Question

How fast would you have to travel on the surface of Earth at the equator to keep up with the Sun (that is, so that the Sun would appear to remain in the same position in the sky)?

Short answer

Approximately 1,668 km/hour.

Step-by-step solution

Understanding Earth's Rotation

Recognize that the Earth takes 24 hours to make a full rotation of 360 degrees. This is the basis for our calculations.

Calculate Earth’s Circumference at the Equator

Earth's circumference at the equator can be approximated using the formula for the circumference of a circle: \[ C = 2 \pi r \]where, \( r \), the radius of the Earth, is approximately 6,371 km. Thus, \[ C = 2 \pi (6,371) \approx 40,030 \text{ km} \]

Determine Needed Speed

Since you need to cover the circumference of the Earth in 24 hours to keep up with the Sun, use the formula for speed: \[ v = \frac{d}{t} \]where, \( d \) is the distance (Earth's circumference at the equator) and \( t \) is the time (24 hours). \[ v = \frac{40,030 \text{ km}}{24 \text{ hours}} \approx 1,668 \text{ km/hour} \]

Key concepts

Circumference Calculation

The circumference of a circle is the distance around it. For Earth, we calculate the circumference at the equator, which is the largest possible circumference around the planet. We use the formula: \[ C = 2 \pi r \] Here, \( r \) represents the radius, and for Earth, it is roughly 6,371 km. After plugging in this value, we get: \[ C = 2 \pi (6,371) \approx 40,030 \text{ km} \] This means Earth’s equatorial circumference is approximately 40,030 kilometers. To visualize, this is like taking a long trip around the globe, which gives us a better understanding of the distance we need to travel to keep up with the Sun.

Speed Formula

Speed is a measure of how fast something is moving over a certain distance in a given amount of time. To find the speed required to keep up with the Sun at Earth’s equator, we use the formula: \[ v = \frac{d}{t} \] Here, \( v \) is the speed, \( d \) is the distance to be covered (Earth’s circumference at the equator), and \( t \) is the time to cover that distance (24 hours). Plugging in the values: \[ v = \frac{40,030 \text{ km}}{24 \text{ hours}} \approx 1,668 \text{ km/hour} \] This calculation tells us that to keep up with the Sun, you’d need to travel at about 1,668 kilometers per hour. This speed is much faster than commercial airplanes!

Earth’s Equator

The equator is an imaginary line running around the middle of the Earth, equidistant from the North and South Poles. It divides the Earth into the Northern and Southern Hemispheres. The equator is significant for several reasons:

• It's the point where the Earth's circumference is the largest.
• The equatorial region experiences nearly consistent, warm temperatures year-round.
• Days and nights are almost equal in length throughout the year at the equator.

Because the equator is the widest part of the Earth, it has the longest circumference, which is why our calculations for rotation speed are based on equatorial measurements. Understanding the equator helps us grasp how Earth's rotation impacts day and night cycles and why different regions experience varying speeds and distances in relation to these cycles.