Question

Help with these question. Please provide clear detailed explanation. Thanks!

Answer 1

Time period of Earth is 1 year. As Halley's comet crosses the Earth every 75 years, Its time period around the Sun is $T=75\,yr$

Time period $T=2\pi\sqrt{\frac{R^3}{GM}}$

Radius of orbit of Halley's comet is $R=\left ( \frac{GM_ST^2}{4\pi^2} \right )^{1/3}$

$R=\left ( \frac{6.67*10^{-11}*(1.99*10^{30})(75*365*24*3600)^2}{4\pi^2} \right )^{1/3}$

$R=26.594*10^{11}\,m$

Radius of comet's orbit is $R=26.594*10^{11}\,m$

b)

The closest the comet gets to Earth is $R-R_E=26.594*10^{11}-1.5*10^{11}=25.094*10^{11}\,m$

c)

Angular speed of comet is $\omega=\frac{2\pi}{T}=\frac{2\pi}{(75*365*24*3600)}=2.657*10^{-9}\,rad/s$

d)

Angular acceleration of comet is zero, since it is moving in a circle with uniform angular velocity.

c)