As an expert in the field of space exploration and physics, I can provide a detailed explanation of the complexities involved in calculating the time it would take to reach the Sun. The question you've asked is a fascinating one and touches upon various aspects of space travel, including the vast distances involved, the speed of spacecraft, and the laws of physics that govern such a journey.

Firstly, it's important to understand that the speed of a spacecraft is not constant throughout its journey. The speed mentioned for Apollo 10 and the New Horizons probe are their respective peak speeds, achieved under specific conditions. Spacecraft do not maintain these speeds indefinitely; they are influenced by gravitational forces, the need for course corrections, and the propulsion systems' capabilities.

The Sun is located at an average distance of approximately 93 million miles (150 million kilometers) from the Earth, a distance we refer to as 1 astronomical unit (AU). The speed of light, which is the fastest speed at which information can travel, is about 186,282 miles per second (299,792 kilometers per second). Even at this incredible speed, it would still take light about 8 minutes and 20 seconds to travel from the Sun to the Earth.

Now, let's consider the speeds you've mentioned. Apollo 10, with a speed of 24,790 mph (40,090 km/h), and the New Horizons probe, with a speed of 36,373 mph (58,513 km/h), are indeed impressive. However, these speeds are far from the speed of light and would take an incredibly long time to reach the Sun if maintained constantly, which is not possible.

Using the speed of Apollo 10, we can calculate the time it would take to reach the Sun as follows:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
\[ \text{Time} = \frac{93,000,000 \text{ miles}}{24,790 \text{ mph}} \]

This calculation does not account for the fact that the spacecraft would need to decelerate as it approached the Sun, which would add significantly to the travel time. Additionally, the spacecraft would need to travel in a straight line, avoiding any obstacles or gravitational influences that could alter its course.

The New Horizons probe's speed is faster, but still not sufficient to reach the Sun in a human-lifetime. Using its speed for the calculation:
\[ \text{Time} = \frac{93,000,000 \text{ miles}}{36,373 \text{ mph}} \]

Again, these calculations are theoretical and do not take into account the practical challenges of space travel, such as the need for life support systems, shielding from solar radiation, and the immense heat that would be encountered as the spacecraft approaches the Sun.

In reality, no human or spacecraft has ever traveled to the Sun. The Parker Solar Probe, launched in 2018, is designed to come closer to the Sun than any previous spacecraft, but it is not intended to land on or orbit the Sun. It uses a combination of a powerful launch vehicle and gravity assists from Venus to achieve its high speed and trajectory.

In conclusion, while the calculations provide a basic understanding of the time it would take to reach the Sun based on certain speeds, the actual process of space travel is far more complex and involves numerous other factors that must be considered. The current state of technology does not allow for a direct journey to the Sun that would be survivable for humans or sustainable for our spacecraft.

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Apollo 10, the fastest manned spacecraft, traveled 24,790 mph. At that speed, it would take about 156 days to reach the Sun. The unmanned NASA New Horizon probe traveled away from the Earth on its path to Mars and beyond at 36,373 mph.read more >>