What is the orbital velocity of Miranda around Uranus?...

What is the orbital velocity of Miranda around Uranus? (Hint: Use the formula for circular orbit velocity, Chapter $5 .$ The formula requires input quantities in $\mathrm{kg}$ and $\mathrm{m}$.) (Note: Necessary data are given in Celestial Profile 9 and Appendix Table A-11.)

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Key Concepts

Orbital Velocity

Orbital velocity is the speed at which an object travels along its orbital path around a central body. It is determined by the balance between the gravitational pull of the central body and the inertia of the orbiting object, ensuring that the object follows a stable orbit, typically computed using the formula v = ?(GM/r) for circular orbits.

Circular Orbit

A circular orbit assumes that the orbiting body is moving in a path with constant radius around the primary mass. This simplification means that forces acting on the body such as gravity provide the exact centripetal force required to keep the object in a stable, circular trajectory.

Gravitational Constant and Central Mass (GM)

The product GM, where G is the universal gravitational constant and M is the mass of the central body, represents the gravitational parameter. This parameter is crucial in determining orbital characteristics as it quantifies the strength of the gravitational field generated by the central body.

Unit Conversion

When applying the formula for orbital velocity, it is essential to use a consistent set of units, typically SI units. This means converting all measurements to meters for distances and kilograms for mass, ensuring that calculations using the gravitational constant are accurate and compatible.

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