The force LRO experiences due to moons gravity?

[Rijad Hadzic]

Homework Statement

The Lunar Reconnaissance Orbiter (LRO) with mass m= 1850, maps the surface of the moon from an orbital altitude of 50 km. what are the magnitude and direction of the force the LRO experiences due to the moons gravity?

Homework Equations

Fg = (GMm)/r^2

The Attempt at a Solution

First I started by changing the units to SI
Mass of moon M = .07x10^24 kg
Mass of orbiter m = 1850 kg
Gravitational constant = 6.637 x 10^-11

the radius = (radius of moon + orbital altitude ) = 1.738 x 10^6 (value from my book) + 50,000 =
1788000

Now I just use the formula: F_g = (6.637x10^{-11})(.07x10^24)(1850) / 1788000^2 = 2688.478434 N

but my books answer is 2.83 x 10^3 N

I don't understand what I did wrong as my answer comes from the formula... is there some trick I am missing??

 

[mfb]

You used the mass of Moon with one significant figure. Why do you expect your result to be accurate to more than that?

 

[Rijad Hadzic]

I see what you mean. Does the method I am using right though?

Sucks that my book would give me mass that would give an inaccurate answer..

 

[mfb]

The method is fine.
With a more precise mass for the Moon the answer will get closer to the book's answer.