"in analyzing distances by apply ing the physics of gravitational forces, an astronomer has obtained the expression
r= √1/([1/140×10^9 meter]^2 - [1/208×10^9]^2)
use your calculator to evaluate r. view available hint(s)
(a) 3.87 x 10-12 meter
(b) 1.72× 1011 meter
(c) 2.58 x 1011 meter
(d) 1.49 x 1011 meter "

The value of R is .

(B) is correct option.

Explanation:

Given that,

In analyzing distances by apply ing the physics of gravitational forces, an astronomer has obtained the expression

We need to calculate this for value of R

So, The nearest option of the value of R is

Hence, The value of R is .

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2