Question

If the 78.0 kg astronaut were in a spacecraft 6R from the center of the earth, what would the astronaut's weight be on earth? 764.4 N760 N764 N in the spacecraft?

Answer 1

a) Weight on Earth: 764.4 N

b) Weight in the spacecraft: 21.27 N

Step-by-step explanation:

According to Newton's law of universal gravitation:

`F=G(Mm)/(R^2)`

Where:

`F` is the module of the attraction force exerted between the Earth and the astronaut

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

`M=5.972(10)^(24)kg` is the mass of the Earth and
`m=78kg` is the mass of the astronaut.

`R=6371km=6371000m` is the distance between Earth and the astronaut (measured from the center of the planet).

So, the weight of the astronaut will be the attraction force exerted between the Earth and the astronaut.

a) When the astronaut is on Earth (on the surface):

`F=W=G(Mm)/(R^2)` (1)

`W=6.674(10)^(-11)(m^(3))/(kgs^(2))((5.972(10)^(24)kg)(78kg))/((6371000m)^2)` (2)

`W=764.4N` (3) Weight of the astronaut on Earth

b) When the astronaut is in the spacecraft:

`F=W=G(Mm)/((6R)^2)` (4)

`W=6.674(10)^(-11)(m^(3))/(kgs^(2))((5.972(10)^(24)kg)(78kg))/(((6)(6371000m))^2)` (5)

`W=21.27N` (6) Weight of the astronaut in the spacecraft at a distance 6R from the Earth center