how much less is the gravity on the lunar surface than on earth?
83.3% (5/6) less than Earth
The gravity on the lunar surface is about 1/6th (16.6%) of the gravity on Earth. To calculate this, we can use Newton's law of universal gravitation and the formula for acceleration due to gravity.
1. Newton's law of universal gravitation states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. The formula is:
F = G * (m1 * m2) / r^2
Where:
- F is the force of gravity
- G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
2. The formula for acceleration due to gravity is:
g = G * M / r^2
Where:
- g is the acceleration due to gravity
- G is the gravitational constant
- M is the mass of the larger object (in this case, Earth)
- r is the radius (distance from the center) of the larger object (Earth)
Now, to calculate the gravity on the lunar surface compared to Earth's gravity, we need to divide the acceleration due to gravity on the Moon by the acceleration due to gravity on Earth.
g_lunar = G * M_lunar / r_lunar^2
g_earth = G * M_earth / r_earth^2
Dividing the two equations, we get:
g_lunar / g_earth = (G * M_lunar / r_lunar^2) / (G * M_earth / r_earth^2)
Simplifying the equation, we find:
g_lunar / g_earth = (M_lunar * r_earth^2) / (M_earth * r_lunar^2)
The mass of the Moon (M_lunar) is approximately 7.34 x 10^22 kg, and the radius of the Moon (r_lunar) is approximately 1.737 x 10^6 meters. The mass of the Earth (M_earth) is approximately 5.972 x 10^24 kg, and the radius of the Earth (r_earth) is approximately 6.371 x 10^6 meters.
Substituting these values into the equation, we can determine that:
g_lunar / g_earth = (7.34 x 10^22 kg * (6.371 x 10^6 meters)^2) / (5.972 x 10^24 kg * (1.737 x 10^6 meters)^2)
Evaluating this equation, we find that the gravity on the lunar surface is approximately 1/6th (16.6%) of the gravity on Earth.