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

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SUMMARY

The gravitational force between Earth and an asteroid can be calculated using the formula Fg = G (m1m2/s²), where G is the universal gravitational constant (6.667 x 10-11 N m²/kg²), m1 is the mass of the asteroid (7.18 x 107 kg), and m2 is the mass of Earth (6.0 x 1024 kg). The distance (s) used in the formula must be the distance between the centers of the two masses, not the distance from the surface. The radius of Earth is 6.3 x 103 km, which must be added to the asteroid's distance from the Earth's surface to find the correct value for s.

PREREQUISITES
  • Understanding of gravitational force and Newton's law of universal gravitation
  • Familiarity with scientific notation and unit conversions
  • Basic algebra skills for manipulating equations
  • Knowledge of mass and distance measurements in physics
NEXT STEPS
  • Calculate gravitational force using the provided masses and distance values
  • Learn about the implications of gravitational attraction in celestial mechanics
  • Explore the concept of gravitational potential energy
  • Investigate how gravitational forces affect asteroid trajectories
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Students studying physics, educators teaching gravitational concepts, and anyone interested in astrophysics and celestial mechanics.

lusterjester
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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?
 
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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
 

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