Indeed, a 4-satellite orbit is probably not a stable one unlike the 3-satellite orbit proposed for LISA. But the 4th satellite already isn't needed due to the conical orbit of the 3-satellite constellation. Fig 5(c) in "On the antenna pattern of an orbiting interferometer" [1] shows the antenna pattern for a LISA-like constellation and it's practically isotropic over a year, and for shorter periods the signals in LISA's sensitive band will be observed for long enough that they will not occupy its less sensitive directions for long and can thus still easily be detected with high SNR.
Comments
Indeed, a 4-satellite orbit is probably not a stable one unlike the 3-satellite orbit proposed for LISA. But the 4th satellite already isn't needed due to the conical orbit of the 3-satellite constellation. Fig 5(c) in "On the antenna pattern of an orbiting interferometer" [1] shows the antenna pattern for a LISA-like constellation and it's practically isotropic over a year, and for shorter periods the signals in LISA's sensitive band will be observed for long enough that they will not occupy its less sensitive directions for long and can thus still easily be detected with high SNR.
[1] https://academic.oup.com/mnras/article-pdf/289/1/185/1819985...