I wonder if we could measure the friction the spacecraft is experiencing and the density of the intergalactic medium, then determine velocity relative to said medium?
Proportional to the frame of reference in which you are stationary, which is the only frame of reference that matters to you.
If you fire a thruster that pushes your ship sideways with an acceleration of 0.1g, you will feel a sideways force of 0.1g, regardless of how fast you might be moving relative to some external object. Changing course in a spaceship is not like steering in a boat, car, or airplane at all. You don’t have a space rudder or steering wheel you can use to change your course by pushing against some external medium. You have to change course by firing thrusters to alter the direction in which your ship is moving.
Now, it is true that if you are moving faster (as seen by some arbitrary external framework) it will take more change in velocity to change your course. But that doesn’t mean that there will be greater forces felt on your ship when you are turning. More likely it means that you’ll have to fire your thrusters at the same force level for a longer period of time to make the required change in velocity.
I’m not quite sure what you’re trying to say here, but applying a constant force at right angles to your direction of motion does indeed result in traveling in a circle.
For an example, consider a satellite in low earth orbit.
Applying a constant force in a constant direction will result in a parabola. If you want it to instead stay at a right angle to your direction of motion, then you need to first establish what your direction of motion is.
Yes, but a space ship’s orientation is independent of its direction of motion. So if you start out with the ship’s nose pointing in the direction of motion and apply thrust to the side of the ship(in line with the ship’s center of mass) you will change the direction of motion without changing the orientation of the ship. As a result the thrust applied to the side of the ship will no longer be perpendicular to the direction of motion.
Right - got it. Force must be applied perpendicular to the direction of motion, which isn’t necessarily at right angles to the ship.
Though in special relativity applying a constant force in the reference frame of the object will actually result in a hyperbola.
I don’t get this response (“though”) to Chronos’s post. Help?
In Newtonian kinematics the trajectory of an object subjected to constant acceleration follows a parabola, in relativistic kinematics the trajectory an object subjected to constant acceleration follows a hyperbola.
It’s more an interesting factoid than directly relevant.