Tension of Rope: Cosmonaut & Spaceship Orbit in Planetary Gravity

[Jorgen1224]

Homework Statement

What is the tension of this rope?
Cosmonaut m=100kg is outside of spaceship M=5 tons on rope with length 64m. Cosmonaut along with his spaceship moves in orbit at a neglible distance.

m=100kg
M=5000kg
L=64m
Planet's mass 6*10^24
Planet's radius 6400km

Homework Equations

Kepler's 3rd law(maybe?)

The Attempt at a Solution

It's from physics olympics, so i bet that it requires one complex idea.
What comes out of universal gravitation law is 8.14208984375×10^-9 N and I'm not sure what to do afterwards.

 

[kuruman]

Is the statement of the problem exactly as it was given in the physics Olympics? I am not sure what "negligible distance" means. Negligible relative to the radius of the planet or negligible relative to 64 m?

 

[jbriggs444]

Is the statement of the problem exactly as it was given in the physics Olympics? I am not sure what "negligible distance" means. Negligible relative to the radius of the planet or negligible relative to 64 m?

My guess is that the "negligible" refers to the orbital altitude above the planet's surface. The input data is good to one significant figure. So the use of reasonable approximations is apparently encouraged.

Perhaps the first order of business is to pick a frame of reference to use. An inertial frame nailed to the planet's center? A rotating frame nailed to the planet as a whole? Then the free body diagrams.

 

[kuruman]

My guess is that the "negligible" refers to the orbital altitude above the planet's surface.

That would also be my guess, because otherwise the answer is trivial. However, I still would like to see the statement of the problem if it is different from the posted one.

 

[berkeman]

Cosmonaut m=100kg is outside of spaceship M=5 tons

M=5000kg

I'm still trying to parse this part...

 

[jbriggs444]

What comes out of universal gravitation law is 8.14208984375×10^-9 N

That is the gravitational attraction between the cosmonaut and the spacecraft based on their respective masses and separation. That could be important if we had a pole holding them apart. But in the case at hand we have a rope holding them together. What other force tends to separate the two?

[Note that it is easier to provide help when more of the work is shown and one does not have to reverse-engineer the result to figure out what went wrong]