Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. How long will it be before the relative to one another. How long will it be before the gravitational attraction brings them 1 cm closer together ?

Options

A. `2.52` days
B. `1.41` days
C. `0.70` days
D. `1.41`s

Answer

B

Explanation

`a_(1)`=acceleration of first astronaut
`=(Gm_(1)m_(2))/(r^(2))xx(1)/(m_(1))=(Gm_(2))/(r^(2))=(6.67xx10^(-11)xx100)/((100)^(2))`
`=6.67xx10^(-13)m s^(-1)`
`a^(2)`=acceleration of second astronaut
`=(Gm_(1))/(r^(2))=(6.67xx10^(-11)xx100)/((100)^(2))=6.67xx10^(13)" m "s^(-1)`
Net acceleration of approach
`a=a_(1)+a_(2)=2xx6.67xx10^(-13)" m s^(-1)`
Now, `s=(1)/(2)at^(2)1xx10^(-2)=(1)/(2)xx6.67xx10^(-13)xx2xxt^(2)`
Solving, we get `t=1.41` days.