Question

a student researches jupiter and saturn and records the following information:

• jupiter is about half the distance to the sun that saturn is.
• jupiter is about three times more massive than saturn.

based on this information, which of the following can be concluded about the gravitational forces between these planets
and the sun?
a there are no gravitational forces between jupiter and the sun or between saturn and the sun.
b there are equal gravitational forces between saturn and the sun and between jupiter and the sun
c there is a greater gravitational force between jupiter and the sun than between saturn and the sun
d there is a greater gravitational force between saturn and the sun than between jupiter and the sun

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force is \(F = G\frac{Mm}{r^{2}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the Sun, \(m\) is the mass of the planet, and \(r\) is the distance between the planet and the Sun.

Step2: Let the mass of Saturn be \(m_{s}\) and its distance from the Sun be \(r_{s}\)

Then the mass of Jupiter \(m_{j}=3m_{s}\), and the distance of Jupiter from the Sun \(r_{j}=\frac{1}{2}r_{s}\)

Step3: Calculate the gravitational force for Saturn \(F_{s}\)

\(F_{s}=G\frac{Mm_{s}}{r_{s}^{2}}\)

Step4: Calculate the gravitational force for Jupiter \(F_{j}\)

\(F_{j}=G\frac{M\times3m_{s}}{(\frac{1}{2}r_{s})^{2}}=G\frac{3Mm_{s}}{\frac{1}{4}r_{s}^{2}} = 12G\frac{Mm_{s}}{r_{s}^{2}}\)

Answer:

C. There is a greater gravitational force between Jupiter and the Sun than between Saturn and the Sun