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# Physics Homework Help?

(a) What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 187 km?

Answer in m/s

(b) What is the period of revolution?

Answer in min

### 1 Answer

- RichardLv 79 years agoFavorite Answer
Mean radius of the earth = 6371 km (from Wikipedia)

Acceleration due to gravity at the earth's surface

= 9.81 m/s^2 (from Wikipedia)

ma = F = G * m * E / r^2

E stands for the mass of the earth

a = K / r^2 where K is simply a calculation constant

K = 9.81 * (6371 * 10^3)^2

Orbital radius of the satellite = 6371 + 187 = 6558 km

Gravitational acceleration at the satellite's altitude

= 9.81 * (6371 / 6558)^2 = 9.2585 m/s^2

= w^2 * r = 6558 * 10^3 * w^2

w = root(9.2585 / (6558 * 10^3)) rad/s

= 0.00118819 rad/s

a)

Orbital speed

= 0.00118819 * 6558 * 10^3 = 7792.134 m/s

b)

Period of revolution

= 2 * pi / (0.00118819 * 60) = 88.604 min