Question

The Helios B spacecraft had a speed of 71 km/s when it was

4.3km from the sun.
Prove that its orbit about the sun was closed
andtherefore eliptical.

Answer 1

Step-by-step explanation:

It is given that,

Speed of the spacecraft, v = 71 km/s = 71000 m/s

Distance between the spacecraft and the Sun,
`d = 4.3* 10^7\ km = 4.3* 10^(10)\ m`

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 :

`v=\sqrt{(GM)/(r)}`

M is the mass of the sun,
`M=2* 10^(30)\ kg`

`v=\sqrt{(6.67* 10^(-11)* 2* 10^(30))/(4.3* 10^(10))}`

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.