You are the science officer aboard the starship Enterprise , leading a scientifi

Question

You are the science officer aboard the starship Enterprise, leading a scientific exploration of a neutron star. Your mission is to send a set of two robotic observation probes near the neutron star's surface to measue local conditions. The probes have a mass of 10 kf each and are linked by a 1 m high tensile stell cable (breaking tension 3.5 x 104 N). To perform their work, the two probes must be oriented such that one probe is always directly above the other. Assume that the neuton star has a 10 km diamter and 2 times the Sun's mass.

What is the minimum altitude the probes can achieve above the neutrons star's surface without snapping the connecting cable?

Explanation / Answer

let minimum altitude is d meters.

writing force balance equation for the lower probe:

breaking tension=gravitational force

==>3.5*10^4=G*mass of the probe*mass of the star/distance^2

==>3.5*10^4=6.674*10^(-11)*2*1.989*10^30*10/(5000+d)^2

==>(5000+d)^2=6.674*10^(-11)*2*1.989*10^30*10/(3.5*10^4)=7.5855*10^16

==>d=2.7541*10^8 m

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