# Help Finding Velocity Needed for Object in Moon's Orbit

• jeffreydim
In summary, the conversation discusses finding the velocity required to keep an object in the moon's orbit. The formula for acceleration and force is mentioned, but the object's mass is not given. The conversation hints at setting the expressions equal to each other and canceling out the mass to find the velocity. It is also mentioned that the object's mass does not affect its ability to remain in orbit, as demonstrated by Galileo. The idea of escape velocity is briefly mentioned, but it is not necessary for staying in orbit. Instead, circular motion and relevant equations are suggested for finding the required velocity.

#### jeffreydim

hello,
find velocity required to keep an object in moon's orbit? so far, a = velocity squared over radius and force equals g constant times mass 1 times mass 2 over radius squared, but the object's mass is not given and mass of moon can be found, any help?

$$F_g = \frac{GMm}{r^2}$$

But what else is this equal to. What kind of motion is the object in if it is in orbit? You should be able to set the above expression equal to another expression involving m, then the m's should cancel. See how far you can now. Good Luck.

The thing is, it is independent of mass of the object. This is essentially what Galileo demonstrated nearly 400 years ago.

Calculate escape velocity, cancelling the m would result from setting it equal to 1/2*mv^2, now v = sqr(GM/r), and the orbit needs to be less than this. interesting stuff...

Sorry, escape velocity is going a bit too far, literally and figuratively. You do not need to be at escape velocity to remain in orbit, because that is partly what escape velocities are, the object will be able to escape from the gravitaional influnce of the moon.

Try in an orbit, we assume it is in circular motion. Think of what equations you need to apply.