It takes Pluto a longer time to travel around the sun than the Earth because Pluto:
a. has farther to go
b. goes slower
c. a and b
d. none of these
Assume circular orbits.
Now let me see
F = Mplanet a where a is v^2/r, the centripetal acceleration with speed v and orbit radius r
F = G Msun Mplanet /r^2
so
Mplanet v^2/r = G Msun Mplanet/r^2
or
v^2 r = G Msun for every planet around sun (I am calling Pluto a planet :)
circumference of orbit = 2 pi r
so time around T = 2 pi r/v
but v = sqrt(G Msun/r)
SO
as r goes up, T goes up
and as r goes up, v goes down
SO
it goes further, and it goes slower.
c. a and b
Pluto takes a longer time to travel around the sun compared to Earth because it has farther to go and it also goes slower.
To determine why it takes Pluto a longer time to travel around the sun than the Earth, let's consider the options provided:
a. has farther to go
b. goes slower
c. a and b
d. none of these
To assess option "a," we can compare the average distances of Pluto and Earth from the sun. The average distance from the sun to Earth is about 93 million miles, while the average distance from the sun to Pluto is about 3.7 billion miles. Therefore, option "a" is accurate - Pluto indeed has farther to go.
Now, let's evaluate option "b." We know that both Earth and Pluto orbit the sun, and their speeds are determined by their distance from the sun and the gravitational pull between them and the sun. The speed of a planet in its orbit depends on its distance from the sun and the gravitational force acting upon it. Since Pluto is farther away from the sun, it experiences a weaker gravitational pull than Earth does. This weaker gravitational force causes Pluto to move more slowly in its orbit compared to Earth. Therefore, option "b" is also correct - Pluto does go slower.
Considering the explanations above, we can conclude that the correct answer is option "c" - Pluto takes a longer time to travel around the sun because it has farther to go, and it goes slower due to its greater distance from the sun and the weaker gravitational force acting upon it.