The orbit of a spacecraft about the sun has a perihelion distance of 0.5 AU and an aphelion of 3.5 AU.? What is the spacecraft’s orbital period?

Question

Clara Avalos · Accepted Answer

The period would be about 2.828 years.

The perihelion distance is #d_p=a(1-e)# and the aphelion distance is #d_a=a(1+e)#. Where #a# is the semi-major axis and #e#is the eccentricity of the orbit. Adding the two equations gives #2a=d_p+d_a#. So the semi-major axis of the space craft is #2a=0.5+3.5#. Hence #a=2#AU. Kepler's third law relates the semi-major axis to the orbital period #T^2=a^3#. For the spacecraft #T^2=8#. This gives an orbital period #T=2.828# years.

Asher Cohen · Answer

undefined The spacecraft's orbital period can be calculated using Kepler's third law of planetary motion. The formula is T^2 = (4π^2 * a^3) / (G * M), where T is the orbital period, a is the semi-major axis (which is the average of the perihelion and aphelion distances), G is the gravitational constant, and M is the mass of the sun. Given the perihelion distance (0.5 AU) and aphelion distance (3.5 AU), the semi-major axis is (0.5 + 3.5) / 2 = 2 AU. With the values of G and M, which are constants, you can calculate the orbital period using the formula.