Answer:
To calculate the weight of an object at different distances from the center of the Earth, we can use the formula for gravitational force:
91 F = \dfrac{G \times m_1 \times m_2}{r^2} 93
Where:
- 40 F 41 is the gravitational force
- 40 G 41 is the gravitational constant (40 6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 41)
- 40 m_1 41 and 40 m_2 41 are the masses of the two objects (in this case, the mass of the object and the mass of the Earth)
- 40 r 41 is the distance between the centers of the two objects
First, we can calculate the mass of the object using the given weight (10 Newtons) at the initial distance (6.4*10^6 meters) from the center of the Earth:
91 F = \dfrac{G \times m_1 \times m_2}{r_1^2} 93
91 10 = \dfrac{(6.674 \times 10^{-11}) \times m_1 \times (5.972 \times 10^{24})}{(6.4 \times 10^6)^2} 93
Solving for 40 m_1 41, we find the mass of the object at the initial distance.
Next, we can use this mass and the new distance (1.28*10^7 meters) to calculate the weight at the new distance using the same formula:
91 F = \dfrac{G \times m_1 \times m_2}{r_2^2} 93
91 F = \dfrac{(6.674 \times 10^{-11}) \times m_1 \times (5.972 \times 10^{24})}{(1.28 \times 10^7)^2} 93
Solving for 40 F 41 gives us the weight of the object at the new distance from the center of the Earth.
