Could a tether be used to boost Phobos’s orbit?

Question

Background:

Phobos, the innermost moon of Mars, is in a decaying orbit which will either crash into Mars or break up in a few million years. It is a very valuable staging port in my universe, due to its vast quantities of subsurface ice and large underground voids, inside which a large base has been built. Therefore, the world governments have commissioned a study into how to stabilize its orbit.

Problem: Phobos is absolutely massive. Approximately 10E15 kg, in fact. There doesn’t seem to be a viable way to move all that stably, unless non-rocket propulsion is considered.

It just so happens that Phobos may have such an option. To facilitate transfer of massive payloads to and from Mars, it has had a tether system similar to this one installed on it. My question is, therefore:

Could using this tether system provide sufficient orbital momentum to counteract Phobos’s orbital decay? If not, what other options would be available?

Any and all answers would be helpful and appreciated. Thank you!

Answer 1

Millions of years? People in your universe plan long ahead.

In fact, if wikipedia is right, then Phobos' orbit decreases by 2 meters every hundred years and it will last another 30-50 million years until it crashes into Mars.

You could increase or stabilize Phobos' orbit with a momentum exchange tether if you are willing to sacrifice some of its mass - although actually you could use any mass for it. Since you have millions of years time that can be done continually, so energy expenditure per, say, one Mars year will not be that large.

You can build a long tether that reaches from Phobos' near side to Low Mars orbit. If you have a mass at the end of the tether, then the center of gravity will shift to a point between Phobos and the mass. Now Phobos goes a little bit too fast for its orbit and the mass on the end of the tether goes too slow for its orbit. As soon as you release the mass from the tether it will fall towards Mars and Phobos will move to a slightly higher orbit. That's how momentum exchange tethers work.

If the mass is small compared to the mass of Phobos, then the orbital change will be miniscule, but that does not matter. Remember, you have millions of years time, so even miniscule changes will add up with time. All you have to do is increase the orbit of the moon by 2 meter every 100 years, then it will not decay.

How much energy do you have to add every 100 years to increase the orbit by 2 meters?

Specific orbital energy is -μ/2a. For Phobos that is -4.282837×10^13 / (2 x 9376000) or -2283936.11 Joule/kg.

Phobos has a mass of 1.0659×10^16 kg, so its orbital energy is -2.4344475 x 10^22 Joule.

If we increase the orbit by 2 meter, we get -2.43444699 x 10^22 Joule. That is a difference of 5.1 x 10^15 Joule or the annual energy output of a 170MW power plant.

Instead of a tether you can use rockets or any machine generating thrust. It needs a power of only 1.7 MW to keep Phobos' orbit stable - the power consumption of a moderately large village.

Answer 2

It's not the tether, but the offworld cargo.

Using your source, Phobos has a 9376 km semi-major axis and an average orbital speed of 2.138 km/s. (I am ignoring eccentricity. After all, the local businessmen probably want a circular orbit to make their satellite orbits more fungible.) With mass 1.0659E+16 kg, we can get angular momentum 2.137E+26 kg m^2/s. Using the article's figure of 2m/100 yr orbital decay = 6E-10 m/s (6 Angstroms per second), we can divide that by the semimajor axis to see it is losing 7E-16 /s of its overall orbital height, at present. Now if I only take the loss of lever arm into account, that gives a loss of 1.5E+11 kg m^2/s; but in practice some amount of that angular momentum (I think half, but I should check) goes into increasing the orbital speed).

Now, suppose we ship a kilogram package to Mars. It lands on Phobos on a ship that matches speed perfectly, though I suppose you could propose cables like on an aircraft carrier to help accelerate the landing field! The kilogram gets on at 9376 km and it gets off at 9369 km (say 7.0 km lower), just past the L1 point. (Budget cuts - sigh - we wanted the 1400 km tether dang it!) Now that package has changed its torque arm by 7 km and its speed by nothing, so it has transferred 7000 m * 2.138 km/s = 1.4E+7 kg m^2/s of angular momentum to speed up Phobos, presumably causing the tether to lean forward a bit in orbit.

Now what I take from all that is that as long as the average cargo entering the tether is five metric tons per second, Phobos won't be losing any altitude. And we're talking about the shipping capacity for an entire planet here - teak, pistachio nuts, killer bionic dogs, colonists, cows, all the usual junk that old mother planets drowning in carbon dioxide are liable to ship out to try to balance their ecosystem and make ready cash while claiming to secure their legacy. It doesn't seem like a big problem, not even in a hundred million years.