Final answer:
The approximate value of Jupiter's average speed of orbit around the sun is 3.657×10⁷ m/s.
Step-by-step explanation:
To find the approximate value of Jupiter's average speed of orbit around the sun, we can use the concept of Kepler's third law of planetary motion. According to this law, the square of the orbital period of a planet is directly proportional to the cube of the average distance from the sun. Since we know the orbital period of Jupiter is 12 years and the average distance of Jupiter's orbit is 5.2 times bigger than that of Earth's, we can set up the following equation:
(Jupiter's period)^2 = (Earth's period)^2 * (Jupiter's orbital distance)^3
Substituting the values, we get:
(12 years)^2 = (1 year)^2 * (5.2)^3
Simplifying, we find that Jupiter's orbital distance is approximately 1218.96 times bigger than Earth's orbital distance. Since the average speed is directly proportional to the distance traveled in a given time period, we can multiply the average speed of the Earth (3×10⁴ m/s) by the scale factor:
Jupiter's average speed = Earth's average speed * scale factor
= 3×10⁴ m/s * 1218.96
≈ 3.657×10⁷ m/s