To find the tangential speed of an orbiting object, you would use the formula:
[tex]\[ v = \frac{2 \pi r}{T} \][/tex]
where:
- [tex]\( v \)[/tex] is the tangential speed,
- [tex]\( r \)[/tex] is the radius of the orbit,
- [tex]\( T \)[/tex] is the orbital period.
This formula is derived from the relationship between the circumference of the orbit and the time taken to complete one full orbit. The tangential speed is essentially the distance traveled along the orbit (which is the circumference, [tex]\( 2 \pi r \)[/tex]) divided by the time it takes to travel that distance (the orbital period, [tex]\( T \)[/tex]).
