設(shè)衛(wèi)星a 質(zhì)量為m1,向心加速度a1,角速度ω1,軌道半徑=R+R=2R,地球質(zhì)量為M,萬有引力常量G,
設(shè)衛(wèi)星b 質(zhì)量為m2,向心加速度a2,角速度ω2,軌道半徑=R+3R=4R,m1a1=Gm1M/(4R)^2,
（ω1）＾2＊（2R）＝MG/(2R)^2,
（ω2）＾2＊（4R）＝MG/(4R)^2,
（ω1）＾2/（ω2）＾2=(4R)^3/(2R)^3,
ω1/ω2=2√2,ω1=2√2ω2,二角速度差為ω1-ω1/2√2
當(dāng)二衛(wèi)星相差180度時(shí)相距最遠(yuǎn),設(shè)從同一相位開始到相隔180度所需時(shí)間為t,
(ω1-ω1/2√2)*t=π,t=π/[ω1(1-1/2√2)],
衛(wèi)星a繞地球周期為T1,T1=2π/ω1,
t/T1=π/[ω1(1-1/2√2)]/(2π/ω1)=（4+√2）/7
a衛(wèi)星至少經(jīng)過（4+√2）/7個(gè)周期后二衛(wèi)星相距最遠(yuǎn)．