On 2/24/17 07:55, Howie DeFelice wrote:

Very interesting Phil, it seems to make sense that this calculation could be used in reverse to calculate the energy needed raise the perigee height of a GTO orbit. Assuming a flight to GTO was available to a 1U or 3U cubesat, if the perigee is not raised the satellite will not stay in orbit very long, if I understand it correctly. Given the limited size of the spacecraft and the prohibition on volatile propellants this poses a difficult challenge. It would be interesting to determine if enough thrust can be generated by electrical thrusters to accomplish this ?

- Howie AB2S

It would be most relevant if you can use a tether to form an electric motor with the earth's magnetic field to raise your orbit.

Otherwise, things are much more complicated with a chemical or electrical rocket because you have to carry your reaction mass with you and then put energy into it to blow it out the nozzle at high speed.

There's a fundamental tradeoff in rocketry between rocket power and propellant mass flow rate. You can produce a given amount of thrust with high power and a low propellant mass flow rate, or with low power and a high propellant mass flow rate.

E.g., to produce a thrust of 1 N with a mass flow rate of 1 kg/s, you have to eject it at 1 N / 1 kg/s = 1 meter/sec. Ignoring relativity, the kinetic energy in 1 second of exhaust (1 kg) will therefore be

1/2 mv^2 = 1/2 * 1 kg * (1 m/s)^2 = 0.5 joules

and since you need 0.5 joules every second, the required power will be 0.5 watts (assuming 100% efficiency).

If you double the exhaust velocity to 2 m/s, you can drop the mass flow rate to only 1/2 kg/s and still get 1 N of thrust (1/2 kg/s * 2 m/s = 1 N). But you'll now need a power of

0.5 * 0.5 kg/s * (2 m/s)^2 = 1 watt

i.e., twice as much power for that same 1 newton of thrust.

So, which do you have more of, propellant mass or energy? In a chemical rocket the energy is stored in the unburned propellant, so the energy per unit mass is set by the propellant chemistry. That's why every propellant combination has a theoretical specific impulse, e.g. 455 seconds for hydrogen/oxygen in vacuum. Specific impulse is just effective exhaust velocity divided by g = 9.8 m/s^2, so the theoretical exhaust velocity for hydrogen/oxygen is 4,462 m/s.

But in an electric rocket the energy source is external to the propellant mass, so the energy/mass ratio can vary; you decide how fast to eject it. If mass is cheaper than energy, then you want a low exhaust velocity. If energy is cheaper than mass, then you want a high exhaust velocity.

Since the rocket is free to move, the kinetic energy it produces will be split between the payload/rocket itself (which you want) and the exhaust (which is effectively wasted). The only way to get 100% of the energy into the payload/rocket and none into the exhaust is to set the exhaust velocity equal to the current velocity of the rocket so that the exhaust comes out stationary. Of course, velocity is relative so you measure it relative to the reference frame in which the rocket is initially stationary. So to minimize energy consumption you want to increase the exhaust velocity as the rocket accelerates. That's the exact idea behind the VASIMR (Variable Specific Impulse Magnetoplasma Rocket).

The recent "EM drive" hype notwithstanding, I know of only one way to produce thrust in vacuum without some kind of propellant: the photon rocket. Even a flashlight will work, but let's do the numbers. The momentum of a photon is equal to its energy divided by the speed of light, so to get 1 newton of thrust from a 100% efficient photon rocket requires a power input of 1 N * c = 300 megawatts!

That kind of power in space requires either a very large solar array or a very big nuclear reactor (which still needs a very large radiator to reject waste heat).

But there's a simpler way to power a photon rocket with the sun. Instead of turning solar photons into electricity and back into photons, why not use solar photons directly? Voila -- that's what a solar sail does. The thrust produced by a solar sail per unit area is equal to the incident solar power per unit area divided by the speed of light. At 1 AU that's about 1361 W/m^2, so the thrust will be 1361 W/m^2 / c = 4.54 micro newton/m^2. That's actually units of pressure, so solar radiation pressure at 1 AU is 4.54 micropascal on a sail normal to the sun that simply absorbs solar photons. If you reflect them back, you'll get twice as much, 9.08 micropascal. Doesn't seem like much, but you'll get it continuously, no local power source or propellant mass needed.

The one big problem with solar sails is that you can't use them in low orbits because they'll generate far more drag than thrust.

73, Phil