# What was Sutton talking about? How to "obtain small accelerations by taking advantage of difference in gravity as a function of altitude"?

Sutton and Biblarz's Rocket Propulsion elements says in Chapter 1, section 1.2 (editions 7, 8, 9, possibly earlier as well) that:

Totally different methods of producing thrust are used in nonthermal types of electric propulsion. As described below, these electric systems use magnetic and/or electric fields to accelerate electrically charged atoms or molecules at very low gas densities. It is also possible to obtain very small accelerations by taking advantage of the difference in gravitational attraction as a function of earth altitude, but this method is not treated in this book.

I find this intriguing, and so my question is; How?

• What edition/printing? Apr 4, 2019 at 3:55
• @OrganicMarble It's in 7, 8, 9 but I'm not sure about earlier ones, I've made another edit.
– uhoh
Apr 4, 2019 at 5:30
• Am I missing something, or is this a complicated way of saying "Earth's gravity is weaker higher up"? Apr 4, 2019 at 5:33
• @uhoh do you mean "accelerations"? "Attraction" is singular. I think Ingolifs might be right in that this is the classical moon acceleration thing. The quote refers explicitly to the distance to Earth. Apr 4, 2019 at 5:53
• @uhoh: If it's resonant in, say, 86:1 and you raise it to be resonant 85:1?
– SF.
Apr 4, 2019 at 11:47

I think that the highlighted sentence in the question is referring to the use of space tethers in gravity gradients for propulsion. (None of the section headings in the 9th edition of Sutton and Biblarz mention tethers, and neither ‘Tethers’ or ‘Space tethers’ appear in the index).

Reactionless propulsion using tethers

An orbiting tethered satellite can propel itself by reaction against the gravitational gradient, with expenditure of energy but with no use of on-board reaction mass.

• Very nice answer! This makes a lot of sense. Can you double check that space tethers are not covered in Sutton? That would be necessary to be compatible with "...but this method is not treated in this book." Thanks!
– uhoh
Apr 25, 2019 at 20:51
• Also, I think it's great that you've chosen to link to the original paper itself, rather than just a Wikipedia page. fyi you may also be interested in the question Could a satellite in LEO “pump” or change mass distribution to gain forward momentum?
– uhoh
Apr 25, 2019 at 20:53
• Great! Also we can have the change in the plane or change in inclination of the satellite by spinning that tether about its longitudinal axis...(Gyroscopic precession) Apr 26, 2019 at 3:52
• I’ve checked that tethers aren’t mentioned in Sutton in Biblarz contents or index, and updated the answer. Apr 26, 2019 at 20:02
• The edit looks good, thank you. By the way I'd put two bounties on this question earlier, and each one expired after 7 days + 1 day grace period. As explained in answer(s) to Any way to award a second +100 bounty to a second answer to the same question? the Stack Exchange software requires each bounty to double. So this one ends up being quite large. You just missed the +200 bounty by less than a day I think. This is a bit unusual, I guess it's your lucky day!
– uhoh
Apr 27, 2019 at 12:56