15000N on earth
2250N on moon
Moon Radius= 1.74x10^6m
Orbital Height 100km
Total orbit 1.84x10^6m
What is orbital speed?
And how to find, I have been working on this for a while, and keep getting a wrong solution. Answer is 45.7m/s, but I cannot get my work to figure properly.
To calculate the orbital speed, we need to use the formula for the gravitational force. The gravitational force between two objects is given by the equation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, we can assume that the mass of the Moon is negligible compared to the mass of the Earth. So, the gravitational force between the Moon and an object on its surface is given by:
F = (G * m_earth * m_object) / (R_moon)^2
Where:
m_earth is the mass of the Earth,
m_object is the mass of the object (given as 15000 N), and
R_moon is the radius of the Moon (given as 1.74 x 10^6 m).
Now, let's calculate the mass of the object:
F = (G * m_earth * m_object) / (R_moon)^2
15000 N = (6.67430 x 10^-11 N m^2/kg^2) * (5.972 × 10^24 kg * m_object) / (1.74 x 10^6 m)^2
Next, we can rearrange the equation to solve for the mass of the object:
m_object = (15000 N * (1.74 x 10^6 m)^2) / (6.67430 x 10^-11 N m^2/kg^2 * 5.972 × 10^24 kg)
Now, we have the mass of the object, and we can calculate the orbital speed using the equation of centrifugal force:
v = sqrt((G * M) / r)
Where:
v is the orbital speed,
G is the gravitational constant,
M is the mass of the Earth, and
r is the orbital radius (given as 1.84 x 10^6 m).
Substituting the values, we get:
v = sqrt((6.67430 x 10^-11 N m^2/kg^2 * 5.972 × 10^24 kg) / (1.84 x 10^6 m))
Now, we can calculate the orbital speed:
v = sqrt((3.9876 x 10^14 m^3/kg/s^2) / (1.84 x 10^6 m))
v = sqrt(2.1686 x 10^8 m^2/s^2)
v = 1.4725 x 10^4 m/s
Therefore, the orbital speed is approximately 1.4725 x 10^4 m/s.