Question

Question 6 of 32

For a satellite to orbit Earth at a constant distance, its
centripetal acceleration must be equal to Earth's gravitational
acceleration. If a satellite is to orbit with a constant circular
radius of 9,500,000 m, what is the approximate required
velocity of the satellite? (Recall that Earth has a mass of 5.97
x 1024 kg and G = 6.67 × 10¯ 11 N•m²/kg².)
A. 7128 m/s
B. 6178 m/s
C. 6892 m/s
D. 6474 m/s

Answer 1

The approximate velocity of the satellite, given that the satellite is to orbit with a constant circular radius of 9500000 m, is 6474 m/s (option D)

How to calculate the velocity of the satellite?

Velocity of orbiting object is given by the following formular:

`v = \sqrt{(GM)/(r)}\\\\`

Where

• v is the velocity of object
• M is the mass of the planet
• r is orbiting radius

With the above formula, we can calculate the velocity of the satellite. This is shown below:

• Radius of orbit (r) = 9500000 m
• Mass of earth (M) = 5.97×10²⁴ Kg
• Gravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²
• Velocity of satellite (v) =?

`v = \sqrt{(GM)/(r)}\\\\v = \sqrt{(6.67*\10^(-11)\ *\ 5.97*10^(24))/(9500000)}\\\\v = 6474\ m/s\\\\`

Thus, we can draw our conclusion that the velocity of the satellite is 6474 m/s. The correct answer is option D