Question

assume that all three satellites are the same distance from the planet.

satellite mass (kg)
a 8,900
b 1,500
c 300

which satellite experiences the weakest force of gravity from earth?

choose 1 answer:
a satellite a
b satellite b
c satellite c

Explanation:

Step1: Recall the law of gravity

The gravitational force \( F \) between two objects is given by \( F = G\frac{Mm}{r^{2}} \), where \( G \) is the gravitational constant, \( M \) is the mass of the planet (Earth here), \( m \) is the mass of the satellite, and \( r \) is the distance between them. Since \( G \), \( M \), and \( r \) are the same for all three satellites, the force \( F \) is directly proportional to the mass \( m \) of the satellite (\( F \propto m \) when \( G \), \( M \), \( r \) are constant).

Step2: Compare the masses of the satellites

We have the masses: Satellite A: \( 8900 \, \text{kg} \), Satellite B: \( 1500 \, \text{kg} \), Satellite C: \( 300 \, \text{kg} \). Since the force is directly proportional to mass (when distance and planet's mass are constant), the smallest mass will experience the weakest gravitational force.

Step3: Identify the satellite with the smallest mass

Among \( 8900 \), \( 1500 \), and \( 300 \), \( 300 \) is the smallest. So Satellite C has the smallest mass.

Answer:

C. satellite C