Answer:
W= 61.3 N
Explanation:
The only force acting on the satellite is the one due to the attraction from Earth, which obeys the Newton's Universal Law of Gravitation, as follows:
Fg =G*ms*me / (res)²
This force, also obeys the Newton's 2nd Law, so we can write the following equation:
G*ms*me*/ (res)² = ms* a = ms*g
We call to the product of the mass times the acceleration caused by gravity (g), the weight of this mass, so we can write as follows:
G*ms*me / (res)² = ms*g = W (1)
where G = 6.67*10⁻11 N*m²/kg², ms= 100 kg, me= 5.97*10²⁴ kg, and
res= 4 *re = 4*6.37*10⁶ m.
Replacing all these known values in (1), we get the value of W:
W =(( 6.67*5.97/(4*6.37)²) *( 10⁻¹¹ * 10²⁴ /10¹²) )* 100 N = 61.3 N
The satellite's weight at the altitude of its orbit is;
61.31 N
Formula for gravitational force is;
F = GMm/R²
Where;
G is gravitational constant = 6.67 × 10⁻¹¹ N.m²/kg²
m is mass of earth = 5.97 × 10²⁴ kg
M is mass of satellite = 100 kg
Now, we are told that the altitude is 3R above the Earth's surface.
At the Earth's surface, the distance from the Earth's center is R where R is radius of earth.
Thus, total altitude from the Earth's center to the satellite it (3R + R) = 4R
Thus;
F = GMm/(4R)²
Where R is radius of earth = 6371 × 10⁶ m
Thus;
F = (6.67 × 10⁻¹¹ × 100 × 5.97 × 10²⁴)/(4 × 6371 × 10⁶)
F = 61.31 N
Now, from Newton's second law of motion, we know that the force is equal to the weight.
Thus;
Weight = 61.31 N
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