Page 70 - analysis-and-interpretation-of-astronomical-sp

Analysis and Interpretation of Astronomical Spectra 70

16 The Measurement of the Rotation Velocity

16.1 Terms and Definitions

The Doppler shift , caused by the different radial

velocities of the eastern and western limb of a rotating
spherical celestial body, allows the determination of
the rotational surface speed. Here we limit ourselves
to the spectroscopically direct measurable portion of
the rotation speed, the so-called value, which

is projected into the visual line to Earth.

This term, read as a formula, allows calculating this
velocity share with given effective equatorial velocity

and the inclination angle between the rotation axis
and the visual line to Earth. The Wikipedia graph
shows here differently as .

If the rotation axis is perpendicular to the sight line to Earth then and s

Exclusively in this special case, we can exactly measure the equatorial velocity .

If , we look directly on a pole of the celestial body and thus the projected rotational

velocity becomes s

16.2 The Rotation Velocity of the Large Planets

If the slit of the spectrograph is aligned with the equator of a rotating planet, the absorption
lines of the reflected light appear slightly leaning. This is caused by the Doppler shift due to
the radial velocity difference between the eastern and western limb of the celestial
body. The rough alignment of the slit can be done by Jupiter with help of its moons and by
Saturn with its ring.

The radial velocity difference is calculated from the obliquity of the spectral lines. For
this purpose from a good quality spectrum two narrow strips, each on the lower and upper
edge are processed and calibrated in wavelength. The difference between the upper and
lower edge gives the Doppler shift and with formula {16} or {20} the velocity difference

can be obtained (detailed procedure, see [30]).

vsin i Δλ

vr
vr

-vr
-vr

-vsin i