Calculating the Hill sphere of the International Space Station

In summary, the International Space Station has a mass of 400,000 kg and orbits 408 km above the Earth's surface with a diameter of 109 m. The equation for determining its orbit is not given, but it involves the semimajor axis and the masses of the space station and the object it orbits. A sketch can help visualize the problem.
  • #1
fema98
3
0

Homework Statement

[/B]
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

: [/B]
R=a(semimajoraxis) cubedroot(m2/3M1)

The Attempt at a Solution

: [/B]
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.
 
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  • #2
fema98 said:
and M2 isn't given my main problem
What does the ISS orbit? You can look up the mass of this object.
fema98 said:
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.
fema98 said:
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?
 
  • #3
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?
 
  • #4
fema98 said:
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.
fema98 said:
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.
 

1. What is the Hill sphere of the International Space Station?

The Hill sphere is a region of gravitational influence surrounding a celestial body, within which the body's gravitational pull is stronger than that of any other nearby objects. For the International Space Station, its Hill sphere is the area around it where its gravitational pull is stronger than that of the Earth's.

2. How is the Hill sphere of the International Space Station calculated?

The Hill sphere of the International Space Station can be calculated using the formula:
RH = a(1-e)3/2(m/3M)1/3, where RH is the radius of the Hill sphere, a is the semi-major axis of the ISS's orbit, e is the eccentricity of the orbit, m is the mass of the ISS, and M is the mass of the Earth.

3. What factors can affect the Hill sphere of the International Space Station?

The Hill sphere of the International Space Station can be affected by the mass and distance of other celestial bodies in the vicinity, as well as the eccentricity of the ISS's orbit. The closer the ISS is to other objects, the smaller its Hill sphere will be.

4. Is the Hill sphere of the International Space Station constant?

No, the Hill sphere of the International Space Station is not constant. It can change depending on the factors mentioned above, such as the eccentricity of the orbit and the presence of other objects in the vicinity.

5. Why is the Hill sphere of the International Space Station important?

The Hill sphere is important for understanding the gravitational influence of the ISS and other objects in its vicinity. This can be useful for predicting potential collisions or understanding the stability of the ISS's orbit. It is also important for space missions that may come close to the ISS, as they must consider the ISS's Hill sphere in their trajectory calculations to avoid any potential disturbances to its orbit.

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