Home work help.. What is the gravitational force between the earth and the moon?...?

Question

Assuming the gravitational force between the earth and the moon is balanced by the centripetal force experienced by the moon, what is the moon's orbital speed?

Answer 1

i think you are going to have to figure out the force first... force first... sounds like a Star Wars political ad...

"Listen to Yoda you will"

wait... what was I saying?  oh, yeah... f = m1m2 etc... you can do that, its in your book.  Then using that #, figure out the moon's acceleration around the Earth.  You can do it.

Yes, we can!

Answer 2

1. "what is the gravitational force between the earth and the moon?". okay i'll help on these, but i won't give you the answers. :)

for calculating the gravitational attraction (or force) between two objects, we use our good friend Sir Isaac Newton. his formula for this problem is:

F = G * m(1) * (m2) / r^2

F is the answer. it is the gravitational force between the two objects your comparing ( m(1) and m(2) )

G is the gravitational constant, 6.6726 x 10^-11

m(1) is the mass of one of the objects you comparing. in your case, it could be defined as either the moon or the earth. take your pick! but on m(2), you have to use the other object. it wouldn't make sense if m(1) and m(2) was earth. make sure this is in kg!

m(2) is the mass of the second object. again, make sure its in kg and not pounds or tons!

r is the distance between the two objects. this value should be in meters.

so lets define the variables.

F = ?

G = 6.6726 x 10^-11

m(1) = mass of earth (5.9742 × 10^24 )

m(2) = mass of moon (7.36 × 10^22)

r = distance between moon and earth (402,336,000 meters)

you might want to get a calculator for this.

so lets rewrite the formula, but this time, including the values.

F = .000000000066726 x 5974200000000000000000000 x 73600000000000000000000 / 402336000 ^2

the just calculate! and thats your answer. the force should be labeled with "N" for newtons, the measurment of force. and gravity is a force!

2. for your second question, we use Kepler's third law to calculate the mean (average) orbital period. his formula for this is:

T= √(4π^2 (r^2) / GM

T is the time (?)

r is the mean satelite orbital radius.

G is the gravitational constant (6.6726 x 10^-11)

M is the mass of the planet the moon is orbiting around.

so lets define our variables with values.

T = ?

r = 402,336,000 (the average distance of the moon from the earth)

M = 5974200000000000000000000 kg

so plug in all the values.

T= √4(3.14 ^2) (402336000 ^2) / (.000000000066726* 5974200000000000000000000 )

get a calculator for that one too! hope this helps!