Chapter 15: Problem 49
Mass of Saturn. The innermost rings of Saturn orbit in a circle with a radius of 67,000 kilometers at a speed of \(23.8 \mathrm{km} / \mathrm{s}\). Use the orbital velocity formula to compute the mass contained within the orbit of those rings. Compare your answer with the mass of Saturn listed in Appendix E.
Short Answer
Step by step solution
Understand the Orbital Velocity Formula
Rearrange the Formula to Solve for Mass
Convert Radius to Meters
Plug in Known Values
Calculate the Mass
Compare with Saturn's Mass
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
mass of Saturn
Besides its role in celestial mechanics, understanding the mass of Saturn helps us deduce various characteristics of its rings. The exercises like the one originally provided challenge us to use orbital parameters to calculate this mass through orbital motion, illustrating the balance in physics governing these gigantic celestial objects.
gravitational constant
- In Calculations: The gravitational constant remains a critical factor in calculations involving celestial bodies.
- Universal Relevance: It is consistent throughout the universe, allowing scientists to make precise calculations.
Without \( G \), calculating the mass of celestial bodies, like Saturn, from observed motions would be impossible, emphasizing its importance in physics.
celestial mechanics
- Orbital Velocity: This is a crucial concept in celestial mechanics. For Saturn's rings, the orbital velocity tells us how fast the rings must move to remain in stable orbit.
- Kepler’s Laws of Planetary Motion: These laws describe how celestial objects move in orbits due to gravitational attraction, a foundation of celestial mechanics.
physics formula derivation
- Rearrangement: This process involves placing the known values in a position to isolate the desired unknown variable.
- Understanding Variables: Knowing what each symbol in a formula represents is crucial, ensuring correct application and interpretation.