The Earth orbits the Sun at an average speed of about 29.8 kilometers per second (18.5 miles per second) or approximately 107,000 kilometers per hour (67,000 miles per hour). This orbital speed is known as the Earth's "mean orbital velocity." It's worth noting that the Earth's orbital speed is not constant throughout the year due to its elliptical orbit, but the average value provides a good approximation.
To estimate how long it would take to travel from one end of our solar system to the other without going around the Sun, we need to define the "ends" of the solar system. The solar system is commonly considered to extend to the outer edge of the heliosphere, which is the region influenced by the Sun's solar wind.
The heliosphere is believed to extend up to the termination shock, located roughly 80 to 100 astronomical units (AU) from the Sun. One AU is the average distance from the Earth to the Sun, approximately 149.6 million kilometers (93 million miles).
If we take a rough estimate of 100 AU as one "end" of the solar system and assume a constant speed, it would take approximately 35 years to travel that distance at the Earth's average orbital velocity.
However, it's important to note that the heliosphere doesn't mark the true boundary of the solar system. Beyond the termination shock lie the heliosheath, the heliopause, and finally, the interstellar medium. Defining the exact boundaries of the solar system is a topic of ongoing scientific research.
Additionally, achieving such a journey in practice would require significant advancements in technology, as well as considerations for the availability of suitable propulsion systems, life support, and other logistical factors.