Acomet is first seen at a distance of d astronomical units from the sun and it is traveling with a speed of q times the earth’s speed. show that the orbit of the comet is hyperbolic, parabolic, or elliptic, depending on whether the quantity q 2d is greater than, equal to, or less than 2, respectively
To solve this problem it is necessary to take into account the concepts of Gravitational Force and Kinetic Energy.
The kinetic energy is given by the equation:
La energía gravitacional por,
Where m is the mass, v is the velocity, G the gravitational constant the mass of the earth, m the mass of the sun and d the distance ..
The sum of the energies, we must be a total energy
By the type of orbit we know that
E> 0 is a hyperbolic orbit
E = 0 is a parabolic orbit
E <0 is a closed orbit.
In the case of hyperbolic orbit
The case of the comet is a closed orbit, so,
For parabolic orbit
For the sun and the earth
For elliptical orbit
the answer for apex is the lowest