Question

The sputnik one satellite orbiting earth mass equals 5.98×10 to the 24th power kilograms in a circle of radius 6.96×10 to the six power meters what was its orbital velocity

Answer 1

Answer:

7572 m/s

Explanation:

The force between two masses separated by a distance r is given as:

$F=G\frac{m_1m_2}{r^2}$

Where F is the attractive force between 2 masses, m1 and m2, r is the distance between the centres of the masses and G is the universal gravitation constant, which is $6.674*10^-11 Nm^2/kg^2$

The mass of the earth ($m_1$) is far greater than the mass of the sputnik ($m_2$). Therefore $m_1m_2=m_1$. The mass of the sputnik is neglected, therefore:

$F=G\frac{m_1}{r^2}=\frac{(6.674*10^{-11})(5.98*10^{24})}{(6.96*10^6)^2} = 8.2389N$

But F is actually centripetal acceleration, a = v²/r

$8.2389 = v^2 / 6.96*10^6\\v=7572m/s$