", and the vast, "empty" distance to the next moons (moonlets?) Out of a purely aesthetic sense of horror vacui, :wink: I've always wondered if there was at least another Jovian...
5. ### I Stability of circular orbits in an arbitrary central force field

In this chapter, the stability of an object orbiting in a circular orbit of radius r_c in an arbitrary force field f is considered. The author arrives at the equation of a harmonic oscillator, for small deviations x from the circular orbit: \ddot{x} + \left[-3\frac{f(r_c)}{r_c} -...
6. ### I Black hole orbital mechanics questions

What are some of the challenges associated with calculating orbital parameters of objects around a black hole (I.e. Orbital velocity, period, semi major axis, kinetic energy). At what point can classical physics no longer provide accurate results?
7. ### Why do we need the hyperbolic excess velocity?

$$V_{HE}=\sqrt{\frac{\mu}{a}}$$ What is the rationale for this formula when we can determine the change in velocity from Earth's orbit to transfer orbit using the vis-viva equation? Likewise, what is the use of defining the radius for the sphere of influence for interplanetary transfer...
8. ### Orbit that does not need maneuvering

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...
9. ### Concerning SOHO's orbit, and its corrections.

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...
10. ### Meaning of "equatorial radius in an orbital plane"

I wish to solve the inverse geodesic problem numerically using http://geographiclib.sourceforge.net/html/classGeographicLib_1_1Geodesic.html#a455300c36e6caa70968115416e1573a4, and to finish off I need to specify the "equatorial radius". I am not too familiar with this, and do not see immediately...
11. ### Continuous thrust orbit changes

Most threads about making orbit changes assume impulsive changes in velocity (short period bursts). What if one wants to increase the radius of a circular orbit with a very small constant thrust? I assume the thrust should be applied tangentially in the direction of travel, but what would be the...
12. ### Satellite Access from state vectors

I've been trying to figure out how to calculate if a satellite is in view of a ground station (and above a certain elevation) using just position vectors for both satellite and ground station. Does anyone know of an equation, algorithm, etc. that does this? Thanks
13. ### Trajectory opimization: Fast preview algorithm

Hello everyone, I have been interested in trajectory optimization for a while now and I have read a few papers on that topic and bought the book "Spacecraft trajectory optimization" from Cambridge University Press and want to start programming with the goal to optimize a trajectory in a...