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?

v = 4.79 10³ m / s

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

the only real purpose of sputnik 1 was to beat the us into space. we were getting close to launching a useful satellite, explorer 1 - which launched on january 31, 1958. the ussr had to beat that, so they launched sputnik 1 on october 4, 19