Show the acceleration due to gravity at the surface of the moon is about one sixth of that at the surface of the earth
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Answers
Explanation:
Mass of Moon = 7.34 × 10²² kg
Radius of moon = 1737 km = 1.737 × 10⁶ m
a = GM / R²
= (6.67 × 10⁻¹¹ × 7.34 × 10²²) / (1.737 × 10⁶)²
= 1.6 m/s²
We know that acceleration due to Earth’s gravity (g) is 9.8 m/s²
Comparing a and g
a = g/6
hope it helps u!!!!!
Answer:
about one sixth of the gravitational acceleration of 9.8 m/s^2 felt on the earth. And because weight is a force that is found by multiplying mass by gravitational acceleration, things with the same mass weigh a sixth of their earth weight on the moon.
Interestingly, the moon isn't a sixth of the mass of the earth. The moon is actually eighty times less massive than the earth. (Earth’s Mass) (Mass of the Moon) The difference in gravity is smaller than the difference in masses because of the equation that determines the acceleration of gravity for a spherical object:
a = -(G * m) / r^2
Where
a = acceleration from gravity
G = A constant number*
m = mass of the object (earth or moon)
r = distance from the center of mass of the object
The negative sign is there to indicate that the force goes toward the center of mass.
The gravitational acceleration of the moon is only six times smaller than the earth because this equation accounts for how far you are from the center of the object. The moon isn't as large as the earth in diameter, so the r is smaller. Most importantly, that r is squared, which means when it changes, it affects the final value of acceleration more than changing the mass.
Because the gravity equation takes into account how large an object is as well as how much mass it has, the acceleration on the moon is smaller than the earth, but not as small is you might expect from an object far less massive.
*G is the gravitational constant. It is equal to 6.67 * 10 ^-11 m^3 kg^-1 s^-2. It makes the values of meters, seconds, and kilograms work in the equation so the answer is given in some form of those same units.