Answer to Question #97719 in Mechanics | Relativity for Nic

Question

It takes a certain satellite exactly 1.9 hours to orbit the Earth. Find:
a) the period of the orbit in seconds
b) the orbital radius
c) the centripetal acceleration
d) the angular velocity
e) the orbital velocity
f) the altitude of the satellite above Earth’s surface

Answer 1

a.

$$T=1.9(3600)=6840\ s$$

b.

$$r^3=\frac{GM}{4\pi^2}T^2$$

$$r^3=\frac{(6.76\cdot 10^{-11})(5.97\cdot 10^{24})}{4\pi^2}6840^2$$

$$r=7.82\cdot 10^{6}m$$

c.

$$g=\frac{GM}{r^2}$$

$$g=\frac{(6.76\cdot 10^{-11})(5.97\cdot 10^{24})}{(7.82\cdot 10^{6})^2}=6.60\frac{m}{s^2}$$

d.

$$\omega=\sqrt{\frac{g}{r}}=\sqrt{\frac{6.6}{7.82\cdot 10^{6}}}=0.000919\frac{rad}{s}$$

e.

$$v=\omega r=(0.000919)(7.82\cdot 10^{6})=7190\frac{m}{s}$$

f.

$$h=r-R=7.82\cdot 10^{6}-6.37\cdot 10^{6}=1.45\cdot 10^{6}m$$