# American artificial planet Pioneer IV

1. Dec 18, 2004

### roger

hi

Im stuck on how to do this question .....can anyone give me any hints :

The American artificial planet Pioneer IV reached its closest approach to the sun 91.7 million mi on march 17 1959.
At aphelion it will be 106.1 million mi from the sun.

What is:
a.) the speed at which it passed perihelion

b.) its sidereal period

thanks

Roger

2. Dec 18, 2004

### futb0l

Use the conservation of mechanical energy equation, remember that capital M is equal to the mass of the sun.

$$E_{total} = \frac{1}{2}mv_p^2 - \frac{mMG}{r} = -\frac{mMG}{2a}$$

a is equal to the semi major axis and 2a is equal to the distance from perihilion + the distance from the aphelion.

The period can be calculated using the following equation:

$$T^2 = \frac{4\pi^2a^3}{MG}$$

;)