Suppose the rocket in the Example was initially on a circular orbit around Earth with a period of 1.6 days. Hint (a) What is its orbital speed (in m/s)? m/s (b) If we want to propel a portion of the rocket to infinity (in the direction tangential to the circular orbit), what's the escape speed from there (in m/s)? m/s

a

The orbital speed is

b

The escape velocity of the rocket is  

Explanation:

Generally angular velocity is mathematically represented as

Where T is the period which is given as 1.6 days =

       Substituting the value

At the point when the rocket is on a circular orbit  

   The gravitational force =  centripetal force and this can be mathematically represented as

Where  G is the universal gravitational constant with a value  

            M is the mass of the earth with a constant value of

            r is the distance between earth and circular orbit where the rocke is found

               Making r the subject

The orbital speed is represented mathematically as

Substituting value

The escape velocity is mathematically represented as

Substituting values

pe = weightxheight = 2000x1000=2,000,000joules