A Titan IV rocket has put your spacecraft in a circular orbit around Earth at an altitude of 270 km. Calculate the force due to gravitational attraction between the Earth and the spacecraft in N if the mass of the spacecraft is 2400 kg.
Use Newton's famous gravitational formula: F=G.M.m/r^2
F=[6.67E-11 x 5.97E24 x 2400] /[6,371,000+270,000]^2
F=21,669.28 newtons-gravitational force on the spacecraft at 270 km above Earth's surface.
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Calculate the force due to gravitational attraction between the Earth and the spacecraft in N.
The Earth's radius is 6370 km.
The orbital radius is r = 6370 km + 270 km = 6640 km away.
The mass of the spacecraft is 2400 kg.
The gravitational acceleration g = 9.81 m/s²
The acceleration of gravity is in 270 km altitude a = 9,02875 m / s²
F = m v² / r
F = m a
m v² / r = m a
v² = r a
F = m * r * a / r
F = 2400 kg * 9.02875 m / s²
F = 21669 (kgm/s²)*(Ns²/kgm)
F = 21669 N
v = √(rg) = √(6 640 000 m * 9.02875 m/s²)
v = 7742.797 m / s
The satellite is drawn with 21669 N center of the earth.
The centrifugal force is equal, namely 21669 N.
It flies at a speed of 7742.797 m/s around the earth.
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