The Sun subtends an angle of about 0.5° to us on Earth, 150 million km away. Estimate the radius of the Sun.

The angular position of an object can be calculated by dividing the arc length by the distance. Its value is altered linearly to the value of the arc length.

Given data:

The subtended angle is\(\theta = 0.5^\circ \).

The distance between the Earth and the Sun is \(d = 150\;{\rm{million}}\;{\rm{km}}\).

The diameter of the Sun can be calculated as:

\(\begin{aligned}{l}D &= d\theta \\D &= \left( {\left( {150\;{\rm{million}}\;{\rm{km}}} \right)\left( {\frac{{{{10}^6}\;{\rm{km}}}}{{{\rm{1}}\;{\rm{million}}\;{\rm{km}}}}} \right)} \right)\left( {\left( {0.5^\circ } \right)\left( {\frac{{2\pi \;{\rm{rad}}}}{{360^\circ }}} \right)} \right)\\D = 1.3089 \times {10^6}\;{\rm{km}}\end{aligned}\)

The radius of the Sun can be calculated as:

\(\begin{aligned}{l}R &= \frac{D}{2}\\R &= \frac{{\left( {1.3089 \times {{10}^6}\;{\rm{km}}} \right)}}{2}\\R = 6.54 \times {10^5}\;{\rm{km}}\end{aligned}\)

Thus, the radius of the Sun is \(6.54 \times {10^5}\;{\rm{km}}\).