Mars has a mass of about 6.4 X 10^23 kg, and its moon Phobos has a mass of about 9.6 X 10^15 kg. If the magnitude of the gravitational force between the two bodies is 4.6 X 10^15 N, how far apart are Mars and Phobos?
the answer is r = 9,438,643.97 m
The magnitude of the gravitational force between two objects can be calculated using the formula:
F = G * (m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force
G is the gravitational constant (approximately 6.67 × 10^-11 Nm^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, we know the magnitudes of the gravitational force (F = 4.6 × 10^15 N), the mass of Mars (m1 = 6.4 × 10^23 kg), and the mass of Phobos (m2 = 9.6 × 10^15 kg). We need to find the distance between Mars and Phobos (r).
Rearranging the formula, we can solve for r:
r = sqrt((G * (m1 * m2)) / F)
Substituting the given values:
r = sqrt((6.67 × 10^-11 Nm^2/kg^2 * (6.4 × 10^23 kg * 9.6 × 10^15 kg)) / (4.6 × 10^15 N))
Calculating this equation will give us the distance between Mars and Phobos.
To find the distance between Mars and Phobos, we need to use the gravitational force formula:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force between the two bodies (4.6 X 10^15 N),
G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2),
m1 is the mass of Mars (6.4 X 10^23 kg),
m2 is the mass of Phobos (9.6 X 10^15 kg),
and r is the distance between Mars and Phobos (what we're trying to find).
First, let's rearrange the formula to solve for r:
r = sqrt((G * m1 * m2) / F)
Now, we can plug in the values given:
G = 6.67430 × 10^-11 m^3 kg^-1 s^-2
m1 = 6.4 X 10^23 kg
m2 = 9.6 X 10^15 kg
F = 4.6 X 10^15 N
Substituting these values, we have:
r = sqrt((6.67430 × 10^-11 m^3 kg^-1 s^-2 * 6.4 X 10^23 kg * 9.6 X 10^15 kg) / (4.6 X 10^15 N))
Now, let's calculate the value of r:
r = sqrt((41872.992 x 10^-11 kg^2 m^3 s^-2) / (4.6 x 10^15 N))
Simplifying further:
r = sqrt(9.1046 * 10^-8 m^2)
Taking the square root:
r ≈ 9.5399 * 10^-5 m
Therefore, Mars and Phobos are approximately 9.5399 * 10^-5 meters or 95.399 kilometers apart.
Gravitational force =
G m M/R^2
Look up G (the universal constant of gravity) and solve for R, which is the distance bewteen the centers of Mars and Phobos.