Answer to Question 1
There are several possible explanations. Hydrogen rich planets will vary greatly in density which is attributable to increases in temperature caused by their proximity to their host stars. Water worlds may be similar to our ice giants, but instead be dependent on when a star clears its nebular gas.
Answer to Question 2
To determine the true space motion of a star both the radial velocity and transverse velocities must be determined. The radial velocity can be determined directly from observing the spectrum and measuring the Doppler shift of the absorption lines. The transverse velocity is calculated from observations of a star's proper motion and distance. The proper motion is the angular motion per year of the star. Once the radial velocity and transverse velocities are known, the space motion of the star is calculated using the Pythagorean theorem (square root of the sum of the squares of the velocities).
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