John Denker noted that you have to take the orbital motion into account as
well. Yep.
But. The problem is even more complex than that.
Next you must also account for both Earth's orbital and rotational
velocities.
Finally, you have to account for angles between the direction of Mercury
and the two orbital velocities (Mercury and Earth) and the direction of
Earth's rotational velocity at the location of the observatory. Since the
inclination of the orbital planes are close to each other you can ignore
that vector angle for a first approximation. Just assume that the
rotational velocity of the limb of Mercury is a radial velocity.
These are non-trivial measurements. It is worth discussing this with intro
students then saying, "but hey, we can do an approximate calculation and
get a close idea of the values." I always reminded students that it is
worth doing a rough and easy calculation first, make sure you are in the
ballpark, then dive into the harder version now that you have some
confidence.
This is a great stepping stone to then bring up the concept of extrasolar
planets and the tiny Doppler shift that happens when a small planet orbits
a big star. To be able to know exact values, Earth's motion must be
accounted for. In this case it is worth noticing that the Sun's motion now
is important, although it can be ignored generally as a uniform offset.
Also, unlike with Mercury, the angles of the orbits are fully in three
dimensions since the exoplanet system is unlikely to be along the ecliptic.
John
- - - -
John E. Sohl, Ph.D.
WSU Brady Presidential Distinguished Professor Emeritus
Department of Physics and Astronomy
Department of Environmental Science
Department of Being Retired and Loving It
Weber State University
cell: (801) 476-0589 (Text me, I don't answer the phone if you are not in
my contacts.)