Question

The New Horizons spacecraft (mass 478 kg) was launched from earth in 2006 and flew past Pluto in 2015. What minimum amount of work has to be done on a spacecraft of this mass to send it from the earth's surface to infinitely far away from the earth? Neglect air resistance and the gravitational effects of the sun, moon, and other planets.

Answer 1

Answer:
`2.98(10)^(10) J`

Step-by-step explanation:

The work
`W` done by the gravitational force is given by:

`W=-\Delta U=-(-(GMm)/(d) - (GMm)/(D))` (1)

Where:

`\Delta U` is the variation in potential energy

`G=6.674(10)^(-11)(m^(3))/(kgs^(2))` is the Gravitational constant

`M=5.972(10)^(24) kg` is the mass of the Earth

`m=478 kg` is the mass of the spacecraft

`d=6371(10)^(3) m` is the distance from the center of the Earth to its surface

`D=7.529(10)^(12) m` is the distance between the Earth and Pluto

Rearranging (1):

`W=GMm((1)/(d) + (1)/(D))` (2)

`W=(6.674(10)^(-11)(m^(3))/(kgs^(2)))(5.972(10)^(24) kg)(478 kg)((1)/(6371(10)^(3) m) + (1)/(7.529(10)^(12) m))` (3)

Finally:

`W=2.98(10)^(10) J`