Mars has a mass of about 6.4*10^23 kg, and it's moon Phobos has a mass of about 9.6*10^15 kg.If the magnitude of the grvitational force between the two bodies is 4.6* 10^15 N, how far apart are Mars and Phobos?
It is simple algebra:
Fg= G M1*M2/distance^2
solve for distance
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 directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The formula is as follows:
F = G * (m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force (4.6 * 10^15 N)
G is the gravitational constant (6.67 * 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects (6.4 * 10^23 kg for Mars, and 9.6 * 10^15 kg for Phobos)
r is the distance between the two objects (unknown)
To find r, we can rearrange the formula as follows:
r = √(G * (m1 * m2) / F)
Now let's plug in the values:
r = √((6.67 * 10^-11 N m^2/kg^2) * (6.4 * 10^23 kg * 9.6 * 10^15 kg) / (4.6 * 10^15 N))
Simplifying the expression:
r = √(4.3657 * 10^39 m^3/kg^2) ≈ 2.09 * 10^19 m
Therefore, the distance between Mars and Phobos is approximately 2.09 * 10^19 meters.