Explanation:
It is given that,
Speed of the spacecraft, v = 71 km/s = 71000 m/s
Distance between the spacecraft and the Sun, [tex]d = 4.3\times 10^7\ km = 4.3\times 10^{10}\ m[/tex]
It is required to proof that its orbit about the sun was closed and therefore elliptical. Let v is the speed with which the spacecraft if it is moving in circular path. It is given by :
[tex]v=\sqrt{\dfrac{GM}{r}}[/tex]
M is the mass of the sun, [tex]M=2\times 10^{30}\ kg[/tex]
[tex]v=\sqrt{\dfrac{6.67\times 10^{-11}\times 2\times 10^{30}}{4.3\times 10^{10}}}[/tex]
v = 55698 m/s
or
v = 55.6 km/s
The given velocity is 71 km/s while the calculated value of velocity is 55.6 km/s. It is clear that the path is not circular. It is elliptical. Hence, this is the required solution.
