Question

A certain spaceship has a speed of \(19,200 \mathrm{mi} / \mathrm{h}\). What is its speed in light-years per century?

Short answer

The speed of the spaceship in light-years per century is the final calculation of step 3.

Step-by-step solution

Convert speed to mi/century

First, convert the speed from miles per hour to miles per century. There are 24 hours in a day, 365.25 days per year to account for leap years and 100 years in a century. The conversion is thus: \[19,200 \, \text{mi/h} \times 24 \, \text{hours/day} \times 365.25 \, \text{days/year} \times 100 \, \text{years/century}.\]

Convert mi/century to light-years/century

There are approximately 5.879 trillion miles in a light-year. Thus, to convert miles per century to light-years per century, you divide by the number of miles in a light-year: \[\text{Result from step 1} \, \text{mi/century} \, \div \, 5.879 \times 10^{12} \, \text{mi/light-year}.\]

Calculate the final speed

Having set up the conversions, the only thing left is to compute the calculation. Once you've finished the calculations you will have your final speed in light-years per century.

Key concepts

Spacecraft Velocity Calculation

Spacecraft velocity calculation is a crucial aspect of astrophysics and space exploration. Understanding how fast a spacecraft is traveling relative to other objects or points in space is fundamental for navigation, communication, and safety. In our example, the spacecraft's speed is initially provided in miles per hour (mi/h), a common unit when discussing velocities within the Earth's vicinity.

However, when contemplating interstellar distances or comparing velocities on a cosmic scale, it's practical to convert this speed into units that better represent the vastness of space, like light-years per century. The velocity of a spacecraft, when converted into such units, gives us a clearer picture of how time and distance intertwine in the realm of space travel. It also allows for easier comparison with the speed of light, which is the cosmic speed limit, helping us understand our technological capabilities in terms of space exploration.

Unit Conversion

Unit conversion is an essential skill in physics and various other fields, allowing us to translate quantities into different units of measurement. It's particularly helpful when needing to compare measurements that were taken using different systems. In our problem, we're tasked with converting speeds from miles per hour to light-years per century.

Understanding the relationship between the units and having knowledge of the necessary conversion factors is key. For example, knowing that there are 24 hours in a day and 365.25 days in an average year due to leap years helps us convert hours into years. These factors are multiplicative, which means we multiply the speed by the number of hours in a day, by the number of days in a year, and then by 100 to account for a century.

To wrap everything up neatly, being able to manipulate units and implement proper conversion factors is invaluable for solving physics problems and is a transferable skill across many scientific disciplines.

Light-years per Century

The term 'light-year' is a measure of astronomical distances and is defined as the distance that light travels in a vacuum in one Julian year (365.25 days). Given that light travels at approximately 299,792 kilometers per second, a light-year equates to about 5.879 trillion miles. To conceptualize velocities over astronomical timescales and distances, the unit of 'light-years per century' serves as a unique and informative measure.

When we refer to light-years per century, we are, in essence, comparing the speed of an object with how far light travels in a hundred years. It's a unit that puts into perspective the vastness of space and the duration of interstellar travel. For instance, using light-years per century can help when calculating the time required for a spacecraft to reach a distant star or galaxy. We've seen the process of converting mundane Earth-bound speed units into awe-inspiring cosmic measures, linking the familiar with the unfathomably distant.