What is the term used to describe the minimum constant velocity a space vehicle must maintain to stay in a fixed circular trajectory surrounding a planet?

The correct option is Orbital velocity.

Explanation:

1. Understanding the Physics:
When a space vehicle (or satellite) moves in a circular path around a celestial body like a planet, it requires a continuous inward force known as the centripetal force to change its direction and keep it in orbit. This centripetal force is provided by the gravitational attraction between the planet and the vehicle.

2. Mathematical Relation:
If a space vehicle of mass $m$ orbits a planet of mass $M$ at a radius $r$ from the center of the planet, the gravitational force is given by:

$F_g=\frac{GMm}{r^2}$

For a circular orbit, this force equals the required centripetal force:

$F_c=\frac{m{v}^2}{r}$

Equating the two forces:

$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$

Solving for velocity $v$:

$v=\sqrt{\frac{GM}{r}}$

This minimum constant speed $v$ required to maintain a stable, fixed circular trajectory around a planet is called the orbital velocity.

3. Breakdown of Options:
• Orbital velocity: The exact speed needed for an object to remain in a stable orbit around a celestial body.
• Escape speed: The minimum speed needed for an object to break free from a planet's gravitational pull entirely without further propulsion.
• Terminal speed: The steady speed achieved by an object falling through a fluid (like air) when drag force equals gravity.
• Relative speed: The velocity of an object measured relative to a specific observer or reference frame.