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Chapter 13: Q. 33 (page 354)

In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1×1016kgand a radius of 8.8km.

a. What is the speed of a satellite orbiting 5kmabove the surface?

b. What is the escape speed from the asteroid?

Short Answer

Expert verified

a. The speed of the satellite is 6.95m/s.

b. The escape speed from the asteroid is12.31m/s.

Step by step solution

01

Given information a

Height = 5000m,mass of asteroid (M) =1.0×1016kg, Radius of asteroid (R) =8800m.

02

Calculation a

For a satellite to revolve around the planet the necessary centripetal force is provided by the gravitational force of attraction between the planet and the satellite.

Fc=centripetal force=mv2r

Where orbital radius of satellite r = R + h

And Fg=GMmr2

NowFc=Fgmv2r=GMmr2v=GMr=GMR+h

Substituting values and solving we get : v=6.95m/s.

03

Final answer a

The speed of the satellite is6.95m/s.

04

Given information b

Mass of the asteroid (M) = 1.0×1016kg,radius of asteroid =8800m.

05

Calculation b

The escape speed from a planet is given by the formula : ve=2GMR

Substituting values in the formula we get : ve=12.31m/s.

06

Final answer b

The escape speed from the planet is12.31m/s.

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