Keeping Up With the Steins

Journey to the Center of the Earth (2008) IMDB rating: 4.90 Plot: Based on the Jules Verne Novel and set in the late 1870’s - A Woman (Victoria Pratt) hires an anthropologist/adventurer (Rick Shroder) to track down her husband (Peter Fonda), who has disappeared while searching for an elusive passage to the center of the earth.

Download

Available versions:

DivX Version (Normal Quality), iPod/iPhone Version

Actors: Rick Schroder,Fonda Peter,Grayhm Steven,Dopud Mike,Brewer Jonathan,Baker Simon,Ken Kirzinger,Puckler Damien,Side Richard,Action,Adventure,Drama,Sci-Fi,

Download Full Version>>

How would i solve this physics question?
A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? This point lies on a line between the centers of the earth and the moon. The distance between the earth and the moon is 3.85×10^8m, and the mass of the earth is 81.4 times as great as that of the moon.

---

=================================
According to Newton’s Law of Universal Gravitation,

" The Force(F) of attraction between any two point masses is directly proportional to the product of the masses and inversely proportional to the square of the distance(r) between them. "

So,

F = GmM/r^2 …..(i)

[NOTE:

G = Universal gravitation constant having value about 6.673 x 10^(-11) Newton-(metre)^2 per (kg)^2

M and 'm' = Masses of two bodies exerting gravitational force on each other]

=================================
=================================
=================================

Now coming back to the given questions and being more specific in terms of notations.

g = acceleration due to gravity of the Earth
g" = acceleration due to gravity of the Moon

Let,
M = mass of the moon
.’. 84.1 M = mass of earth

m = mass of spacecraft.

Let, ‘R’ = distance between the earth and the moon
.’. R = 3.85×10^8 metres

Let, the point where the gravitational force exerted by the earth and the moon are equal, be ‘x’ metres away from the earth.

.’. Distance of that point from moon = ‘R-x’ metres

=================================
At the point when forces are equal:

Gravitational force between earth and spacecraft,
F = G (84.1M)m/(x)^2

Gravitational force between moon and spacecraft,
F" = GMm/(R-x)^2

Since gravitational forces are equal, therefore

F = F"

G84.1Mm/(x)^2 = GMm/(R-x)^2

84.1/(x)^2 = 1/(R-x)^2

*Taking square roots*

9.1706/(x) = 1/(R-x)

9.1706 (R - x) = x

(R - x)/x = 1/9.1706

R/x - 1 = 0.109044

R/x = 1.109044

x = R/1.109044

*Put value of R*

x = 3.471*10^8 metres from earth!

=================================
lostFREE
=================================

| Oct 10, 2009

---

force of gravity = Gmm/r^2
m1=earth
m2=moon
m3=spacecraft
x=distance from earth to moon
total force on spacecraft = Gm1m3/r^2-Gm2m3/(x-r)^2
want total force to be 0, so
Gm1m3/r^2=Gm2m3/(x-r)^2
m1/81.4=m2
m1/r^2=m2/(x-r)^2
m1x^2-2m1xr+m1r^2=m1/81.4r^2
(402m1/407)r^2-2m1xr+m1x^2=0
quadratic formula to solve for r
a=402m1/407
b=-2m1x
c=m1x^2
x=(-b+-sqrt(b^2-4ac))/(2a)
you can plug stuff in.
mass of earth is 5.9742 ? 10^24 kilograms

make it a good day
climberguy12 | Oct 10, 2009