The force LRO experiences due to moons gravity?

In summary, the Lunar Reconnaissance Orbiter, with a mass of 1850 kg, maps the surface of the moon from an orbital altitude of 50 km. Using the formula for gravitational force, the magnitude and direction of the force it experiences due to the moon's gravity is approximately 2688.478434 N. However, due to the inaccuracy of using the mass of the moon with one significant figure, the answer may differ from the book's answer of 2.83 x 10^3 N.

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?

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??

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

Buzz Bloom
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..

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

1. What exactly is the "force LRO experiences due to moons gravity"?

The force LRO experiences due to moons gravity refers to the gravitational force exerted on the Lunar Reconnaissance Orbiter (LRO) spacecraft by the Earth's moon. This force is responsible for keeping the LRO in orbit around the moon.

2. How is the force LRO experiences due to moons gravity calculated?

The force LRO experiences due to moons gravity can be calculated using Newton's Law of Universal Gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

3. What factors affect the force LRO experiences due to moons gravity?

The force LRO experiences due to moons gravity is affected by the mass of the moon, the mass of the LRO spacecraft, and the distance between them. Additionally, the gravitational force can be influenced by other celestial bodies and their gravitational pull.

4. How does the force LRO experiences due to moons gravity impact the orbit of the spacecraft?

The force LRO experiences due to moons gravity plays a crucial role in maintaining the spacecraft's orbit around the moon. Without this force, the LRO would not be able to stay in a stable orbit and would eventually drift away from the moon.

5. Can the force LRO experiences due to moons gravity be used for any scientific purposes?

Yes, the force LRO experiences due to moons gravity can be used for scientific purposes. By studying the effects of this force on the spacecraft's orbit, scientists can gain a better understanding of the moon's gravitational field and its influence on other objects in space.

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