Question

The planet Mercury travels in an elliptical orbit with eccentricity 0.203. Its minimum distance from the Sun is 4.5 x 10^7 km. If the perihelion distance from a planet to the Sun is a(1 - e) and the aphelion distance is a(1 + e), find the maximum distance (in km) from Mercury to the Sun.Pick from the following:1. 7.7 x 10^7 km.2. 6.6 x 10^7 km.3. 6.8 x 10^7 km.

Answer 1

Option C

Explanation:

From the question we are told that:

Eccentricity
`e=0.203`

Minimum distance from the Sun
`d_s= 4.5 x 10^7 km`

Perihelion distance from a planet to the Sun is
`r= a(1 - e)`

Aphelion distance
`r'=a(1 + e)`

Generally the equation for Perihelion distance is mathematically given by

`4.5 * 10^7= a(1 - 0.203)`

`4.5 * 10^7 = 0.797a`

`a = 56.46 * 10^6 km`

Generally the equation for Aperihelion distance is mathematically given by

`r' = a(1 + e)`

`r' = 56.4617 * 10^6 (1 + 0.203)`

`r'=6.8 * 10^7 km`

Option C