Final answer:
To find the weight of the satellite at a distance of 1.28 × 10^7 m from the Earth's surface, we first need to calculate its mass. Using the formula for gravitational force, we can determine the mass of the satellite and then calculate its weight at the given distance. The weight of the satellite is approximately 1.44 × 10^5 N.
Step-by-step explanation:
To calculate the weight of the satellite at a distance of 1.28 × 10^7 m from the surface of the Earth, we need to use the formula for gravitational force:
F = G · (m1 · m2) / r^2
Where F is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 N · (m/kg)^2), m1 is the mass of the Earth, m2 is the mass of the satellite, and r is the distance between the Earth's center and the satellite.
Since we are only given the weight of the satellite, we cannot directly use this equation. However, weight is equal to the gravitational force acting on an object, so we can say that the weight of the satellite on the Earth's surface is equal to the gravitational force between the satellite and the Earth's surface. Therefore, we can write:
F = G · (m1 · m2) / r^2 = W
Where W is the weight of the satellite and m1 is the mass of the Earth.
Now, we can use this equation to find the mass of the satellite:
m2 = (W · r^2) / (G · m1)
Substituting the given values, we have:
m2 = (2000 N · (1.28 × 10^7 m)^2) / (6.67430 × 10^-11 N · (m/kg)^2 · m1)
The mass of the Earth, m1, is approximately 5.972 × 10^24 kg. Plugging this value into the equation, we can calculate the mass of the satellite:
m2 = (2000 N · (1.28 × 10^7 m)^2) / (6.67430 × 10^-11 N · (m/kg)^2 · 5.972 × 10^24 kg)
Calculating this gives us m2 ≈ 1.47 × 10^4 kg.
Finally, we can calculate the weight of the satellite at the given distance:
Weight = m2 · g
Where g is the acceleration due to gravity at the given distance from the Earth's surface. Substitute the values and calculate:
Weight = (1.47 × 10^4 kg) · 9.8 m/s²
Weight ≈ 1.44 × 10^5 N
Therefore, the weight of the satellite when it is at a distance of 1.28 × 10^7 m from the surface of the Earth is approximately 1.44 × 10^5 N.