Final answer:
If half of the Sun's mass disappeared, Earth's orbit would become more elliptical and its distance from the Sun would likely increase. The Earth's orbital period would also increase due to the reduced gravitational pull from the Sun.
Step-by-step explanation:
If half of the sun's mass were suddenly to disappear, Earth's orbit would be significantly affected due to the change in the Sun's gravitational pull. According to Kepler's third law, the orbital period of a planet is related to its distance from the Sun and the mass of the Sun. With half the mass gone, the gravitational force exerted on Earth would decrease, leading to a less tight orbit.
Currently, Earth's orbit is nearly circular due to the balance between Earth's velocity and the Sun's gravity. If the Sun's mass suddenly halved, this balance would be disturbed, causing Earth to move into a more elliptical orbit, potentially increasing the distance between the Earth and the Sun. This change could lead to drastic climatic changes, possibly rendering Earth uninhabitable.
Moreover, the period of Earth's revolution around the Sun would increase as the orbital distance becomes greater. The loss of the Sun's mass would mean a decreased gravitational pull, extending Earth's orbital period, thus, Earth would take longer to complete one revolution around the Sun.