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8

Constellations and asterisms are generally not proximate in space, but rather happen to be nearby only when viewed from Earth. From Wikipedia's article on asterisms: Like constellations, asterisms are in most cases composed of stars which, while they are visible in the same general direction, are not physically related, often being at significantly ...


5

Following the convention $\mathbf{r} = \mathbf{r}_2-\mathbf{r}_1$, $M = m_1+m_2$, in the center-of-mass frame we have, by definition, $$\begin{eqnarray*}\mathbf{r}_1 = -\frac{m_2}{M}\mathbf{r}\text{,}\quad&\mathbf{r}_2 = \frac{m_1}{M}\mathbf{r}\text{.}\end{eqnarray*}$$ Hence, $\ddot{\mathbf{r}} = -GM\hat{\mathbf{r}}/r^2$ implies that the individual ...


4

According to wikipedia and other sources, a planet and a star always move in a circular orbit around the common center of mass of the both bodies ... This is not true. In the absence of other gravitational sources, a planet and a star move in elliptical orbits about the common center of mass. Ancient scientists assumed circular orbits, but only because ...


3

Only very rare instances would get close to such stars being on a plane, if any can be found. A nice graphic image showing how the Big Dipper stars appear on an imaginary plane as viewed from Earth combined with a side-view showing approximate distances can be seen at this earthsky.org page.


3

The orbit of a planet does not in any way depend in its moons, mass or own gravity. The orbit is the same for a grain of dust as for a giant planet. It only depends on the mass on the Sun and the distance to the Sun. The eccentricity of the orbit is then given by the initial angular momentum of the orbiting object. This might explain it a bit better. This ...


2

Yes, a planetoid such as Pluto will be able to orbit no matter how small its mass, so long as its angular momentum is within a range determined by its distance from the sun. In the case of Pluto and its primary moon, Charon, however, things are even more interesting. If Charon were to magically disappear (ejection would be another story), the point on the ...


2

Like the above: they can be significantly separated by space. One way to visualize this is to turn on constellations in Celestia then travel to a different star. The constellation outlines can shift significantly. Celestia is an open source visualization thing, it is available at: http://www.shatters.net/celestia/


1

The stars are not in the same plane and move in different directions. See this youtube video.


1

As ganbustein says, this is not too difficult to imagine. The simplest case (approximating with circular orbits and only the Sun, Earth and Satellite) would have the satellite orbit orthogonally to the Earth with a 1 year orbit. The Satellite will pass the Earth orbit plane in two places, call these "down crossing" and "up crossing" points. To minimize ...


1

You must apply Newton's law $$ m\frac{\mathrm{d}\boldsymbol{v}}{\mathrm{d}t} = \boldsymbol{F}$$ which related the force $\boldsymbol{F}$ to the acceleration (=change of velocity). Note that positions, velocities, and forces are all vector quantities. Also note that as the objects move (change position), their mutual forces change (both direction and ...


1

David Hammen wrote People are using planetary equations coupled with geometric integration techniques... You could also try (what I call) a simple finite-step simulation using Newton's laws to operate on object masses, positions, velocities and accelerations. I'm not sure if this falls within what David calls "geometric integration techniques". My ...


1

The Galactic rotation period at the Sun's Galactocentric radius is about 230 million years (with a five percent uncertainty) and the Sun, as stated in user8's answer is 4.57 billion years old - giving $\sim 20\pm 1$ orbits. However, the idea of a Galactic year is misleading. For instance, the Milky Way rotation curve is quite flat between 1 and 10 kpc from ...



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