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Let's assume that Earth and Venus have circular, coplanar orbits. The spacecraft advances 180° in heliocentric ecliptic longitude in 143 days; meanwhile, Venus advances 241° and Earth advances 141°. When the spacecraft departs from Earth (left), Venus should be 61° behind Earth as seen from the Sun. When the spacecraft arrives at Venus (right)...

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I'm assuming you're talking about physical distances (as opposed to any of the other distance measures in cosmology). The comoving distance to a galaxy at redshift $z$ is $$d_C(z) = \frac{c}{H_0}\int_0^z \frac{dz}{\sqrt{ \Omega_r(1+z)^4 + \Omega_m(1+z)^3 + \Omega_k(1+z)^2 + \Omega_\Lambda }},$$ ...

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My question is, then, how does the Moon's orbit manage to not have any concavity, no matter how minute, while transitioning from the full moon to the new moon positions? Isn't that not a mathematical impossibility? TL;DR answer: Because the gravitational acceleration of the Moon toward the Sun is about twice the gravitational acceleration of the Moon toward ...

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