Gravitational Fields and Density.

In summary, the conversation discusses calculating the density of a planet based on its diameter and the parameters of one of its satellites. After converting the values to meters and using the equation GMm/r^2 = mw^2r, there were errors in the calculation process such as adding the radii, using the angular frequency instead of the period, and not cubing the value for the volume. The correct calculation should use the period, ω = 2π/T, and the volume formula (4/3)πr^3.
  • #1
FlyingSpartan
5
0

Homework Statement


If a planet has a diameter of 6*103km and, one of it's satellites is in a circular orbit of radius 9.0*103km with a time period of 8.0 hours.
What is the density of the planet?

Homework Equations


ρ=m/v - density v=4/3 *∏*r2
GMm/r2 = mw2r

The Attempt at a Solution


Firstly convert the Km into M,
Diameter of planet = 6*106 → 3*103
Radius of Satellite = 9.3*106
Time period = 28800s

Where G = 6.7*10-11

Therefore I used

GMm/r2 = mw2rAnd subbing in the values;(6.7*10-11)Mm/(9.3*106+3*106)=m.288002(9.3*106+3*106)So I canceled out the little m and rearranged the equation for M,Giving M an answer as 1.87*1033

I then subbed it into the equation for Density,1.87*1033/4/3*∏(3*106) which gives me an answer of 4.96*1019,

However the given answer is 4.6*103, Any guidance would be appreciated ;D.
 
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  • #2
FlyingSpartan said:
Therefore I used

GMm/r2 = mw2r
OK.
And subbing in the values;


(6.7*10-11)Mm/(9.3*106+3*106)=m.288002(9.3*106+3*106)
(1) Why did you add the radii?
(2) ω is the angular frequency, not the period.
(3) On the left side, that radius must be squared.
 
  • #3
volume is (4/3)πr^3 you have written (4/3)πr^2 and you have not cubed the value in your calculation
Also ω = 2π/T and you have used T as pointed out by Doc Al
 
Last edited:

1. What is a gravitational field?

A gravitational field is the region around a massive object where other objects experience a force due to the object's gravitational pull. This force is what causes objects to fall towards the surface of the Earth.

2. How is the strength of a gravitational field determined?

The strength of a gravitational field is determined by the mass of the object creating the field. The larger the mass, the stronger the gravitational field.

3. What is the relationship between density and gravitational fields?

Density is a measure of how much mass is packed into a certain volume. In the case of gravitational fields, the greater the density of an object, the stronger its gravitational field will be. This is because more mass is packed into a smaller space, resulting in a stronger gravitational pull.

4. How does the distance between two objects affect the gravitational field between them?

The strength of a gravitational field decreases as the distance between two objects increases. This is known as the inverse square law, where the force of gravity decreases by a factor of 4 as the distance between two objects doubles.

5. Can gravitational fields be manipulated or controlled?

Currently, there is no known way to manipulate or control gravitational fields. However, scientists are studying the concept of gravitational waves which could potentially lead to new technologies in the future.

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