Need help with Gravitational Field Strength question

[ultimatesoulx]

Homework Statement

A satellite orbites Earth at a distance of 3rEARTH, above Earth's surface. What is the magnitude of gravitational field strength at the point where the satellite is?

Homework Equations

Fg= Gm1m2/d^2 (m1=mass 1, m2=mass2)
F1/F2 = D2^2/D2^2 (D1 is a variable, and so is D2, so it represents Distance 1 and Distance 2)

The Attempt at a Solution

I don't understand how it works? You have the equation for the radius of Earth, 6400km, but not much else other than the G which is 6.67x10^-11. I'm not sure how to tackle this, and it's confusing me a lot. I tried applying Fg= Gm1m2/d^2, but there is no mass on them.P.s on a secondary note, if I am doing a question where it compares 2 masses that have an attraction (i.e 36N, how do you find the distances/mass?)

 

[ehild]

Homework Statement

A satellite orbites Earth at a distance of 3rEARTH, above Earth's surface. What is the magnitude of gravitational field strength at the point where the satellite is?

Homework Equations

Fg= Gm1m2/d^2 (m1=mass 1, m2=mass2)
F1/F2 = D2^2/D2^2 (D1 is a variable, and so is D2, so it represents Distance 1 and Distance 2)

The Attempt at a Solution

I don't understand how it works? You have the equation for the radius of Earth, 6400km, but not much else other than the G which is 6.67x10^-11. I'm not sure how to tackle this, and it's confusing me a lot. I tried applying Fg= Gm1m2/d^2, but there is no mass on them.


P.s on a secondary note, if I am doing a question where it compares 2 masses that have an attraction (i.e 36N, how do you find the distances/mass?)

The gravitational attraction between masses m₁ and m₂, d distance apart, is F=Gm₁m₂/d². If the objects are spheres d means the distance between their centres.

The gravitational field strength means the force of gravity exerted on unit mass. At the surface of the Earth it is g=9.8 m/s²:

9.8=GM(Earth)/R², where R is the radius of the Earth.

The gravitational field strength at distance d from the centre of Earth is g'=GM(Earth) /d².
If you divide the equations in bold you get

g'/9.8=R²/d².

The satellite is 3R above the surface of Earth. How far is it from the centre of Earth?

ehild

 

[voko]

The gravity of the Earth at some distance is inversely proportional to the square of the distance from its center. At the surface, this is g. That, and the distance of the satellite from the Earth, should be enough.

 

[ultimatesoulx]

I understand the question now, thanks for the help!

 

[Nickie]

Hi there,

Thank you for reaching out for help with your gravitational field strength question. I can understand how this topic can be confusing, but let me try to explain it to you in a simpler way.

First, let's start with the equation you mentioned: Fg= Gm1m2/d^2. This is the equation for the gravitational force between two objects, where G is the universal gravitational constant (6.67x10^-11), m1 and m2 are the masses of the two objects, and d is the distance between them.

In this case, we are dealing with a satellite orbiting Earth at a distance of 3rEARTH, which is three times the radius of Earth. So, we can rewrite the equation as follows:

Fg= GmEARTHmsatellite/(3rEARTH)^2

Where mEARTH is the mass of Earth and msatellite is the mass of the satellite. Now, since we are only interested in the magnitude of the gravitational field strength, we can simplify this equation further by dividing both sides by msatellite:

Fg/msatellite= GmEARTH/(3rEARTH)^2

Now, let's plug in the values for G (6.67x10^-11) and the radius of Earth (6400km) to get:

Fg/msatellite= (6.67x10^-11)(5.97x10^24kg)/(3(6400km))^2

Note: I converted the mass of Earth from kg to g (5.97x10^24kg = 5.97x10^27g) so that the units will match.

Now, we can solve for the magnitude of the gravitational field strength (Fg/msatellite):

Fg/msatellite= 0.0098 N/kg

Therefore, the magnitude of the gravitational field strength at the point where the satellite is orbiting is 0.0098 N/kg. This means that for every kilogram of mass on the satellite, there is a gravitational force of 0.0098 Newtons pulling it towards the center of Earth.

I hope this explanation helps you understand the concept of gravitational field strength better. As for your secondary question, if you are given a gravitational force (e.g. 36N) and you want to find the distance/mass, you will need to rearrange the equation Fg= Gm