The wavelength of light emitted by a moving object is shifted. To get it really right, you should understand the Special Theory of Relativity.
It tells us whether a star (or galaxy, or other object) is moving towards us, or away from us; and how fast.
It indicates how fast an object is moving away from us.
It doesn't. The Doppler shift can tell you how fast something is moving towards us or away from us; not how far it is. Only in the case of distant galaxies can this be used to estimate the galaxy's distance, because of the expansion of the Universe (galaxies that move away from us faster are generally farther away).
The star attracts the planet; the planet attracts the star. As a result of the latter, the star changes position. If this change is such that the star moves away from us during one part of the planet's orbit, and towards us at another (or more generally, the star's speed towards us, or away from us, changes slightly), then this can be detected as a Doppler shift.
No. The Doppler shift tells us if the object is moving toward us or away, and how fast. But it says nothing at all about whether, or how fast, the object is moving to the side. Doppler tells us about the part of the velocity that is TOWARD or AWAY. It says nothing about its velocity left, right, up or down.
It tells us whether a star (or galaxy, or other object) is moving towards us, or away from us; and how fast.
True
When an object moves away from us, or towards us.
If there is no observable Doppler shift, then the star is probably not moving very fast. This refers to the component of the star's movement toward us, or away from us - the "sideways" part of the movement can't be determined by the Doppler effect.
A Doppler red-shift is a shift in recognizable features of a star's spectrum from the wavelengths where we know they belong toward longer wavelengths. Such a shift can be caused by the star's moving away from us, and that's how it's interpreted when astronomers see it. A Doppler blue-shift is a shift in recognizable features of a star's spectrum from the wavelengths where we know they belong toward shorter wavelengths. Such a shift can be caused by the star's moving toward us, and that's how it's interpreted when astronomers see it.
A blue-shift means an object is moving towards us, a red-shift means it is moving away from us. Blue-shift and red-shift are changes in frequency of the light we receive, due to the relative movement. This is called the Doppler effect.
They let us see the speed of the stars around the common center of mass. More precisely, the Doppler shift will only detect the component of this speed in our direction - that is, towards us, or away from us.
Doppler effect Red Shift
It indicates how fast an object is moving away from us.
There is a Doppler shift which results from the relative motion of the star in question, either toward or away from us as we observe it.
In that case, the star must be approaching us.
It doesn't. The Doppler shift can tell you how fast something is moving towards us or away from us; not how far it is. Only in the case of distant galaxies can this be used to estimate the galaxy's distance, because of the expansion of the Universe (galaxies that move away from us faster are generally farther away).