To keep the Sun perpetually setting, you would need to travel at a speed that compensates for the Earth's rotation. The Earth rotates once every 24 hours, completing a full rotation of 360 degrees. Therefore, to keep up with this rotation and ensure the Sun remains on the horizon, you would need to travel at a speed equal to the rotational speed of the Earth at your specific location.
The speed required would vary depending on your latitude since the rotational speed of the Earth decreases as you move closer to the poles. At the equator, the Earth's rotational speed is approximately 1670 kilometers per hour (km/h) or 1037 miles per hour (mph). This is the speed you would need to match to keep the Sun continuously setting.
However, as you move away from the equator towards higher latitudes, the rotational speed decreases. At the North or South Pole, the rotational speed becomes zero since the axis of rotation passes through these points. Therefore, at the poles, you wouldn't need to travel at all to keep the Sun perpetually setting.
Keep in mind that achieving and sustaining such high speeds is currently beyond our technological capabilities. Moreover, it's worth noting that the concept of keeping the Sun perpetually setting would result in an unconventional experience of day and night, with potential implications for various natural cycles and ecosystems on Earth.