Calculate the force of gravity on a spacecraft 19200 km (3 earth radii) above the Earth's surface if its mass is 1000 kg.
what equation would i use
they gave you 3 earth radii so you really do not have to do it out
1 earth radius out from center
W = m g = 1000(9.81) = 9810 N
3 radius above = 4 radii from center
F = 1/(4)^2 value at surface
=(1/16)(9810)
To calculate the force of gravity on a spacecraft, you can use Newton's law of universal gravitation. This law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The equation you would use is:
F = (G * m1 * m2) / r^2
where:
F is the force of gravity,
G is the gravitational constant (6.67430 x 10^-11 N(m/kg)^2),
m1 is the mass of one object (the spacecraft in this case),
m2 is the mass of the other object (the Earth),
r is the distance between the centers of the two objects.
In this case, the mass of the spacecraft is 1000 kg, and the distance from the Earth's surface is 19200 km (3 Earth radii). Let's convert the distance to meters first.
1 Earth radius is approximately 6,371 km, so 3 Earth radii would be 3 * 6,371 km = 19,113 km.
Converting this to meters, we get:
19,113 km * 1000 m/km = 19,113,000 m
Now, you can plug the values into the equation:
F = (G * m1 * m2) / r^2
F = (6.67430 x 10^-11 N(m/kg)^2) * (1000 kg) * (5.972 x 10^24 kg) / (19,113,000 m)^2
Calculating the force will give you the answer to your question.