Chapter 13: Newton’s Theory of Gravity

In $2000$, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of $1\times {10}^{16}kg$and a radius of $8.8km.$

a. What is the speed of a satellite orbiting $5km$above the surface?

b. What is the escape speed from the asteroid?

Pluto moves in a fairly elliptical orbit around the sun. Pluto’s speed at its closest approach of $4.43\times {10}^9$km is 6.12 km/s. What is Pluto’s speed at the most distant point in its orbit, where it is$7.30\times {10}^9$km from the sun?

FIGURE P13.35 shows three masses. What are the magnitude and the direction of the net gravitational force on (a) the 20.0 kg mass and (b) the 5.0 kg mass? Give the direction as an angle cw or ccw from the y-axis.

What are the magnitude and direction of the net gravitational

force on the 20.0 kg mass in FIGURE P13.36?

What is the total gravitational potential energy of the three masses in $FIGUREP13.35?$

What is the total gravitational potential energy of the three masses in $FIGUREP13.36?$

Two spherical objects have a combined mass of $150kg.$The gravitational attraction between them is $8.00\times {10}^{-6}N$when their centers are $20cm$apart. What is the mass of each?

How far away from the earth must an orbiting spacecraft be for the astronauts inside to be weightless? Explain.

What is the force of attraction between a $50kg$woman and a $70kg$man sitting $1.0m$apart?

Two$100kg$lead spheres are suspended from $100-m$-long massless cables. The tops of the cables have been carefully anchored exactly $1m$apart. By how much is the distance between the centers of the spheres less than $1m?$