Perihelion and aphelion are two terms used in astronomy to describe the closest and farthest points in a planet's orbit around the sun, respectively. Perihelion is the point in the orbit where the planet is closest to the sun, while aphelion is the point where the planet is farthest from the sun. These points are important because they can affect the planet's climate and seasons due to the varying distance from the sun. For example, Earth is closest to the sun during its perihelion in early January and farthest from the sun during its aphelion in early July. **

The Earth is faster when it is in perihelion because it is closest to the sun at this point in its orbit. According to Kepler's second law of planetary motion, a planet travels faster in its orbit when it is closer to the sun and slower when it is farther away. This means that when the Earth is in perihelion, it is moving at its fastest speed as it orbits around the sun. As the Earth moves away from the sun in its orbit, it slows down, reaching its slowest speed when it is in aphelion, the point farthest from the sun. **

The aphelion distance can be calculated using the perihelion distance and the orbital period by using Kepler's second law. Kepler's second law states that a planet sweeps out equal areas in equal times, meaning that the area of the ellipse swept out by the planet's orbit is constant. By knowing the orbital period and the perihelion distance, one can calculate the semi-major axis of the orbit. With the semi-major axis known, the aphelion distance can be calculated by adding the semi-major axis to the perihelion distance. **

The popularity of cycling or skiing can vary depending on the location and time of year. In general, cycling tends to be more popular in urban areas and during the warmer months, while skiing is more popular in mountainous regions and during the winter. However, it's difficult to determine which activity is followed more overall without specific data on participation rates in different regions and seasons. **

The excitement level of ice hockey versus soccer is subjective and can vary depending on personal preferences. Ice hockey is known for its fast-paced, physical nature with constant action and scoring opportunities. On the other hand, soccer is a more strategic game with longer periods of build-up play and intense moments during goal-scoring opportunities. Both sports have passionate fan bases and offer unique thrills, making it difficult to definitively say which is more exciting. **

It is highly unlikely that soccer will replace American football, basketball, baseball, and ice hockey as the most popular sports in the USA. These sports have deep-rooted cultural and historical significance in American society, and they have large and dedicated fan bases. Additionally, American football, basketball, baseball, and ice hockey have well-established professional leagues and infrastructure in the USA, which would make it difficult for soccer to overtake them in popularity. While soccer has been growing in popularity in the USA, it is more likely to continue to coexist alongside these other sports rather than replace them. **

To calculate the aphelion of an orbit, you can use the formula for the semi-major axis of an ellipse, which is the average of the perihelion and aphelion distances. Since the perihelion is given as 88,106 km, and the orbital period is approximately 75 years, you can use Kepler's third law to find the semi-major axis. Once you have the semi-major axis, you can calculate the aphelion by subtracting the perihelion distance from twice the semi-major axis. **

To calculate the aphelion of an orbit given the perihelion and orbital period, you can use Kepler's laws of planetary motion. The formula to calculate the aphelion distance is aphelion = 2 * perihelion - perihelion. In this case, the perihelion is 88,106 km, so the aphelion would be 2 * 88,106 km - 88,106 km = 176,212 km - 88,106 km = 88,106 km. Therefore, the aphelion of the orbit would also be 88,106 km. **