What causes the apparent retrograde motion of the planets? a) as earth passes another planet, its gravitational pull slows down the other planet so that it appears to be traveling backward. b) when planets are farther from the sun, they move slower than when they are nearer the sun; it is during this slower period that they appear to move backwards. c) the other planets never really appear to move backward; the background stars shift due to earth's revolution around the sun. d) as earth passes another planet, the other planet appears to move backward witlh respect to the background stars, but the planet's motion does not actually change. e) apparent retrograde motion is an illusion created by turbulence in earth's atmosphere.

D) As Earth passes another planet, the other planet appears to move backward with respect to the background stars, but the planet's motion does not actually change.

Explanation:

Celestial objects in the night sky have a movement from west to east, but planets do not always follow that direction. During some months of the year their path in the sky starts to go backward (from east to west), then after passing that few months they continue with the same normal direction that have all of the other objects in the sky (from west to east).

That apparent retrograde motion is an illusion due to the motion of the Earth compared to the motion of  another planet around the sun, since the Earth is orbiting faster than the superior planets (Mars, Jupiter). Hence, when the Earth overtakes and passes them, they appear to move backward with respect to the background stars. The same case is seen with inferior planets (Mercury, Venus), but in this scenario they overpass Earth since they are moving faster.

It is important to remember that the orbital speed decreases if the distance increases (inversely proportional) as is shown in equation (1):

  (1)

Where G is the gravitational constant, M is the mass of the object and r is the radius of the orbit.

The form of the path from the apparent retrograde motion on the celestial sphere can be represented by a zigzag or a loop.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2