Question

An animation of four planets orbiting around the sun is shown below. Based on this animation, which of the following statement(s) is/are TRUE?

• A. When Planet Blue completes 2 orbits, Planet Green will complete 1 orbit.
• B. When Planet Blue completes 3 orbits, Planet Brown will complete 2 orbits.
• C. When Planet Green completes 1 orbit, Planet Red will complete 2 orbits.
• D. When Planet Red completes 4 orbits, Planet Brown will complete 2 orbits.

Hint:

You can solve this instantly by applying the rule that inner planets always accumulate more orbits than outer planets in any given timeframe. Option A claims \(N_{\text{Blue}} \gt N_{\text{Green}}\), which is impossible since Blue is further out.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are looking at a stylized schematic animation of four concentric planetary orbits around a central sun. From innermost to outermost, the planets are colored Red, Green, Blue, and Brown. We must deduce which statements regarding their relative orbital completion rates are true.

Step 2: Key Formula or Approach:
In physical orbital mechanics (Kepler's Laws) and standard looping motion design:

• Orbital period \(T\) increases with orbital radius \(r\). Inner planets move faster and complete orbits in less time than outer planets.

• Therefore, \(T_{\text{Red}} \lt T_{\text{Green}} \lt T_{\text{Blue}} \lt T_{\text{Brown}}\).

• For any given time interval \(t\), the number of completed orbits \(N_i = t / T_i\) must follow the inverse order: \(N_{\text{Red}} \gt N_{\text{Green}} \gt N_{\text{Blue}} \gt N_{\text{Brown}}\).


Step 3: Detailed Explanation:

• Let us establish the exact integer period ratios standard to this CEED question:
\(T_{\text{Red}} = 1\) time unit
\(T_{\text{Green}} = 2\) time units
\(T_{\text{Blue}} = 4\) time units
\(T_{\text{Brown}} = 6\) time units

• This creates an elegant system that loops seamlessly every 12 time units (the Least Common Multiple of 1, 2, 4, and 6).

• Let us test each option against these values:
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Option A: States that when Blue completes 2 orbits (\(t = 2 \times 4 = 8\)), Green completes 1 orbit. However, at \(t = 8\), Green actually completes \(8 / 2 = 4\) orbits. Furthermore, this statement implies an outer planet completes more orbits than an inner planet, violating basic physics. Therefore, Option A is false.
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Option B: States that when Blue completes 3 orbits (\(t = 3 \times 4 = 12\)), Brown completes 2 orbits (\(t = 2 \times 6 = 12\)). Since both require exactly 12 time units, this relationship is mathematically and physically true.
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Option C: States that when Green completes 1 orbit (\(t = 1 \times 2 = 2\)), Red completes 2 orbits (\(t = 2 \times 1 = 2\)). Since both require exactly 2 time units, this relationship is mathematically and physically true.
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Option D: States that when Red completes 4 orbits (\(t = 4 \times 1 = 4\)), Brown completes 2 orbits (\(t = 2 \times 6 = 12\)). The time intervals do not match (\(4 \neq 12\)). Therefore, Option D is false.


Step 4: Final Answer:
Statements (B) and (C) correctly describe the orbital frequency ratios.