# Cargo delivery from the ISS to Tiangong

Consider I have a 10 kg object I want to deliver from the ISS to Tiangong-1 station. The object can not go through the land and launch again cycle.

Can any of the present day spacecrafts do the delivery for me?

I am okay with re-fueling on the ISS if possible, EVA if needed, installing alternative docking systems and other "routine works".

EDIT:

Here's some info relating to the orbit of each:

• Tiangong-1 42.78 inclination, 343x350 km orbit.
• ISS- 51.65 inclination, 413x418 km orbit
• Does T-1 have to remain intact after the 10-kg delivery arrives? Mar 9 '19 at 4:34
• I'd say yes. Projectiles is another story. Mar 13 '19 at 10:22

## 1 Answer

Okay, first of all, let's assume that the two space stations are aligned properly. How often does this happen? The key thing is that each satellite will drift westward each day, due to what is known as Nodal Precession. Wikipedia gives us an approximate formula:

• $\omega_{p} = -\frac{3}{2}\frac{R_E^2}{(a(1-e^2))^2} J_2 \omega \cos i$

That gives each of them a precession value of (Using Heaven's Above values):

Thus, the relative differences are 1.06978147735 degrees. Thus, you can use the minimum solution once every 336 days.

Okay, so they line up properly, now what do you do? I don't have access to a simulator, so I'm going to break this in to two parts, the inclination change, and the raising of the orbit. In reality, these would be done together with an improved result, but it should give you an idea.

Well, let's assume that the change in eccentricity happens at the orbit of the ISS, as eccentricity changes are more effective in higher orbits. Also, let's assume a maximum efficiency transfer. Let's start with the harder of the two, the inclination change. I'm going to use the simplified formula for circular orbits, as the orbit is almost so. Thus, it is:

$\Delta{v_i}= {2v\, \sin \left(\frac{\Delta{i}}{2} \right)}$

Given that, the delta v is 1.084 km/s. Likewise, we can calculate the delta V to raise or lower the orbit appropriately. The quick way is to assume twice the change in orbital velocity (Once to raise the apogee, once to raise the perigee). Using this calculator, I find the ISS velocity is 7662.5112 m/s, and Tiangong is 7694.277. Thus, there is a change in velocity of only about 70 m/s required to raise the orbit thus.

Bottom line is, the major requirement to raise the orbit is the inclination change. I'm confident that a delta v of 1.2 km/s would be enough to make the change, if you did it at the right time of the orbit. This is less than the delta v to get to the Moon, so there are plenty of rockets that can manage the change.

So, the total momentum required to move the hypothetical 10 kg object between stations is 12 kN*s. Hydrazine, a very common fuel for on orbit purposes, has an ISP of about 220. Taking away the mass for fuel and engine, the Hydrazine required to do such a maneuver is only 5 kg. Virtually any reasonably sized spacecraft engine has that much maneuvering capability.

However, there is also the added complexity of getting it exactly right, as is required in a rendezvous. The best bet would be something like the Dragon capsule, modified to make sure it had enough fuel. Any of the spacecraft currently used for the ISS resupply could do that, possibly with slight modifications to increase the fuel load. In addition, given enough fuel, the Space Shuttle, Soyuz, and Apollo missions have demonstrated such capacity, although the first two would probably require more fuel than is typically done for a manned mission, they could be modified to have more fuel and run unmanned to make it happen.

• That 5 kg prop mass number is... very misleading. For instance, taking the dry mass of the entire thing (including your package) to be a ludicrously low 100 kg requires about 75 kg of hydrazine (from the rocket equation). While I don't doubt that it can be done with some upper stage, it's not easy.
– user29
Sep 17 '13 at 13:29
• @Chris: Any system capable of GTO to GSO, orbiting another planet or the Moon, leaving Earth's gravity well, or maintaining GSO for 25 years would qualify at a minimum. Pulled with help from en.wikipedia.org/wiki/Delta-v_budget Sep 17 '13 at 13:51
• @PearsonArtPhoto: just to clarify. Any of the GTO-to-GSO capable or interplanetary capable etc system is able to perform the controlled precision approach within... (what's the canadarm length?) 15 meter accuracy? Sep 17 '13 at 14:58
• @horsh: No, they meet the delta V requirements, however. I haven't thought about this from the perspective of precision, but that would just be a bit more mass to the vehicle, that's all. Sep 17 '13 at 15:26
• That brings us back to the question of the existing spacecrafts capable of doing the delivery. While we see that technically such spacecraft can be easily designed using many existing systems for the propulsion, it is not obvious there currently exists one capable to perform the delivery mission. Sep 17 '13 at 16:19