Question

s c.6.p.13.2
two planets are the same distance from a star, but planet x has more mass than planet y. which is true about the stars gravitational pull on the planets?
the star pulls planet x more because it has more mass.
the star pulls planet y more because it is smaller.
the star pulls both planets equally because distance is the only factor.
there is no gravitational pull in space.

Explanation:

Step1: Recall gravitational - force formula

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

Step2: Analyze given conditions

The two planets are at the same distance $r$ from the star ($r$ is the same for both), and the mass of the star $M$ is constant. Planet $X$ has more mass ($m_X>m_Y$).

Step3: Determine gravitational - force relationship

Since $F = G\frac{Mm}{r^{2}}$, when $M$ and $r$ are the same, the greater the mass $m$ of the planet, the greater the gravitational force $F$. So the star exerts a greater gravitational pull on Planet $X$ because it has more mass.

Answer:

The star pulls Planet X more because it has more mass.