Final answer:
The Earth's orbit around the sun is described by its eccentricity, perihelion distance, and aphelion distance. The average speed of Earth in its orbit can be calculated using the formula v = 2πr/T, where r is the average radius of Earth's orbit and T is the orbital period. The area inside Earth's orbit can be calculated using the formula for the area of an ellipse, which is given by A = πab.
Step-by-step explanation:
The Earth's orbit around the sun is described by its eccentricity, which refers to how elongated or circular the orbit is. An eccentricity of 0 would represent a perfect circle, while a value close to 1 indicates a highly elliptical orbit. The distance from the Earth to the sun also varies throughout the orbit. The perihelion distance is the closest distance between Earth and the Sun, while the aphelion distance is the farthest distance.
(a) The linear speed of Earth in its orbit is given by the formula v = 2πr/T, where r is the average radius of Earth's orbit and T is the orbital period. To calculate the average speed, you can divide the circumference of the orbit by the orbital period.
(b) The area inside Earth's orbit can be calculated using the formula for the area of an ellipse, which is given by A = πab, where a and b are the semi-major and semi-minor axes of the ellipse respectively.