Question

From the gravitational law, calculate the weight W (gravitational force with respect to the earth) of a 70 kg spacecraft traveling in a circular orbit 275 km above the earth's surface. Express W in Newtons and pounds.

Answer 1

The value in Newton is
`W =  631.92 \  N`

The value in pounds is
`W  = 142 \ lb`

Step-by-step explanation:

From the question we are told that

The mass of the spacecraft is
`m =  70 \  kg`

The distance above the earth is
`d =  275 \  km  =  275000 \  m`

Generally the gravitational force with respect to the earth is mathematically represented as

`W =  (G * m *  m_e)/( (d + r_e)^2)`

Here
`m_e` is the mass of earth with value
`m_e =  5.978 *10^(24) \  kg`

`r_e` is the radius of the earth with value
`r_e  =  6371  \ km  =  6371000 \ m`

G is the gravitational constant with value
`G  =  6.67 *10^(-11)  \  m^3/ kg\cdot s^2`

So

`W =  ( 6.67 *10^(-11) *  70 *  5.978 *10^(24))/( (275000 + 6371000)^2)`

`W =  631.92 \  N`

Converting to pounds

`W =  (631.92  )/(4.45)`

`W  = 142 \ lb`