How Do You Calculate Gravitational Force Between Earth and an Asteroid?

[lusterjester]

Homework Statement

We just have learned about Gravitational Attraction. The formula (for those who don't know is Fg = G (m1m2/s Squared)
M meaning Mass
G meaning universital gravity
S meaning distance between

I had to research the mass/radius of the Earth. I was given the mass/radius of an unknown asteroid.

Earth mass = 6.0 * 10 to the 24th Kg
Earth Radius = 6.3 * 10 to the 3rd Km

Unknown Asteroid mass = 7.18 * 10 to the 7th
Radius = 5.00 x 10 to the -1.

We were given this chart to fill out that had the fallowing Catagories within it (i'll give a sample of the first row to give you all an idea).
----------------------------------------------------
Asteroid's Distance from the Earth's Surface
1.00 x 10 to the 3rd

Displacment between their centers (km)

Force of gravitational Attraction (N)
--------------------------------------------------------

Homework Equations

G = 6.667 x 10 to the -11
S squared = Square root of ( G(m1m2)/Fg)

The Attempt at a Solution

Now I know my information looks like this (at least I think it does)

m1 = 7.18 * 10 to the 7th
m2 = 6.0 * 10 to the 24th Kg
s squared = ?
G = 6.667 8 10 to the -11
Fg = ?

I've been totally lost ever since. I know I can't figure something out without having S or Fg all ready found. Any one have an answer for me?

 

[Andrew Mason]

Draw a picture.

In Newton's formula, S is the distance between the centres of mass of the two masses. You are given the distance between the surfaces. What is the distance between their centres? Just plug that into the formula.

AM

 

[ogb p]

I can confirm that the formula for gravitational attraction is indeed Fg = G(m1m2/s^2), where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and s is the distance between their centers.

In order to calculate the force of gravitational attraction between the Earth and the unknown asteroid, we first need to convert the given values for mass and radius into SI units (kilograms and meters). The mass of the asteroid is 7.18 x 10^7 kg and its radius is 5.00 x 10^-1 km, which is equal to 5.00 x 10^2 m. The mass of the Earth is 6.0 x 10^24 kg and its radius is 6.3 x 10^3 km, which is equal to 6.3 x 10^6 m.

Next, we can use the formula s^2 = (G(m1m2))/Fg) to solve for the distance between the two objects. Plugging in the values for G, m1, and m2, we get s^2 = (6.667 x 10^-11 * 7.18 x 10^7 * 6.0 x 10^24)/Fg. We can rearrange this equation to solve for Fg, which is the force of gravitational attraction between the Earth and the asteroid.

Once we have found the value for Fg, we can use it to fill out the chart given in the homework, by plugging in the distance between the Earth and the asteroid (which we calculated above) and the displacement between their centers (which is simply the sum of the Earth's radius and the asteroid's radius). This will give us the force of gravitational attraction for different distances between the two objects.

I hope this helps you to better understand the concept of gravitational attraction and how to apply the formula to solve for unknown values. Keep up the good work in your studies!