Final answer:
To calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface, we can use Newton's law of universal gravitation. The force of Earth's gravity on the spacecraft is approximately 1700 N.
Step-by-step explanation:
To calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface, we can use Newton's law of universal gravitation. According to Newton's law of gravitation, the force of gravity between two objects is given by the equation:
F = G * (m1 * m2) / r²
Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
In this case, the mass of the spacecraft is given as 1650 kg and the distance between the spacecraft and the center of the Earth is 2.00 Earth radii, which is equivalent to 2.00 times the radius of the Earth.
First, we need to find the radius of the Earth. The radius of the Earth is given as 6.38 × 10^6 m. We can multiply this value by 2.00 to find the distance between the spacecraft and the center of the Earth: 2.00 * 6.38 × 10^6 m = 12.76 × 10^6 m.
Now, we can substitute the values into the equation:
F = (6.67 × 10^-11 N*m^2/kg²) * (1650 kg * 5.97 × 10^24 kg) / (12.76 × 10^6 m)²
Simplifying the calculation, we get:
Therefore, the force of Earth's gravity on the spacecraft 2.00 Earth radii above the Earth's surface is approximately 1700 N.