If a 3000 kg satellite orbits the Earth, what is the approximate value of its orbit radius, using the mass of the Earth as 6 × 10^24 kg?

If a 3000 kg satellite orbits the Earth, what is the approximate value of its orbit radius, using the mass of the Earth as 6 × 10^24 kg?

• A. 4.0 x 10^6 m
• B. 6.0 x 10^7 m
• C. 8.0 x 10^7 m
• D. 10.0 x 10^7 m

Answer: (B)

To determine the orbit radius of a satellite, we can utilize the relationship between gravitational force and the centripetal force required for circular motion. The gravitational force acting on the satellite is given by Newton's law of gravitation: \[ F = \frac{G \cdot M \cdot m}{r^2} \] where: - \( F \) is the force of gravity, - \( G \) is the gravitational constant (\( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \)), - \( M \) is the mass of the Earth (\( 6 \times 10^{24} \, \text{kg} \)), - \( m \) is the mass of the satellite (\( 3000 \, \text{kg} \)), - \( r \) is the distance from the center of the Earth to the satellite. For an object in circular motion, the required centripetal force is also expressed as: \[ F = \frac{m \cdot v^2}{r} \] Setting these two expressions for force equal to one another, we can derive the following: \[ \

To determine the orbit radius of a satellite, we can utilize the relationship between gravitational force and the centripetal force required for circular motion. The gravitational force acting on the satellite is given by Newton's law of gravitation:

[ F = \frac{G \cdot M \cdot m}{r^2} ]

where:

• ( F ) is the force of gravity,

• ( G ) is the gravitational constant (( 6.674 \times 10^{-11} , \text{N m}^2/\text{kg}^2 )),

• ( M ) is the mass of the Earth (( 6 \times 10^{24} , \text{kg} )),

• ( m ) is the mass of the satellite (( 3000 , \text{kg} )),

• ( r ) is the distance from the center of the Earth to the satellite.

For an object in circular motion, the required centripetal force is also expressed as:

[ F = \frac{m \cdot v^2}{r} ]

Setting these two expressions for force equal to one another, we can derive the following:

[ \