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Does the path of a rocket or anything going straight up look curved because the mass of the earth is curving space-time?

If we assume the earth, the rocket and all the celestial bodies whose gravitational field reaches the earth to be massless then will the rocket follow truly a straight line, because there would be nothing curving the space-time?

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  • $\begingroup$ Rockets most certainly do not follow straight paths, if only for the fact that their motors are steerable. $\endgroup$
    – Mick
    Jan 16 '18 at 20:31
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    $\begingroup$ Rockets often follow curved paths into space. If they only went straight up, they'd basically just fall straight back down. To stay in space, you need to orbit. As an example of rockets following curved trajectories into space, try reading about something known as a Gravity Turn. $\endgroup$
    – zephyr
    Jan 16 '18 at 21:06
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    $\begingroup$ A massless rocket would travel at the speed of light and never accelerate or decelerate. $\endgroup$
    – StephenG
    Jan 16 '18 at 22:28
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This is partly space exploration and partly physics.

Rockets do not normally go straight up. They start off going up, to get into thinner air, then they steer to turn themselves eventually to a horizontal path, until they are going fast enough to stay in orbit.

In general relativity, an object that is free to move in the Earth's gravitational field will appear to accelerate towards the ground as it is following a path (called a geodesic) in curved spacetime. This is not specific to rockets; a cricket ball will follow a curved path when thrown due to the curvature of spacetime around the Earth. And if one is far from any gravitational field, then a cricket ball will travel in a straight line.

To directly answer your question: The path of a rocket going straight up will not look curved, it will look like it is going straight up.

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