# Hundred dollars a kg/Note 1

In theory, with a high efficiency device such as a moving-cable space elevator, the electrical energy to lift a kg from the surface of the earth to GEO is only14.75 kWh/kg. That is under $0.15 at the target price for electric power. This would pay back the lift energy in about 15 hours for a 1kg/kW power satellite or 30 hours for a 2kg/kW unit.

400 GW/year production rate for 2kg/kW power sats would require lifting 2,200,000kg/day. Over a 24hr/day is 91,700 kg/hr. Multiplying this by 14.75 kW/kg gives 1.35 GW. For scale, the aircraft carrier Enterprise produces 0.21 GW, and the installed coal-fired capacity in the US is about 300 GW. Alas, elevator cable strong enough for a space elevator does not yet exist.

## Rockets

We can lift power-satellite parts with rockets. This has been dismissed for decades as being too costly. The short space elevator energy payback and an email from a veteran rocket engineer prompted an energy payback analysis. The rocket used in this analysis is here:

http://www.ilr.tu-berlin.de/koelle/Neptun/NEP2015.pdf

The Neptune design is about 3 times the capacity of a Saturn V, and some of the same people who designed it designed the Saturn V; i.e., it is solid engineering.

This reusable vehicle delivers 350 metric tonnes to LEO, and 100 t to lunar orbit or GEO. To lift 100 t to GEO Neptune uses 3762 mt of propellant for the first stage, 1,072 mt for the second stage, and 249 mt for the third, totaling 5,077 mt.

Space shuttle main engine O_{2} to H_{2} ratio is 6 to 1.

That is, 1 part in 7 of the propellant is liquid hydrogen (LH), or about 725 mt of LH. The launch site would make electrolytic hydrogen out of water (the only long-term source). That costs about 50 kWh/kg plus another 15 kWh to liquefy the H2. Add 5 kWh for liquefying oxygen at 6 x 0.8 kWh/kg.

That would be 70 MWh per mt, or 70 GW hours for 1000 tons, or 50.8 GWh for 725 mt. At a kg/kW, 100 mt of satellite produces 100,000 kW, or 0.1 GW. Thus, it would take 508 hours to pay back the lift energy or 21.2 days, 42.4 days for 2kg/kW, or ~100 days for 5kg/kW. This does not account for the energy that goes into structural parts, photovoltaic cells (or heat engines) and transmitter. The current energy payback for ground based solar panels (including supports) is about 3 years. This would drop to a few months in space because of the higher continuous light on the cells.

Energy cost would be $5.08/kg for fuel. Rocket efficiency would be 14.75kWh/kg / 508kWh/kg or 2.9%.

The real problem is the cost of aerospace hardware. The cost of the rocket is estimated in the above paper at $1.5 billion each, and maintenance and operations about the same. The rockets are in theory reusable up to 200 times. If we count on a conservative 100 uses, a rocket delivers 10 M kg of payload at a cost of $3000 M or $300 a kg delivered to GEO, three times above the $100/kg needed for dollar a gallon fuels. (This does not count RDT&E or the investment in ground based facilities. For this large a traffic model, they should be a small part of the total cost.)