Mars has a mass of about 6.59 × 1023 kg, and its moon Phobos has a mass of about 9.4 × 1015 kg.
If the magnitude of the gravitational force between the two bodies is 4.35 × 1015 N, how far apart are Mars and Phobos? The value of the universal gravitational constant is 6.673 × 10−11 N · m2/kg2.
Answer in units of m
To find the distance between Mars and Phobos, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
Rearranging the equation, we can solve for the distance r:
r = sqrt((G * m1 * m2) / F)
Now let's substitute the known values:
G = 6.673 × 10^(-11) N · m^2/kg^2
m1 = mass of Mars = 6.59 × 10^23 kg
m2 = mass of Phobos = 9.4 × 10^15 kg
F = 4.35 × 10^15 N
Plugging the values into the equation:
r = sqrt((6.673 × 10^(-11) N · m^2/kg^2 * 6.59 × 10^23 kg * 9.4 × 10^15 kg) / (4.35 × 10^15 N))
Now we can calculate the distance:
r = sqrt((4.1108474 × 10^(-2) m^3/kg^2 * kg * kg) / (1))
Simplifying, we get:
r = sqrt(4.1108474 × 10^(-2) m^3) = 2.028516 × 10^(-1) m
Therefore, the distance between Mars and Phobos is approximately 0.203 m.