To calculate the amount of light reflected by Jupiter as a fraction of the total light emitted by the Sun, we need to consider two key points:

1. Inverse Square Law: The intensity of light diminishes with the square of the distance from the source. So, the light that reaches Jupiter from the Sun will be less intense compared to the light that reaches Earth.

2. Reflectivity of Jupiter: Since we're neglecting any difference in reflectivity (albedo) between Earth and Jupiter, we treat their reflective properties as identical.

Step-by-Step Calculation:

1. Distance from Sun to Earth ($d_{\text{Earth}}$): $d_{\text{Earth}} \approx 1 \, \text{Astronomical Unit} \, (\text{AU}) = 1.496 \times 10^8 \, \text{km}$

2. Distance from Sun to Jupiter ($d_{\text{Jupiter}}$): $d_{\text{Jupiter}} \approx 5.2 \, \text{AU} = 5.2 \times 1.496 \times 10^8 \, \text{km} = 7.79 \times 10^8 \, \text{km}$

3. Light Intensity at Jupiter: According to the inverse square law, the intensity of sunlight at Jupiter compared to Earth is inversely proportional to the square of their distances from the Sun: $I_{\text{Jupiter}} = I_{\text{Earth}} \times \left( \frac{d_{\text{Earth}}}{d_{\text{Jupiter}}} \right)^2$ Substituting the values: $I_{\text{Jupiter}} = I_{\text{Earth}} \times \left( \frac{1}{5.2} \right)^2 = I_{\text{Earth}} \times \frac{1}{27.04}$ Therefore, the intensity of sunlight at Jupiter is roughly 1/27th of that at Earth.

4. Fraction of Light Reflected by Jupiter: If we assume that both Earth and Jupiter have the same reflectivity (albedo), the fraction of the Sun’s total light that Jupiter reflects will be proportional to the amount of sunlight it receives, which is 1/27th of what Earth would reflect at the same distance.

Thus, the amount of light reflected by Jupiter as a fraction of the total light emitted by the Sun is: $\text{Fraction of light reflected by Jupiter} = \frac{1}{27.04}$

Conclusion:

Jupiter reflects about $\frac{1}{27}$ of the sunlight it receives, assuming equal reflectivity with Earth.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How does Jupiter's albedo compare with Earth's?
2. How would the distance from the Sun affect the brightness of a planet's reflected light?
3. What is the effect of atmospheric composition on a planet’s reflectivity?
4. Can we calculate the exact fraction of sunlight reflected by all planets combined?
5. How does Jupiter's size impact the total light it reflects?

Tip: Reflectivity (albedo) plays a significant role in determining how much sunlight a planet reflects. Higher albedo means a planet reflects more light.