Question

If the masa of the sun deacreases gravity is earth moving away from sun beacause of deacreases in the gravity of sun

Answer 1

If the mass of the sun decreases gravity is earth moving away from sun because of decreases in the gravity of sun?

Solution

Let the initial mass of the sun is $M$ . The initial orbit of Earth is very similar to circle with radius $R$ , the initial velocity of Earth around the Sun is $v$ .

Let the mass of the sun after decreases of mass is $M'$ . If $v < v_{\text{escape}} = \sqrt{\frac{2GM'}{R}}$ , $v_{\text{escape}}$ is new escape velocity in distance $R$ from Earth, the new orbit of Earth will be ellipse with semi-major axis greater than $R$ . If $v = v_{\text{escape}} = \sqrt{\frac{2GM'}{R}}$ , the new orbit of Earth will be parabolic, Earth will move away to infinity. If $v > v_{\text{escape}} = \sqrt{\frac{2GM'}{R}}$ , the new orbit of Earth will be hyperbolic, Earth will move away from to infinity too.

Fig-1: Types of paths