Want to solve for

Lagrange points

yourself? An

undergraduate

student who’s

taken an advanced

mechanics class

and vector algebra

has all the tools

they need to find

those solutions.

The Math That Helps the

James Webb Space Telescope

Sit Steady in Space

18 May/June 2022

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Deep Math

5

// BY MANASEE WAGH //

A

BOUT 250 YEARS AGO, MATHEMATI-

cians wrote the first equations describing

where the James Webb Space Telescope,

launched on Christmas Day 2021, now

resides. Webb will stay put for around 20

years at its cosmic parking spot, survey-

ing the universe’s galaxies. And we don’t

have to worry about it wandering away: Its new

home is a gravitationally balanced spot relative to

Earth and the sun, called a Lagrange point.

Webb experiences the pull of gravity from both

our own planet and the sun at Lagrange point 2

(L2), one of five such points in the sun-Earth sys-

tem. Centripetal force—which makes objects

move in a circle around an object with gravity—

also accelerates the telescope into orbit with that

system, causing it to revolve around, and get

pulled toward, L2. Space explorers love Lagrange

points because when viewed from Earth, the points

appear to stay in fixed locations, making them con-