Two theory questions involving Earth/Moon. Should be easy for you guys.

[DLxX]

I need help with the following questions because I don't fully understand the theory behind these questions.

1. If the Earth's mass were double what it is, in what ways would the Moon's orbit be different?

2.Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?

 

[quasar987]

2.Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?

I'm certain you can figure that out yourself. The answer to the first question will be obtained in comparing the equation of the gravitationnal force exerted on both object (on by the other). The answer to the second question follows from comparing the accelerations given by F = ma applied to both objects

$$\vec{F}_{earth \rightarrow moon} = m_{moon}\vec{a}_{moon}$$

and

$$\vec{F}_{moon \rightarrow Earth } = m_{earth}\vec{a}_{earth}$$

after you've found the relationship between these two forces.

Hint: ask yourself "what would be 'a' if the moon and the Earth had the same mass"? And what about if the mass of the moon is smaller than that of the earth?

 

[quasar987]

After thinking about it for 30 minutes, I think, I think, that if the mass of the Earth were to sudently double, the moons orbit would gradually drop to an orbit of radius twice as small. I have considered the moon's orbit as circular.

(I am bothered by the radial part of the acceleration in polar coordinates...

$$a_r=\ddot{r}-r\dot{\theta}^2$$

How do you read that?! "The radial component of acceleration equals the radial acceleration minus the centripetal acceleration" ?! That doesn't sound right!)

 

[cepheid]

quasar...

What you have written looks like the magnitude of the entire acceleration to me, not just the radial component. Are you sure it was a _r, and not simply a?

By the way...I have no idea what would happen to the moon's orbit if the Earth's mass suddenly doubled.

DlxX: Another way of thinking about question 2 is to consider two of Newton's three laws...which the equation that quasar told you to consider definitely satisfy. Quasar already wrote out Newton's 2nd law to answer the second part of 2. But do you know which of his laws that I am hinting at immediatly states the answer to the first part of 2?

 

[vincentchan]

if the mass of the Earth were to sudently double,the moons orbit would gradually drop to an orbit of radius twice as small. I have considered the moon's orbit as circular.

WRONG...use conservation of energy... the orbit of the moon will become an ellipse...

edit: and conservation of angular momentum