Final answer:
To calculate the Earth's kinetic energy associated with its motion about the Sun, you can use the equation for kinetic energy and potential energy. The ratio of potential energy to kinetic energy is approximately 1:10^4.
Step-by-step explanation:
To calculate the Earth's kinetic energy associated with its motion about the Sun, we can use the equation for kinetic energy:
Kinetic Energy = 1/2 * mass * velocity^2
Since the Earth's mass and velocity are constants, we can calculate the potential energy using the equation:
Potential Energy = mass * acceleration due to gravity * height
To find the ratio of potential energy to kinetic energy, we can divide the potential energy by the kinetic energy.
Let's assume the mass of the Earth is 5.972 × 10^24 kg, the average orbital speed is 29.78 km/s, the acceleration due to gravity is 9.81 m/s^2, and the average distance from the Earth to the Sun is 149.6 million km.
Using these values, the kinetic energy of the Earth is approximately 2.647 × 10^29 joules and the potential energy is approximately 2.647 × 10^33 joules. Therefore, the ratio of potential energy to kinetic energy is approximately 1:10^4.