Earth's orbit around the sun is slightly elliptical. thus, earth actually gets closer to the sun during part of the year. what happens to earth's orbital speed when it is closer to the sun?

a)earth's orbital speed is less when it is closer to the sun than when it is farther from the sun.
b)earth's orbital speed is the same whether it is closer to the sun or farther from the sun.
c)earth's orbital speed is greater when it is closer to the sun than when it is farther from the sun.

C)Earth's orbital speed is greater when it is closer to the Sun than when it is farther from the Sun.

Explanation:

We can use Kepler's 2nd law or the law of area to answer this question.

The law states that the rate of area swept out by a planet's orbit is same throughout the orbit. For the farthest point since the distance is large as compared to to the nearest point, the possibility that area swept is large. Hence, to compensate the extra swept area. the orbital speed has to decrease  at the largest point.

Hence, planet's speed is greater when it is closer to sun than the speed when it is farther.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y