Question

Halley's Comet revolves around the sun for a time period of 76 years. The aphelion distance if perihelion is given by 8.9 × 10¹⁰ m, will be ______.

(Take, the mass of sun = 2 × 10³⁰ kg and G = 6.67 × 10^-11 Nm³/kg²)

Options

• 4.7 × 10¹¹ m

• 3.23 × 10¹² m

• 5.3 × 10¹² m

• 7.63 × 10¹¹ m

Answer 1

Halley's Comet revolves around the sun for a time period of 76 years. The aphelion distance if perihelion is given by 8.9 × 10¹⁰ m, will be 5.3 × 10¹² m.

Explanation:

According to Kepler's third law, the time period

`T^2 = (4pi^2)/(GM)a^3`

where a is the semi-major axis.

⇒ `a = [(76 xx 86400 xx 365 xx 6.67 xx 2 xx 10^30)/(4 xx 3.14 xx 3.14)]^{1"/"3}`

= 2.7 × 10¹² m

Also in the case of the ellipse, 2a = perihelion + aphelion

⇒ Aphelion = 2a - perihelion

= `2 xx 2.7 xx 10^12 - 8.9 xx 10^10 ≈ 5.3 xx 10^12` m