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If Earth had no atmosphere, then would a standard gravity turn still be the most optimal path to orbit?

Why or why not?

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The optimal trajectory for reaching the cheapest ("altitude zero" circular) orbit around a perfectly spherical, airless body involves turning immediately after lift-off so that the vertical component of thrust only offsets gravity drag (weight minus centrifugal force) providing no vertical acceleration, and all the remainder of thrust goes towards horizontal acceleration - so a deep tilt immediately after achieving lift-off.

Obviously no body is perfectly spherical, so in reality more of thrust will go towards gaining some altitude, but that component may still be very small - it's more efficient to move to a higher orbit after achieving the initial low orbit, than to launch directly into a higher orbit. That may not be true with launches directly into escape trajectory, where achieving orbit (raising the periapsis above surface level) is not required, and similarly for very high orbits (where raising the periapsis through an apoapsis burn is cheap.)

As the "depth" of the gravity turn maneuver (ratio between thrust "up" and "sideways) varies with launch conditions (rocket type, atmosphere), this is a "degenerate" situation where almost no thrust goes towards raising the flight altitude initially, so it's arguable whether this launch profile can still be called "gravity turn".

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A gravity turn is the most optimal path to orbit, assuming no atmosphere or staging. On Earth, launch vehicles use a modified flight path accounting for those differences, generally resulting in a more vertical trajectory than would be the case otherwise

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    $\begingroup$ Source? You just state that it's optimum without any supporting info. $\endgroup$ – Organic Marble Jun 9 at 10:58
  • $\begingroup$ because prograde burns are the most efficient @OrganicMarble $\endgroup$ – JCRM Jun 9 at 19:07
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There are two things to know about a gravity turn:

  1. is to optimise the ascent to an orbit at a certain altitude.
  2. is the fact that the spacecraft cannot accelerate instantly.

If there is no atmosphere (and Earth was a perfect sphere), why not just orbit at an altitude of 1 foot off the ground, accelerating instantly to orbital velocity?

Also, for real world purposes - note the Lunar Module ascent stage used a gravity turn with no atmosphere.

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