Question

Astronomers have discovered a new comet that’s moving at 53 km/s as it crosses Earth’s orbit. The comet then passes the Sun and heads off into space. Will it ever return? The Sun’s mass is 2 × 1030 kg and the radius of Earth’s orbit is 1.5 × 1011 m.

Answer 1

given
v = 53 km/s
M_sun = 2*10^30 kg
r = 1.5*10^11 m
escape speed at the location of Earth's orbit from the sun gravitational field,

vo = sqrt(G*M_sun/r)

= sqrt(6.67*10^-11*2*10^30/(1.5*10^11))

= 29821 m/s

= 29.821 km/s

clearly the speed of comet(53 km/s) > Escape speed (29.821 km/s)

so, the comet will not return.