Question

The minor planet (33340) 1998 VG44 makes exactly two orbits of the sun during the time that Neptune makes three orbits. The eccentricity of the orbit of this minor planet is 0.25, and the orbit radius of Neptune is 4.5×1012m. Find the semi-major axis of this minor planet

Answer 1

The time period of the planet is, T= 21 I = 27, GM Here M is the mass of the Sun. The time period of minor planet is TM = and time period of Neptune is Tyb. So we have, t=21m = 3Ty

Solve the equation for r., the semi major axis of minor planet. 2 x 27. V GM = 3 x 27, V GM = (4.5x109 m) = 5.9x102 m Thus, the semi major axis of minor planet is. = 5.9x10 m