A rocket has put your spacecraft in a circular orbit around Earth at an altitude of 350 km. Calculate the force due to gravitational between the Earth and the spacecraft in N if the mass of the spacecraft is 2450 kg.
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To calculate the force due to gravity between Earth and the spacecraft, you can use Newton's law of universal gravitation, which is given by the equation:
F = (G * m1 * m2) / r^2
Where:
F is the force of gravity
G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)^2)
m1 is the mass of one object (in this case, the Earth)
m2 is the mass of the other object (in this case, the spacecraft)
r is the distance between the centers of the two objects (in this case, the sum of Earth's radius and the altitude of the spacecraft)
First, we need to calculate the distance between the center of the Earth and the spacecraft. Since the spacecraft is in a circular orbit, its distance from the Earth's center is equal to the sum of Earth's radius and the altitude of the spacecraft:
r = Earth's radius + altitude
r = (6371 km + 350 km) x 1000 m/km (converting km to meters)
r = 6721 km (converting back to km for convenience)
Now we can substitute the values into the equation:
F = (G * m1 * m2) / r^2
F = (6.674 × 10^-11 N(m/kg)^2 * (5.972 × 10^24 kg) * (2450 kg)) / (6721 km)^2
Calculating this equation will give you the force due to gravity between Earth and the spacecraft in Newtons (N).