Undergrad How does the moon's gravity affect the orbit of the ISS?

[PeterHarrison84]

I was recently listening to a favorite podcast of mine (AstronomyCast) and they went over the tidal effects the moon's gravity has on the Earth. I just happened to be thinking about the tidal effects after that and was wondering if the moon's gravity effects things in orbit of Earth. More specifically the ISS. When I tried to look this up the closest answer I found was that the ISS's orbit changes from about 320 km to 345 km, but it didn't say why this was. I can assume it probably has to do with a number of different things (eccentricity of the orbit or intentional altitude control) but I was wondering if anyone knew if the moon had any effect of this at all?

Thanks.

 

[Janus]

I would very much expect the Moon to have some tidal effect on objects in Earth orbit, after all, the Sun exerts a tidal effect on the Moon's orbit which causes a variance in its eccentricity.

 

[mgb_phys]

There are a couple of different effects here:
There is a tidal torque from the Earth on any non spherical object in orbit, so that would include the space station.
There would also be an effect where if the ISS was between the Earth and the moon it would receive a small pull toward the moon and away from the earth, when it on the other side of the Earth and the Earth and moon are alinged it will receive a very slightly larger pull toward the earth.
I don't know how big this effect is, the change in height you quoted of 25km would be 0.5% of the distance to centre of the Earth.

 

[D H]

More specifically the ISS. When I tried to look this up the closest answer I found was that the ISS's orbit changes from about 320 km to 345 km, but it didn't say why this was.

Aerodynamic drag makes the ISS slowly lose altitude. When the ISS falls below its lower operation limit (about 320 km), it performs an altitude maintenance maneuver to raise the altitude to about 345 km. Rinse and repeat.

Third body effects are small compared to aero drag for a vehicle in low-Earth orbit. This is especially true in the case of the ISS, which has a huge cross section due to its big arrays.

 

[DaveC426913]

...it performs an altitude maintenance maneuver... Third body effects are small compared to aero drag for a vehicle in low-Earth orbit. This is especially true in the case of the ISS, which has a huge cross section due to its big arrays.

See now, if they oriented the arrays horizontal to the Earth's surface, and gave them an aerofoil-shaped camber...


Well, they could save all that orbit-maintaining fuel now couldn't they?

 

[D H]

Well, they could save all that orbit-maintaining fuel now couldn't they?

In a sense, they do. The Station is in a "torque equilibrium attitude". The aerodynamic drag on the ISS does not act through the center of mass: It induces a torque as well as a force on the ISS. The gradient of the gravitational acceleration also induces a torque on the vehicle (this is yet another tide-like effect and varies with 1/R<sup>3 as do most tidal effects). The aero torque and gravity gradient torque will counterbalance when the vehicle is in just the right attitude. This torque equilibrium attitude is the ISS' nominal attitude.

There is one tidal effect that is smaller than 1/R^3. The moon and sun create the sea tides we all know about. The not-so-solid Earth also undergoes deformations, smaller in height than the sea tides, but much greater in mass. These solid-body tides subtly affect the orbits of low-earth orbit satellites. For more on this, google "k2 Love number".

Note: k2 is the most significant of several Love numbers. Googling "Love number" without the k2 results in TMI.</sup>