Calculate the force of gravity on a spacecraft 12,800 km (2 earth radii) aboce the Earth\'s surface if its mass is 1400 kg.
Ok for this question I first converted to meters for the radius
then applied newtons law
net force radial = m1 a radial = Fg = r^-2 G m1 m2
Fg = (1.28 E 7 m)^-2 (6.67 E -11 kg^-1 m^3 s^-2) (1400 kg) (5.98 E 24 kg)
I\'m getting 3400 N
back of book tells me
1.52 E 3 N
don\'t know were i went wrong
Hmmm. If it is 2 earth radii from the EArth, that means comparing g at the surface of earth (1 earth radi) to "g" at 3 earth radi is 1/9 gsurface
So the gravitaional force field is g=1/9*9.8N/kg
force on spacecraft= mass* 1/9*9.8 N/kg
=1400kg*1.09N/kg=not your answer.
Your error is in r. IT is 2 Eradii above the surface of Earth, so it is 3Earth radi from the center.
but i thought you were suppose to treat the Earth as the a whole object or something...
my book said to think of it as one particle because everything is attracte4d to it no just the center of the plannet like even a person standing on the earth\'s surface has a nearly infinitly small gravitaional force on the object or somehthing and that you were suppose to think of it as the whole plannet as a point particle not just a pull to the center
Nuts to that thinking. One considers planets point particles, and for Newtons laws, one measures distance from the center. Newton himself had to prove this, and invented calculus to prove it. If you add all the force of gravity for each little rock all over the Earth, it acts as if the calculation was done for all the earth mass just at the center. Use the center.
see the section estimating g from Newton's laws..
http://en.wikipedia.org/wiki/Earth%27s_gravity
To calculate the force of gravity on a spacecraft, you need to use Newton's law of universal gravitation. The formula is:
Fg = G * ((m1 * m2) / r^2)
Where:
Fg is the force of gravity
G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2)
m1 and m2 are the masses of two objects involved in the gravitational interaction
r is the distance between the centers of the two objects
In this case, you want to find the force of gravity on a spacecraft positioned 12,800 km above the Earth's surface, which is equivalent to 2 Earth radii.
First, you need to convert the distance from kilometers to meters. Since 1 kilometer is equal to 1000 meters, you can multiply the distance by 1000:
r = 12,800 km * 1000 = 12,800,000 meters
Now you can substitute the values into the formula and solve for Fg:
Fg = (6.67 x 10^-11 N m^2/kg^2) * [(1400 kg) * (5.98 x 10^24 kg)] / (12,800,000)^2
Fg = (6.67 x 10^-11 N m^2/kg^2) * (8.37 x 10^27 kg) / (163,840,000,000 m^2)
Fg ≈ 1.52 x 10^3 N
So, the force of gravity acting on the spacecraft 12,800 km above the Earth's surface is approximately 1.52 x 10^3 N, which matches the answer in the back of the book.