Small Body Orbiting A Central Body
Under standard assumptions in astrodynamics we have:
where m is the mass of the orbiting body, M is the mass of the central body, and G is the gravitational constant.
For all circular orbits around a given central body:
where r is the orbit radius, v is the orbital speed, ω is the angular speed, and T is the orbital period.
The last equality has a very simple generalization to elliptic orbits:
where a is the semi-major axis. See Kepler's third law.
For all parabolic trajectories rv2 is constant and equal to 2μ. For elliptic and hyperbolic orbits μ = 2a|ε|, where ε is the specific orbital energy.
Read more about this topic: Standard Gravitational Parameter
Famous quotes containing the words small, body, orbiting and/or central:
“Y’know, George, I feel that in a small way we’re doing something important. It’s satisfying a fundamental urge. It’s deep in the race for a man to want his own roof and walls and fireplace. And we’re helping him get those things in our shabby little office.”
—Frances Goodrich (1891–1984)
“By my troth, Nerissa, my little body is aweary of this great world.”
—William Shakespeare (1564–1616)
“Our roots are in the dark; the earth is our country. Why did we look up for blessing—instead of around, and down? What hope we have lies there. Not in the sky full of orbiting spy-eyes and weaponry, but in the earth we have looked down upon. Not from above, but from below. Not in the light that blinds, but in the dark that nourishes, where human beings grow human souls.”
—Ursula K. Le Guin (b. 1929)
“Et in Arcadia ego.
[I too am in Arcadia.]”
—Anonymous, Anonymous.
Tomb inscription, appearing in classical paintings by Guercino and Poussin, among others. The words probably mean that even the most ideal earthly lives are mortal. Arcadia, a mountainous region in the central Peloponnese, Greece, was the rustic abode of Pan, depicted in literature and art as a land of innocence and ease, and was the title of Sir Philip Sidney’s pastoral romance (1590)