Answers to "Challenge" Page


All information to solve these problems can be found on the site for the Universal Law of gravity, and on the "Earth in Orbit" page of the Web Quest.

1.  What is the force of gravity (Fg) of the Sun on the Earth?
Formula: Fg = (G(mass1)(mass2)) / Distance^2
G is a constant, it always equals 6.627 x 10^-11 m^3/kgsec^2
mass1 = the Sun's mass 1.99 x 10^30 kg
mass2 = the Earth's mass 5.97 x 10^24 kg
Distance of Earth from Sun = 15 x 10^7 km
so Fg = ((6.627 x 10^-11)(1.99 x 10^30)(5.97 x 10^24)) / (15 x 10^7)^2
plug into graphing calculator
Fg = 3.52 x 10^28 m^3/kgsec^2

2. Fg of Earth on the Moon?
Earth's mass 5.97 x 10^24 kg
Moon's mass = 7.35 x 10^22kg
Distance = 384 km
so Fg = ((6.627 x 10^-11)(5.97 x 10^24)(5.97 x 10^24)) / 384^2
Fg = 1.99 x 10^32

3.  The student must determine their weight in kg.  (e.g. 125lbs equals 56.625kg or 125 x .453)
Mass of boulder = 4.3 x 10^5
Distance = 5 km
so Fg = ((6.627 x 10^-11)(4.3 x 10^5)(student mass)) /5^2
answers will vary

4.   Solve for D. 
5.06 x 10^-10 = ((6.627 x 10^-11)(70.8)(56.625) / D^2
5.06 x 10^-10 = (2.67 x 10^-7) / D^2
Undo the division by multiplying D^2 on both sides.  You now have D^2(5.06 x 10^-10) = (2.67 x 10^-7).  Divide by 5.06 x 10^-10 on both sides. So D^2 = 527.67.  Find the square root.  D = 22.97km.

5.  Earth's Fg on Asteroid?
Fg = ((6.627 x 10^-11)(4.03 x 10^13)(5.97 x 10^24)) / 1673^2
Fg = 5.739 x 10^21
to determine if the asteroid will collide with the Earth or with the Moon, you must determine the Moon's Fg on the asteroid.  The distance must also be found in order to solve the equation.  Since you know the asteroid is 1673km away from the Earth, and the Moon is 384 km away from the Earth, 1673-384 = 1289km, or the distance the asteroid is from the Moon.  Now you can solve the equation to find the Fg.
use the moon's mass and the asteroid's mass, so Fg of the Moon on the asteroid is Fg = ((6.627 x 10^-11)(4.03 x 10^13)(7.35 x 10^22)) / 1289^2. Fg =  1.189 x 10^20.  Compare the two Fg's.  Earth's pull is stronger so the asteroid will collide with Earth.  But, will the Earth survive?  Just compare the two masses:  Earth's mass = 5.97 x 10^24 kg  and the asteroid's mass = 4.03 x 10^13kg.  Subtract the asteroid from the Earth to see the difference in size of 5.97 x 10^24!  In other words, the difference is so small that the asteroid wouldn't even dent the Earth.  Its like a speck of dust compared to the size of Earth.

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