LISA is a space-based gravitational wave observatory that is anticipated to launch in 2034. Its constellation of three spacecraft will be located at the vertices of an equilateral triangle that will follow the Earth about the Sun. The spacecraft will be deployed in three heliocentric elliptical orbits that, to first order in their eccentricity, maintain the observatory's size and configuration. How LISA accomplishes this is an ideal illustration of basic orbital dynamics. The physics underlying the choice of orbits is explained at a level suitable for introductory undergraduate physics students.

1.
B. P.
Abbott
 et al., “
Observation of gravitational waves from a binary black hole merger
,”
Phys. Rev. Lett.
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,
061102
(
2016
).
2.

According to Kepler's 3rd law, the orbital period T of a binary black hole is given by T2/R3=4π2/GMtot, where R is the separation of the bodies and Mtot is their total mass. The bodies merge when R2GMtot/c2, the sum of their Schwarzschild radii. The maximum orbital frequency before coalescence is therefore fmax=Tmin1Mtot1. Since the GW frequency fGW=2f, the minimum radiated wavelength is directly proportional to Mtot. Just as for the detection of radio waves, the longer the wavelength, the larger the antenna must be.

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,”
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5.
A nice treatment of a similar problem, by similar methods, is given by
E. I.
Butikov
, “
Relative motion of orbiting bodies
,”
Am. J. Phys.
69
,
63
67
(
2001
).
6.
This approximation was first used by ancient Greek astronomers to describe the motion of the Moon and Sun within their geocentric system of the world. See
Arthur
Berry
, “
A Short History of Astronomy
” (
1898
), available from Dover Publications.
7.
For an easy derivation of these transformation equations, see
J. C.
Amato
and
E. J.
Galvez
, Physics from Planet Earth, Chap. 2, Problem 2.18.
8.
This topic is treated on higher mathematical level by
S. V.
Dhurandhar
 et al., “
Fundamentals of the LISA stable flight formation
,”
Classical Quantum Gravity
22
,
481
487
(
2005
).
9.
ESTEC (European Space Research and Technology Centre) CDF Team
, “
LISA phase 0 CDF study—Internal final presentation
,” in
ESTEC (European Space Research and Technology Centre) Conference
, Noordwijk, Netherlands, 8 March– 5 May (
2017
), Slide 7, p.
110
.
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