Question

the sputnik 1 satellite orbited earth (mass=5.98 x 10^24 kg) in a circle of radius 6.96 x 10^6 m. what was its orbital velocity?

Answer 1

7570 m/s

Step-by-step explanation:

take the square root of: 6.67E-11× 5.98E24/6.96E6

Answer 2

v = 4.79 10³ m / s

Step-by-step explanation:

For this exercise we will use the universal law of gravitation and Newton's second law

F = G M m / r²

where G is the gravitational constant, m the mass of the satellite, M the mass of the Earth, r the distance from the center of the planet to the satellite

F = m a

since the satellite has a circular path, the acceleration is centripetal

a = v² / r

we substitute

G M m / r² = m v² / r

G M / r = v²

We calculate

v² = 6.67 10⁻¹¹ 5.98 10²⁴ / 6.96 10⁶

v = √ (22.94 10⁶)

v = 4.79 10³ m / s