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Answer :
This will give you the force of gravity acting on the rocket at a height of 4000 miles above the Earth's surface.
we need to consider the gravitational force acting on it. The weight of an object is given by the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity.
Given that the rocket has a mass of 10 metric tons, we can convert this to kilograms by multiplying it by 1000, as there are 1000 kilograms in a metric ton. So the mass of the rocket is 10,000 kilograms.
The acceleration due to gravity can be approximated as 9.8 m/s^2.
To find the weight of the rocket, we can substitute the values into the formula:
W = mg
W = 10,000 kg * 9.8 m/s^2
W = 98,000 N
Therefore, the weight of the 10 metric ton rocket is 98,000 Newtons.
Using this weight, we can calculate the force of gravity acting on the rocket when it is 4000 miles above the surface of the Earth. However, to do this, we need to convert miles to meters.
1 mile is approximately equal to 1609.34 meters. So, 4000 miles is equal to 4000 * 1609.34 meters.
Using the formula for the force of gravity, F = G * (m1 * m2) / r^2, 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 the centers of the two objects, we can calculate the force of gravity.
Substituting the values into the formula:
F = (6.67430 * 10^-11 N m^2/kg^2) * ((5.972 * 10^24 kg) * (10,000 kg)) / (4000 * 1609.34 meters)^2
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