Radial velocity

Radial velocity was the velocity of a target along the line of sight of an observer. In general, this kinematic quantity could also be the velocity of an object along a radial line from the origin of a coordinate system with a radial coordinate. Examples of such a coordinate system were the polar and spherical coordinate systems. For this definition, the quantity had the dimensions of length per unit time.

This quantity was also the angular velocity around the yaw, pitch or roll axis, or a combination of angular velocities around these axes. Under this definition, the quantity had the dimensions of angle per unit time. (DIS: "Kobayashi Maru")

In the real world, the term "radial velocity" does not have this second definition.

In 3190, scans made by the sensors of the USS Discovery recorded the radial velocity of Deep Space Repair Beta Six as 22 degrees per second. After repairs were made to the station, the radial velocity had dropped down to 38%. (DIS: "Kobayashi Maru")

In the real world, radial velocity cannot have measurement units of degrees per second, or in general, the dimensions of angle per unit time, since the term does not have the second definition.

Background Information

When the Discovery finds Deep Space Repair Beta Six, the station was shown tumbling out of control, with both translational (linear) motion and rotational (angular) motion, with the angular motion looking like a combination of yaw, pitch, and roll. Tilly quantified the tumbling, saying, "Scans show the station moving at 720 kilometers per second with a radial velocity of 22 degrees per second."

And after she, Tal, Nalas and his crew got the station's thrusters working, and the station's rotation was shown to decrease, she asked Burnham for confirmation that all the thrusters were working, and in reply, Burnham reported, "Radial velocity's decreased to 38% and counting."

So, the radial velocity that Tilly and Burnham mentioned is, in the real world, not radial velocity, but angular velocity.

On the other hand, two other characters used real-world terms to describe the angular motion of the station: Nalas said, "Well, I can fix thrusters, that'll stop the spin."

And Owosekun said, "I can get coordinates within an acceptable margin of error if Keyla can match speed and rotation." In the real world, speed is a scalar and is the same as the magnitude of velocity, while velocity is a vector with both magnitude and direction, and with the appropriate adjective, the term "speed" can be used for both linear and angular motion as in "linear speed" and "angular speed," but "speed" is usually used by itself to mean "linear speed." So, by "speed and rotation," Owosekun meant "linear speed and rotation" (or for consistency in physical concepts, "linear and angular speeds" or "translation and rotation").

In addition, since Tilly provided only the magnitudes but not the directions for the linear and angular velocities she reported, then she was really giving only linear and angular speeds.

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