Question

the planet mars orbits the sun. mars is much less massive than the sun.
models of marss orbit are shown below. each model shows mars as a dot, at one position along its orbit.
which model correctly shows the gravitational forces that mars and the sun exert on each other?
the sizes of mars and the sun are not shown to scale.
choose 1 answer:
a
image
b
image
c
image
d
image

Explanation:

To determine the correct model, we use Newton's third law of motion, which states that the gravitational force exerted by Mars on the Sun is equal in magnitude and opposite in direction to the force exerted by the Sun on Mars. Also, the forces should be along the line connecting their centers (since gravity is a central force).

• Option A: Only shows the force on the Sun (from Mars) or vice versa? No, we need two forces (action - reaction) along the line connecting them.
• Option B: The forces are not along the line connecting Mars and the Sun, so this is incorrect.
• Option C: The two forces (one on Mars, one on the Sun) are along the line connecting their centers, equal in magnitude (since gravitational force $F = G\frac{Mm}{r^{2}}$ is the same for both, just opposite in direction), and opposite in direction. This follows Newton's third law.
• Option D: The forces are not along the line connecting Mars and the Sun, so this is incorrect.

Answer:

C. The model where the gravitational force on Mars (from the Sun) and the gravitational force on the Sun (from Mars) are along the line connecting their centers, equal in magnitude, and opposite in direction.