A spaceship is `10^14` km away from a massive star. The gravitational force between them is 70N. Calculate the distance between them , if the force between them is increased to `7xx10^5` N.

Explanation

Given : Force `(F_1) = 70N`
Distance `(r_1) = 10^14 km = 10^7m`
Force `(F_2) = 7xx10^5 N`
To find : Distance (`r_2`)
`F=(Gm_1m_2)/(r^2)`
Calculation : From formula
For `r_1 = 10^7m : F_1 = (Gm_1m_2)/((r_1)^2)`
`70=(Gm_1m_2)/((10^17)^2) " " ....(1)`
For `r_2 : F_2 = (Gm_1m_2)/((r_2)^2)`
Dividing equation (1) by (2) , we have ,
`(70)/(7xx10^5) = (r_2^2)/((10^17)^2)`
`therefore r_2^2 = (70)/(7xx10^5) xx10^34 = 10^30`
`r_2 = 10^15 m = 10^12km`