Calculating the Hill sphere of the International Space Station

[fema98]

Homework Statement

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The International Space Station (ISS) has a mass of 400,000 kg and orbits 408 km
above the Earth’s surface. The ISS is 109 m across.

Homework Equations

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R=a(semimajoraxis) cubedroot(m2/3M1)

The Attempt at a Solution

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ive tried multiple ways with multiple equations, I just can't figure out what the variable are sipposed to be I am assuming that M1 is 400,000Kg, and M2 isn't given my main problem is what do 408Km and 109M represent, is the 109 M the Hill sphere, so would the euation work out to be 109=204 cubedroot (m/3*400,000kg)? or is this just a conceptual question and I am way overthinking this?

PS. if your wondering where the 204 came from i assumed the 408 distance from Earth to the ISS was the major axis so semimajor was 204.

 

[mfb]

and M2 isn't given my main problem

What does the ISS orbit? You can look up the mass of this object.

is the 109 M the Hill sphere

No, it is the physical diameter of the space station.

408 km is the height of the space station above the surface of Earth. That is written in the problem statement, I don't see what could be unclear here.

PS. if your wondering where the 204 came from i assumed the 408 distance from Earth to the ISS was the major axis so semimajor was 204.

(a) work with units, then you would have spotted one error here already
(b) 408 km is the height of the ISS above the surface of Earth (that is literally given in the problem statement), it is not the distance to the center of Earth.

Did you draw a sketch?

 

[fema98]

Firstly thanks for the clarification. And no i didn't draw it, never been able to visualize math/physics problems. Also i would presume that aslong as i get a positive number than that would indicate that theoretically there could be another station that could orbit the ISS aslong as it was within that Hill sphere?

 

[mfb]

And no i didn't draw it, never been able to visualize math/physics problems.

That makes it difficult to solve problems. Drawing a sketch will help to visualize it.

Also i would presume that aslong as i get a positive number than that would indicate that theoretically there could be another station that could orbit the ISS aslong as it was within that Hill sphere?

Not if the orbit would have to physically go through the station.