Calculate the force of gravity on a spacecraft 19200 km (3 earth radii) above the Earth's surface if its mass is 1600 kg.
Hint: At three earth radii from the surface of the Earth, the gravity force (weight) of the spacecraft will be reduced to
(1/4)^2 = 1/16 of the weight when the spacecraft is at the Earth's surface, since it is 4 times farther from the Earth's center.
(1/16) x M g = ?
g is the value at the Earth's surface, 9.8 m/s^2. M = 1600 kg.
9040
Simply use Newton's law of Universal Gravitation, FG = G*(m1m2)/r^2 where G = 6.67e-11 N*m^2/kg^2
Using this we get (6.67e-11)*((1600kg)(5.98e24kg))/(19200km*1000)^2
which should give you: 1730N of force. The most common mistake to make for this problem is forgetting to convert the distance from km to m.
Correct
To calculate the force of gravity on the spacecraft 19200 km above the Earth's surface, we will use the relationship:
Force of gravity = mass x acceleration due to gravity
First, we need to determine the acceleration due to gravity at the Earth's surface (g). The value for g is given as 9.8 m/s^2.
Next, we will calculate the weight of the spacecraft at the Earth's surface:
Weight = mass x acceleration due to gravity
Weight = 1600 kg x 9.8 m/s^2
Now, we need to find the weight of the spacecraft 19200 km above the Earth's surface. According to the hint provided, the weight (force of gravity) will be reduced to 1/16th of the weight at the Earth's surface.
Weight at 19200 km = (1/16) x Weight at Earth's surface
Weight at 19200 km = (1/16) x (1600 kg x 9.8 m/s^2)
Hence, the force of gravity on the spacecraft 19200 km above the Earth's surface would be:
Force of gravity = (1/16) x (1600 kg x 9.8 m/s^2)