Calculate the force of Earth’s gravity on a spacecraft
2.00 Earth radii above the Earth’s surface if its mass is
1850 kg.
To calculate the force of Earth's gravity on a spacecraft, you can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.673 × 10^-11 N*m^2/kg^2)
m1 is the mass of the spacecraft
m2 is the mass of the Earth
r is the distance between the center of the spacecraft and the center of the Earth
In this case, the mass of the spacecraft is 1850 kg and the distance from the Earth's surface is 2.00 Earth radii.
First, let's calculate the distance from the center of the Earth to the spacecraft:
Earth radius = 6371 km (approximately)
Distance from Earth's surface = 2.00 Earth radii = 2.00 * 6371 km
Next, we need to convert this distance to meters, as the gravitational constant is given in meters:
Distance from Earth's surface = 2.00 * 6371 km * 1000 m/km
Now, we can substitute the values in the formula:
F = (G * m1 * m2) / r^2
F = (6.673 × 10^-11 N*m^2/kg^2 * 1850 kg * m2) / (r^2)
Finally, substitute the values and calculate the force:
F = (6.673 × 10^-11 N*m^2/kg^2 * 1850 kg * (5.972 × 10^24 kg)) / ((2.00 * 6371 km * 1000 m/km)^2)
By evaluating this expression, you can find the force of Earth's gravity on the spacecraft.