Mars has a mass of about 6.45 × 10
23
kg,
and its moon Phobos has a mass of about
9.4 × 10
15
kg.
If the magnitude of the gravitational force
between the two bodies is 4.68 × 10
15
N,
how far apart are Mars and Phobos? The
value of the universal gravitational constant
is 6.673 × 10
−11
N · m2
/kg
2
All you have to do is solve the gravitational attraction equation for R:
F = 4.68 × 10^-15 N = G m*M/R^2
where
G = 6.673 × 10^−11 N·m^2/kg^2
m = Phobos' mass
M = Mars' mass
R^2=G*M*m/F
or,R=(G*M*m/F)^1/2
To find the distance between Mars and Phobos, we can use the formula for the gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two bodies
G is the universal gravitational constant (6.673 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of Mars and Phobos respectively
r is the distance between the two bodies
We can rearrange the formula to solve for the distance, r:
r = sqrt((G * m1 * m2) / F)
Plugging in the given values:
m1 (mass of Mars) = 6.45 × 10^23 kg
m2 (mass of Phobos) = 9.4 × 10^15 kg
F (gravitational force) = 4.68 × 10^15 N
G (universal gravitational constant) = 6.673 × 10^-11 N · m^2/kg^2
Let's calculate the distance:
To find the distance between Mars and Phobos, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where F is the magnitude of the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between them.
Let's plug in the given values into the formula:
F = 4.68 × 10^15 N
G = 6.673 × 10^-11 N · m^2 / kg^2
m1 = mass of Mars = 6.45 × 10^23 kg
m2 = mass of Phobos = 9.4 × 10^15 kg
Now, let's rearrange the formula to solve for the distance (r):
r^2 = G * (m1 * m2) / F
r^2 = (6.673 × 10^-11 N · m^2 / kg^2) * ((6.45 × 10^23 kg) * (9.4 × 10^15 kg) / (4.68 × 10^15 N))
r^2 = (6.673 × 10^-11 N · m^2 / kg^2) * (6.0453 × 10^39 kg^2) / (4.68 × 10^15 N)
r^2 = 9.1583 × 10^13 m^2
Taking the square root of both sides:
r = sqrt(9.1583 × 10^13 m^2)
r ≈ 3.026 × 10^6 m
Therefore, the distance between Mars and Phobos is approximately 3.026 × 10^6 meters.