From his measurements, Roemer estimated that it took 22 min for light to travel a distance equal to the diameter of Earth's orbit around the Sun. (a) Use this estimate along with the known diameter of Earth's orbit to obtain a rough value of the speed of light. (b) Light actually takes \(16.5 \mathrm{min}\) to travel this distance. Use this time to calculate the speed of light.

Roemer's light speed estimation is a historical and significant milestone in the scientific understanding of the nature of light and its propagation speed. In the late 17th century, Danish astronomer Ole Rømer observed eclipses of Jupiter's moon Io and noticed discrepancies in its eclipsing schedule depending on Earth's position in its orbit around the Sun. Interpreting these variations, Rømer concluded that light takes time to travel across the vast distances of space.

He estimated that it took approximately 22 minutes for light to travel a distance equal to the diameter of Earth's orbit around the Sun. Although his estimate was rough, it provided the first quantitative evidence that the speed of light was finite and very fast, challenging the prevailing belief that light's speed was infinite. Today, we know that the actual time taken for light to traverse this distance is closer to 16.5 minutes, and this intellectual legacy of Rømer's remains foundational to modern astrophysics.

The conversion of units in physics is an essential skill, as it enables consistent and accurate communication of measurements within the scientific community. In physics, standardized units such as meters per second (m/s) for speed, kilograms (kg) for mass, and seconds (s) for time are used to eliminate confusion and facilitate comparison of results.

When solving problems, it's crucial to convert all measurements into a consistent set of units before performing calculations. For example, in the step-by-step solution, time was initially given in minutes, which is not standard for calculating speed in physics. Thus, the time was converted from minutes to seconds—multiplying by 60—since the commonly accepted units for speed are meters per second or kilometers per second. Such conversions ensure accuracy and are vital for solving physics problems correctly.

Calculating physical quantities is fundamental in physics, as it allows us to derive measurable properties of objects and phenomena using mathematical formulas. One such quantity is speed, which is calculated by dividing the distance an object travels by the time taken to travel that distance. The speed of light, one of the most important constants in physics, is also determined using this method.

In the given exercise, the distance is the diameter of Earth's orbit, and the time is how long it takes for light to cover that distance. To find the speed of light, you substitute the known distance and time into the speed formula. Furthermore, ensuring that all variables are in proper units before substituting them into the equation is crucial for obtaining a correct and meaningful speed value. Missteps in unit conversion can easily lead to significant errors in the final result, reinforcing the importance of diligent unit conversion and calculation in physics.