Suppose that the Earth's orbit around the Sun is perfectly circular. At some instant in time the sun suddenly loses 1/4 of its mass (it just dissapears). Neglect the motion of the Sun.
a) Employing conservation arguments, find the value of the eccentricity e of the orbit.
b) Find the distance of closest approach (perihilion) of the new orbit in termsof the radius ro of the original circular orbit.