If the temperature of the sun was to increase from T to 2 T...

If the temperature of the sun was to increase from $T$ to $2 T$ and its radius from $R$ to $2 R$, then the ratio of the radiant energy received on earth to what it was previously will be
(A) 4
(B) 16
(C) 32
(D) 64

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Key Concepts

Stefan-Boltzmann Law

This law states that the power radiated per unit area of a black body is proportional to the fourth power of its temperature. It is fundamental in astrophysics for relating a star's surface temperature to its emitted radiation, which is critical when analyzing changes in luminosity due to temperature variations.

Luminosity

Luminosity is the total energy emitted by a star per unit time, and it depends on both the surface area and the temperature of the star. Given that the surface area scales with the square of the radius and the emitted energy scales with the fourth power of the temperature, changes in these parameters have a compounded effect on the star's total energy output.

Inverse Square Law

This law explains how the intensity of radiation from a source diminishes with the square of the distance from that source. Although changes in a star's properties affect its intrinsic luminosity, the energy received by an observer is also modulated by the inverse square law, as the radiation spreads over a larger area with increasing distance.

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