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what "flying sideways" looks like

Imagine a vehicle like the dragon capsule, but the chair is on the bottom and facing forward, and the thrusters are directly behind it as illustrated above. When flying in space towards some planet, can the astronauts tell they're facing down and flying not forward relative to the direction they're facing?

Edit

To add clarity, my question is not about the logistics of space travel, but the physics of the drawing. Assuming a craft like the one above, with thrusters on or off, the craft flying in the direction of the arrow, and the astronaut sitting as depicted... Would he/she be able to tell that they're flying "headfirst" as opposed to the traditional concept of "forward" like you would when flying an airplane?

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    $\begingroup$ What do you mean by "facing down"? There's no up and down in open space. If the thrusters are working, they produce acceleration which will with some force press the astronauts to the floor to which the chair is attached, so in this case the direction to the floor and opposite to "forward" will be "down". Is this the situation you mean? $\endgroup$ – Yellow Sky Jul 18 at 0:39
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    $\begingroup$ I've boosted the contrast of your drawing for clarity, it's an interesting question, I'm curious why you chose Astronomy SE instead of Space Exploration SE though. $\endgroup$ – uhoh Jul 18 at 3:19
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    $\begingroup$ Thrusters aren’t generally used to propel the capsule forward. If any thruster is being used, the occupant will know which way it’s thrusting because they will “fall” in the opposite direction. If it’s thrusting sideways, they’ll “fall” away from the direction of thrust. $\endgroup$ – Chappo Hasn't Forgotten Monica Jul 18 at 3:41
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    $\begingroup$ FWIW, with current rocket technology, we don't use thrusters during the whole journey. They're only used at take-off, and for short burns to modify the craft's orbit (and for landings on airless worlds, like the Moon). For most of the journey to (for example) Mars, the craft is in free-fall. $\endgroup$ – PM 2Ring Jul 18 at 9:58
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    $\begingroup$ I’m voting to close this question because this is not about astronomy but about space exploration. $\endgroup$ – antispinwards Jul 18 at 11:16