Question

question 11(multiple choice worth 5 points)
(06.01 hc)
the following table shows the distance from the sun of some unknown planets of equal mass.

distance from sun

planet	distance from sun
z	0.39 au

which of the following best explains which planet revolves at a slower speed?

• planet y, because the sun pulls it with a greater force
• planet z, because the sun pulls it with a greater force
• planet y, because the gravitational force is weakened by distance
• planet z, because the gravitational force is strengthened by distance

Explanation:

To determine which planet revolves slower, we use Newton's law of gravitation ($F = G\frac{Mm}{r^2}$) and orbital mechanics. Gravitational force weakens with distance ($r$). Planet Y is farther (1 AU) than Z (0.39 AU). A weaker gravitational force (due to greater distance) means a slower orbital speed (since centripetal force for orbit is from gravity: $F = \frac{mv^2}{r}$, so weaker $F$ at larger $r$ leads to slower $v$). So Planet Y has weaker gravity from the Sun (due to distance) and thus slower speed.

Answer:

Planet Y, because the gravitational force is weakened by distance