No, the area swept out per unit time by Earth moving around the sun is not equal to the area swept out per unit time by Mars moving around the sun.

This is due to Kepler's Second Law of Planetary Motion, which states:

"A line joining a planet and the Sun sweeps out equal areas in equal intervals of time."

While the law holds true for both Earth and Mars, the areas swept out will be different because:

* Orbital Period: Mars has a longer orbital period than Earth, meaning it takes longer to complete one orbit around the Sun.

* Orbital Speed: Mars has a slower average orbital speed than Earth.

Therefore, even though both planets sweep out equal areas in equal intervals of time, the actual areas swept out per unit time will be different due to their differing orbital periods and speeds.