Light from the Sun travels to the Earth at a speed of 3.0 × 108 m / s.The time for the complete journey is 500 s.What is the average orbital speed of the Earth in its orbit around the Sun

To calculate the average orbital speed of the Earth, we first need to find the distance the light travels from the Sun to the Earth.

Step 1: Calculate the distance We know that speed = distance/time. We can rearrange this formula to find distance = speed * time. Given that the speed of light is 3.0 × 10^8 m/s and the time it takes for light to reach Earth is 500 seconds, we can substitute these values into the formula:

Distance = (3.0 × 10^8 m/s) * 500 s = 1.5 × 10^11 meters

This is the average distance from the Earth to the Sun, also known as 1 Astronomical Unit (AU).

Step 2: Calculate the orbital circumference The Earth's orbit around the Sun is nearly a perfect circle. The formula for the circumference of a circle is 2πr, where r is the radius of the circle. In this case, the radius is the distance from the Earth to the Sun, which we found to be 1.5 × 10^11 meters.

Orbital circumference = 2π * (1.5 × 10^11 m) = 9.42 × 10^11 meters

Step 3: Calculate the orbital speed The Earth takes one year to orbit the Sun. We need this time in seconds to match the units of our distance. There are approximately 31,536,000 seconds in a year (60 seconds/minute * 60 minutes/hour * 24 hours/day * 365.25 days/year to account for leap years).

Now we can use the speed = distance/time formula again to find the Earth's orbital speed:

Orbital speed = (9.42 × 10^11 m) / (31,536,000 s) = 29,884 m/s

So, the average orbital speed of the Earth in its orbit around the Sun is approximately 29,884 m/s.