Hi guys, can someone help me with this question:
The mass of Earth is 6.0*10^24 kg and the amass of the moon is 7.4*10^22 kg. The radius of the earth is 6.4*10^6 metres and the radius of the moon is 1.7*10^6 metres. The orbital radius of the moon around the Earth taken from the centre of the Moon and the centre of the Earth is 3.8*10^8 metres.
1) Calculate the gravitational force acting between the Earth and the moon
2) Calculate to two decimal places how long it takes for the moon to orbit the Earth in days
3) Calculate the orbital speed of the moon around the earth in km/hr
1) Use
, and substitute in the given values.
2)
which means that
. Now you can substitute in the radius of the moons orbit around earth, the gravitational constant and the mass of earth. Remember to use the mass of the body which is being orbited around, not the mass of the body in orbit.
3)
. Now you can substitute in the gravitational constant, the mass of the earth and the radius of the orbit.
So with these sorts of questions, firstly write down all the variables that you are given, and then write down the ones you are trying to find. Then take the circular motion formulas and rearrange them until you find the value you are looking for. Once you've got enough practice, these questions can be done quite quickly as long as you know what value you're looking for and what formula you need to find it.