Forever Sunset

Here's an interesting question. How fast would you need to drive or fly west to watch the sunset last forever? Would it be possible with modern technology?

Basically, we just have to find out how fast the Earth is moving, which is easy with a bit of math.

Warp Speed

What if you lived on the equator, and had unlimited money to spend on any vehicle. How fast is the earth moving under your feet? First, find the circumference of the Earth, and divide that by one day, which is one full rotation.

$$C = 2\pi R$$

$$V = \frac{C}{D} = \frac{2 \pi R}{24\text{h}} \approx 0.2618R$$

From a quick Google search, the radius of the Earth at the equator is about 6,378km, or 3,963mi. Plugging that into our equation, we get 1,670 km/hr or 1,038 mph. For reference, the average speed of a drag racer is in the 300 mph (500 km/hr) range. So, a land vehicle won't do.

The fastest jet in the world is the SR-71 Blackbird, achieving a record speed of 3,529.6 km/hr, or 2,193.2 mph. We could fly in one of these bad boys at just under half throttle and watch the sunset for a full day, assuming we had enough fuel.

Drag Speed

Okay, let's say we have unlimited money and resources, but hate flying. So, we decide to build a long, straight road and bridges across the oceans to create a "ring" around the earth. Like mentioned before, we simply don't have any land vehicle fast enough to watch the sunset forever, even if we did have this long, straight road.

Sorry flat Earthers, remember that Earth is a sphere*! So, we don't have to go around the equator. If we move further north or south, the circumference actually decreases, which means the ground we need to cover also decreases!

*Because Earth rotates, it is not a perfect sphere. Rather, it is squished a bit vertically and stretched at the equator. In my equator example, I used the approximate measurement for the radius of Earth's equator, and going forward, I will use the geometric radius of Earth: 6371km.

$$R = R_{\text{geo}}\cos(\text{lat})$$

$$C = 2 \pi R_{\text{geo}}\cos(\text{lat})$$

Now, $R$ is a function of our latitude. We can plug this in to the previous formula to get the ground speed.

$$V = \frac{2 \pi \times 6371\text{km}\times\cos(\text{lat})}{24\text{h}} \approx 1668\cos(\text{lat}) \left[\frac{\text{km}}{\text{h}}\right]$$

Using our shiny new 500 km/hr drag racer, where would we have to build our road in order to watch the sunset forever driving westbound?

$$500 = 1668\cos(\text{lat})$$

$$\text{lat} = \arccos\left(\frac{500}{1668}\right) \approx 1.266 \approx 72.5^{\circ}$$

This can be 72.5 degrees North or South. That's pretty far from the equator, and actually beyond the arctic (or antarctic) circle! 72.5 degrees North passes through parts of Russia, Greenland, and the northern tip of Baffin Island, Canada. 72.5 degrees South is completely contained by Antarctica, with a few stretches through the Southern Ocean.

At least it doesn't cut right through any major cities. Enjoy the sunset!

Disclaimer

I know, Earth rotates on a tilted axis. Let's just say that this only works on the equinox(es). Otherwise, you might have to build a different road, that uses much more complicated mathematics.