# How much thrust is “high” thrust (for orbital transfers)

I understand that chemical rockets and nuclear thermal rockets (and possibly very high power electrical thrusters) are considered to provide "high" thrust for orbital transfers, while electrical thrusters and solar sails are considered to provide "low" thrust, which makes them unsuitable for using the Oberth effect, makes shorter trips (such as the inner solar system) take a long time, and adds delta-V overhead.

But where is the boundary? 0.1g? 0.01 g?

This answer will be satisfying or unsatisfying depending on each reader's perspective.

## Impulse

This answer to Ratio of low-thrust slow spiral to Hohmann transfer $$\Delta V$$? explains that the total impulse for an assymptotically low thrust spiral from one circular orbit to a higher one is higher than that needed for a Hohman two impulse transfer by a factor that ranges from unity up to $$1+\sqrt{2}$$ at infinity.

@MarkAdler's answer contains the solution for a bi-elliptic transfer as well but I'll leave that plot as an exercise for the reader.

So one criteria for high thrust might be how close to a theoretical Hohmann transfer the a given engine might be in terms of impulse.

## Time

In Low-thrust spiraling to escape, is the flight path angle (gamma) at C3=0 always 39 degrees? I plot some slow spirals of a low impulse trajectory. Another criteria for high thrust might be how close to a theoretical Hohmann transfer the a given engine might be in terms of time.  ...where $$x$$ is the ratio of the higher orbit radius to the lower orbit radius, assuming (without loss of generality) that the lower orbit radius is $$1$$ and $$\mu$$ is $$1$$.

import numpy as np
import matplotlib.pyplot as plt

def Hoh(x):
return np.sqrt(2.*x / (x+1.)) + np.sqrt(1./x) - np.sqrt(2./(x*(x+1.))) - 1.

def Low(x):
return 1. - np.sqrt(1./x)

x = np.logspace(0, 6, 601)[1:]

plt.figure()
plt.plot(x, Low(x) / Hoh(x))
plt.xscale('log')
plt.xlabel('x', fontsize=16)
plt.ylabel('"Low to Hoh" total impulse ratio', fontsize=16)
plt.show()

• one more spirally-related question: Spiraling out from circular orbit to escape via low thrust, what is γ (gamma)? – uhoh May 17 at 1:28
• What does "x" represent in the lower plot? – Russell Borogove May 17 at 3:02
• @RussellBorogove it's MarkAdler's "x", ratio of the final to initial circular orbit radius, so for example Earth to Jupiter would be about x = 5.5 I'll clarify the post in another hour or so when I get to a decent keyboard. Thanks! – uhoh May 17 at 3:20