Kepler's Laws and Gravitation

Two satellites orbit the Earth at the same speed in identical orbits. Satellite A is twice the mass of Satellite B. How does the centripetal ACCELERATION of Satellite A compare with that of Satellite B?

• Four times as much

• Twice as much

• The same

• One-half as much

Two satellites orbit the Earth at the same speed in identical orbits. Satellite A is twice the mass of Satellite B. How does the centripetal FORCE of Satellite A compare with that of Satellite B?

• Four times as much

• Twice as much

• The same

• One-half as much

 $6.2\times10^6\ N$  A satellite orbits the Earth at a distance of 100 km. The mass of the satellite is 100 kg, while the mass of the Earth is approximately  $6.0\times10^{24}\ kg.$  The radius of the Earth is approximately  $6.4\times10^6\ m.$  What is the approximate force of gravity acting on the satellite?

•  $9.5\times10^2\ N$  

•  $6.2\times10^6\ N$  

•  $9.5\times10^8\ N$  

•  $6.2\times10^9\ N$  

A 70-kg astronaut floats at a distance of 10 m from a 50,000-kg spacecraft. What is the force of attraction between the astronaut and spacecraft?

• $2.3\times10^{-6}\ N$

• $2.3\times10^{-5}\ N$

• $2.3\times10^5\ N$

• $2.3\times10^6\ N$

A car moves around a curve in a horizontal circle with a radius of 100 m. The tangential speed of the car is constant at a value of 30 m/s. What is the car's acceleration.

• 9 m/s/s toward the center of the circle

• 9 m/s/s away from the center of the circle

• 9 m/s/s tangent to its circular path

• 0 m/s/s

A 1000-kg car moves around a curve in a horizontal circle with a radius of 100 m. The tangential speed of the car is constant at a value of 30 m/s. What is the force of friction acting on the car?

• 3000 N toward the center

• 3000 N away from the center

• 9000 N away from the center

• 9000 N toward the center

A satellite orbits the Earth at a distance of 100 km. The mass of the satellite is 100 kg, while the mass of the Earth is approximately  $6.0\times10^{24}\ kg.$  The radius of the Earth is approximately  $6.4\times10^6\ m.$  What is the approximate force of gravity acting on the satellite?

•  $9.5\times10^2\ N$  

•  $6.2\times10^6\ N$  

•  $9.5\times10^8\ N$  

•  $6.2\times10^9\ N$  

A satellite orbits the Earth at a distance of 200 km. If the mass of the Earth is  $6.0\times10^{24}\ kg$  and the Earth's radius is  $6.4\times10^6\ m$  , what is the satellite's speed?

•  $1.0\times10^3\ \frac{m}{s}$  

•  $3.5\times10^3\ \frac{m}{s}$  

•  $7.8\times10^3\ \frac{m}{s}$  

•  $5.0\times10^6\ \frac{m}{s}$  

If the Earth were a gaseous planet with twice the radius and double the mass determine gravitational field strength at the surface of the gaseous planet.

• 2 m/s/s

• 5 m/s/s

• 10 m/s/s

• 20 m/s/s

In 1798, Henry Cavendish experimentally dtermined the value of the universal gravitational constant, G, which, in turn, enabled him to calculate the mass of the Earth. Given the Earth's surface gravitational field strength (g), the radius of the Earth  $\left(R_E\right)$  and G, which of the following expressions may be used to calculate the mass of the Earth?

•  $M_E=\frac{\left(gR_E^2\right)}{G}$  

•  $M_E=GgR_E^2$  

•  $M_E=\frac{G}{\left(gR_E^2\right)}$  

•  $M_E=\frac{\left(gR_E\right)}{G}$