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Let's say the James Webb Space Telescope wants to move from observing the Andromeda galaxy millions of light years away to looking at the Trappist-1e planet some dozens of light years away, what actions are need to change targets and find and resolve that target?

I think I read it has jet propulsion for movement, but does it have a different system for fine movement? It seems like jetting around would be extremely finicky.

I imagine Hubble has to do something similar but I never heard how that works either.

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It's true that James Webb carries fuel, and you're right that it is not used for positioning, at least not directly (see below). Fuel is used for maintaining its orbit around L2, and was also used three times on its journey to L2, as "corrections burns". Note that the distance to the target is irrelevant. A nearby exoplanet and a distant galaxy are both "infinitely far away" for observing purposes (although of course in general more distant object are fainter).

Reaction wheels

To acquire a target, James Webb (and other space telescopes) uses a number of reaction wheels, one for each "axis". At least three are needed, but James Webb has six; more allows for easier control, but are also heavier. These wheels rotate constantly, thus storing a large amount of angular momentum to keep the telescope steady. Changing the angular speed of one of the action wheels causes Webb to change its direction along that wheel's axis.

Edit thanks to @KarlKastor: While James Webb observes, the photon pressure of the Sun's light exerts a torque on the telescope. To maintain its position, this is counteracted by adjusting the spin of the reaction wheels. This causes angular momentum to build up, which must occasionally be dumped by firings Webb's thrusters once per week or so (JWST Momentum Management).

Gyroscopes

Additionally, Webb has six gyroscopes which tell the telescope which direction it's currently pointing, and how fast it's turning. Unlike Hubble's gyroscopes, however, which are mechanical, Webb uses Hemispherical Resonator Gyroscopes, which have no moving parts susceptible to wear, instead measuring the precession of vibration patterns in a crystal.

Star tracking

Finally, to ensure a perfect pointing, one of Webb's four instruments, NIRISS, is equipped with a "Fine Guidance Sensor" which "locks" the telescope on a target by observing the exact position of a star in its field of view.

Edit thanks to @David Hammen: In addition to the Fine Guidance Sensor, the JWST also has a few regular star trackers.

To power its various moving parts, James Webb has its solar array, capable of providing 2 kW, twice the needed amount.

You can read more about the positioning system at the NASA FAQ.

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    $\begingroup$ It's not entirely accurate to say no fuel is used for attitude control: the reaction wheels have to be desaturated with thrusters several times per month: "[...], angular momentum accumulates in the reaction wheels. [...] Each momentum unload activity takes a few hours. The observatory slews to a particular orientation to minimize the impact on the orbit, then fires thrusters to allow the spin rates of the reaction wheels to be adjusted." jwst-docs.stsci.edu/jwst-observatory-hardware/… $\endgroup$
    – KarlKastor
    Aug 1, 2022 at 12:02
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    $\begingroup$ In addition to the HRGs and fine guidance sensor, the JWST also has star trackers. A rate gyro measures angular rate rather than angular position. Without an occasional update from an angular position sensor such as a star tracker, even the very best rate gyro will eventually succumb to the dead reckoning problem. The fine guidance sensor is essentially an extremely sensitive kind of star tracker. In addition to the fine guidance sensor, the JWST also has two or three (the references I found are in conflict) plain old vanilla star trackers. $\endgroup$ Aug 1, 2022 at 13:22
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    $\begingroup$ @Fattie the big focus knob stays on infinity always. Its nearest focus point is about 3 km. The math is here: space.stackexchange.com/a/58766/1235 $\endgroup$ Aug 1, 2022 at 14:19
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    $\begingroup$ reaction wheels I had to use those in Kerbal! That's the big piece I was missing. Thank you for a perfect answer. $\endgroup$
    – joeyfb
    Aug 1, 2022 at 21:03
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    $\begingroup$ @joeyfb note the Kerbal ones don't saturate or require unloading $\endgroup$
    – user253751
    Aug 2, 2022 at 19:00

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