A Russian Soyuz module, with three astronauts and a full load of cargo, has a mass of $7100$ kg $.$ The International Space Station $($ISS$)$ has a mass of $\backslash (420,000\backslash$mathrm$\{$~kg$\}\backslash ).$ When Soyuz docks at the ISS, the two centers of mass are separated by $8\mathrm{.}5$ m $.$

Part A

Find the average of the gravitational force of attraction between the two spacecraft when Soyuz is docked and when it is $115$ m from the ISS.

Express your answer to two significant figures and include appropriate units.

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Ready to give it a try? Part B

If Soyuz approached the ISS from rest at a distance of $115$ m $,$ a thruster would have to counteract the average force of gravitational attraction between it and the ISS. If this thruster has an exhaust velocity of $\backslash (580\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ at what average rate must it burn fuel $($in $\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}\backslash ))$ to counteract the pull of the ISS?

Express your answer in kilograms per second to two significant figures.

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$\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}$

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Part C

If the approach requires $310$ s $,$ how much fuel will the thruster burn in order to counteract the gravitational attraction?

Express your answer to two significant figures and include appropriate units.