Final answer:
The average speed of Earth in its orbit around the Sun is approximately 29,783 m/s. This speed is calculated by dividing the circumference of Earth's circular orbit by the time it takes to complete one orbit, which is one year expressed in seconds.
Step-by-step explanation:
The question asks to calculate the average speed of Earth in its orbit around the Sun, which we assume to be circular. The average distance between Earth and the Sun is given as 1.5 × 10¹¹ meters (m). The Earth completes one orbit around the Sun in one year, which contains about 365.25 days.
Given that a day has 86,400 seconds, we can find the orbital period in seconds:
Orbital period (T) = 365.25 × 86,400 s
The circumference (C) of Earth's orbit can be calculated using the formula:
C = 2πr where r is the orbital radius (1.5 × 10¹¹ m).
Thus, C = 2 × 3.14159 × (1.5 × 10¹¹ m).
Now, the average speed (v) is the orbit circumference divided by the orbital period:
v = C / T
After calculating, the average speed comes out to approximately 29,783 m/s, which coincides with option (a) 29,783 m/s.