Does the Earth lose mass as it moves closer to the Sun?

Answer 1

No, but the Earth loses speed though. For some ungodly reason, the Earth, and every other object that orbits around another object (a star, a black hole, a planet, another sattellite, you name it...) loses speed when it is at its periapsis (in earths case, it's called a perihelion - and in the case of any other object orbiting the sun) and gains speed when at its apsis. The periapsis is the point in the orbit, closest to the object which is being orbited, the apsis is the point furthest away.

The only thing losing mass when being close to the sun, is us humans, when we go out sunbathing in the summer. For maximum effect, visit Australia.

Answer 2

No, the mass remains the same. The effect of gravity increases.