Extension on my last question about A2 newton's gravitational law?

Question

Hey. I'm stuck on an A2 question. please help me!

''Calculate the gravitational pull of the Earth on each of the following bodies:

1-The Moon

2- Satellite A with mass 100kg at a distance from the Earth's Centre 4.2 x 10^7 m

3- Satellite B mass 80kg at a distance from the Earth's centre 8.0 x 10^6 m''

Useful Data given:

G= 6.67 x 10^ -11 N m^2 kg^ -2

Earth's Mass = 5.07 x 10^ 24 kg

Moon's Mass = 7.34 x 10^ 22 kg

Radius of the moon = 1.64 x 10^ 6 m

Radius of the Earth = 6.37 x 10^ 6m

Earth-Moon distance = 3.8 x 10^ 5 km

Equations that can be used:

g = F/m

F = [(G)(m1)(m2)] / r^2

g = [(G)(M)] / r^2

F = [(G)(M)(m)] / r^2

I'm sorry. i should have been clearer. Ive done the first part. on the second and the third parts, i was wondering if i take away the radius of the earth from the distance of the satellites to the earth's centre. or do i add the radius' for the moon question because (i thought) gravity comes from the centre of the Earth. i donno. thats why i need help.

Answer 1

In each case you want the distance from the centre of the earth to the centre of the other object. So for 2 & 3 you use the distance given. For part 1, you need to add both the moons radius and the earths radius to the diatnce between.

Answer 2

In gravitational problems, you treat the mass of a sphere as if it were localised at the centre of the sphere.

So you need to check out carefully what is meant by "earth-moon distance". if it means distance of centres, that is the number to use.  But since you are given the radius of the moon and the earth, I guess it must mean the surface to surface distance, in which case you need to add on both the earth radius and the moon radius.

Answer 3

Just take the dist to the center of the earth. They ask you "pull of the Earth".... So its between the earth and the object in question, period.  

Answer 4

It depends on what you decide beforehand. i would say the gravitational pull of the moon is negligible compared to the earth's pull on the satellite. Also, with the same predetermined hypothesis, you can view all the objects as dots (infinitesimally small), which means you take entire distance from the center of the earth (radius + distance). Ignore the moon.  

ps. the plural of radius is radii.

double check my answer though.

Answer 5

firstly the pull of the earth on an object on the earth is the same as the earth pulls on the object.

e.g. if i weigh 600 newtons that is a measure of the force acting between me and the earth thus meaning that i pull the earth at a force of 600 newtons in the opposite direction

secondly it will be best to use the equation f = G [(m1*m2)/r^2) where f is the fore acting between those 2 objects due to gravity.

lets do the first object you mentioned the moon.

let m1 be the moons weight in kg [Moon's Mass = 7.34 x 10^ 22 kg]

let m2 be the earths weight in kg [Earth's Mass = 5.07 x 10^ 24 kg]

now we just need the radius... as asked

the radius is the distance from the CENTER of the earth to the CENTER of the moon. SO we need to take both radius' into account when working out the gravitational force acting between the two objects.

so r = [radius of the moon] + [radius of the earth] + [distance between the 2 objects]

Radius of the moon = 1.64 x 10^ 6 m

Radius of the Earth = 6.37 x 10^ 6m

Earth-Moon distance = 3.8 x 10^ 5 km

i don't have a calculator on me at the moment that will deal with scientific notation or massive streams of numbers.

SO add those values up to find the radius then plug the values in to the original equation REMEMBERING that G = 9.8ms^-2

SO DO NOT ASK ME FOR G BECAUSE IT IS A CONSTANT AND NEVER CHANGES - P.S. make a new thread if anyone wants to discuss this rather than messing up this question