Question

Use the ratio version of Kepler’s third law and the orbital information of Mars to determine Earth’s distance from the Sun. Mars’s orbital period is 687 days, and Mars’s distance from the Sun is 2.279 × 1011 m. 1.49 × 1011 m 1.49 × 1033 m 3.34 × 1011 m 3.34 × 1033 m

The answer is A 1.49x1011m

Answer 1

To determine Earth's distance from the Sun, we can use the ratio version of Kepler’s third law and compare Mars's orbital period and distance from the Sun to Earth's. Using the equation P^2 = a^3, we can calculate Earth's distance from the Sun as approximately 1.49 × 10^11 m.

Step-by-step explanation:

To determine Earth's distance from the Sun using the ratio version of Kepler’s third law, we can compare Mars's orbital period and distance from the Sun to Earth's. Mars's orbital period is 687 days and its distance from the Sun is 2.279 × 10^11 m. We can use the equation P^2 = a^3, where P is the period in years and a is the semimajor axis in astronomical units. Rearranging the equation, we can find Earth's distance from the Sun:

Earth's distance from the Sun = (Earth's orbital period / Mars's orbital period)^(2/3) * Mars's distance from the Sun

Plugging in the values, we get:

Earth's distance from the Sun = (365.26 / 687)^(2/3) * 2.279 × 10^11 m

Simplifying the calculation, we find that Earth's distance from the Sun is approximately 1.49 × 10^11 m.