alleryStart learning →Earth's closest approach to the sun is 1.47 x 10^8 km, and its farthest distance is 1.52 x 10^8 km. What is the area enclosed by Earth's orbit?
A2.23 x 10^16 km^2
B6.79 x 10^16 km^2
C7.02 x 10^16 km^2
D7.26 x 10^16 km^2
Answer & Solution
Correct answer: C. 7.02 x 10^16 km^2
1. Semi-major axis a = (r_a + r_p)/2 = (1.52 + 1.47) x 10^8 / 2 = 1.495 x 10^8 km.
2. Semi-minor axis b = square root of (r_a x r_p) = square root of (1.52 x 1.47) x 10^8 = 1.4948 x 10^8 km.
3. Area = pi x a x b = pi x (1.495 x 10^8)(1.4948 x 10^8) = 7.02 x 10^16 km^2.
_Source: OpenStax Physics (CC BY 4.0), Ch 7 "Newton's Law of Gravitation", section 7.1 Kepler's Laws of Planetary Motion_
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