Question

As Halley’s comet orbits the sun, its distance from the sun changes dramatically. If the comet’s speed at a distance of 9.8 × 1010 m from the sun is 5.3 × 104 m/s and angular momentum is conserved, what is its speed when it is 3.6 × 1012 m from the sun? Assume the comet can be treated as a point mass. Ignore radial components of momentum

Answer 1

Answer:

The speed of comet is 1442.77 m/s.

Explanation:

Given that,

Speed of comet's $v_{c}= 5.3\times10^{4}\ m/s$

Distance from the sun $r_{d}=9.8\times10^{10}\ m$

Distance $r_{far}=3.6\times10^{12}\ m$

We need to calculate the speed of comet

Using conservation of angular momentum

$L_{f}=L_{i}$

$I\omega=I\omega$

Here. $v = r\omega$

$\omega=\dfrac{v}{r}$

$mr_{far}^2\times\dfrac{v_{far}}{r_{far}}=mr_{d}^2\times\dfrac{v_{d}}{r_{d}}$

$r_{far}\times v_{far}=r_{d}\times v_{d}$

Put the value into the formula

$3.6\times10^{12}\times v_{far}=9.8\times10^{10}\times5.3\times10^{4}$

$v_{far}=\dfrac{9.8\times10^{10}\times5.3\times10^{4}}{3.6\times10^{12}}$

$v_{far}=1442.77\ m/s$

Hence, The speed of comet is 1442.77 m/s.