The moon has a mass of 7.35 E 22 kg and is located 3.84 E 8 meters from the Earth. If Ellen, an earthling, has a mass of 47 kg, what is the gravitational force between Ellen and the moon?
I believe it would look something like this...
Fg = (Gm1m2)/d^2
m1= 7.35
m2 = 47
d^2 = 3.84
Fg = (7.35)(47)/3.84
89.9 N
To calculate the gravitational force between Ellen and the moon, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2),
m1 is the mass of one object (Ellen),
m2 is the mass of the other object (the moon),
and r is the distance between the centers of the two objects.
Let's substitute the values into the formula:
F = (6.67430 × 10^-11 N(m/kg)^2) * (47 kg) * (7.35 E 22 kg) / (3.84 E 8 meters)^2
First, let's simplify the masses:
F = (6.67430 × 10^-11 N(m/kg)^2) * (47 kg) * (7.35 E 22 kg) / (3.84 E 8 meters)^2
= (3.1184715 × 10^10 N(m/kg)^2) * (7.35 E 22 kg) / (3.84 E 8 meters)^2
Next, let's simplify the distance:
F = (3.1184715 × 10^10 N(m/kg)^2) * (7.35 E 22 kg) / (3.84 E 8 meters)^2
= (3.1184715 × 10^10 N(m/kg)^2) * (7.35 E 22 kg) / (1.47456 E 17 meters^2)
Now, let's multiply the masses and divide by the square of the distance:
F = (3.1184715 × 10^10 N(m/kg)^2) * (7.35 E 22 kg) / (1.47456 E 17 meters^2)
= 2.29282582552 × 10^4 N (Newtons)
Therefore, the gravitational force between Ellen and the moon is approximately 2.29282582552 × 10^4 N (Newtons).
To calculate the gravitational force between Ellen and the moon, we can use the equation for gravitational force:
F = (G * m1 * m2) / d^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^−1⋅s^−2),
m1 and m2 are the masses of the two objects (Ellen and the moon),
d is the distance between the centers of the two objects.
In this case, m1 is the mass of Ellen (47 kg), m2 is the mass of the moon (7.35 × 10^22 kg), and d is the distance between the Earth and the moon (3.84 × 10^8 meters).
Plugging in the values, we get:
F = (6.67430 × 10^-11 * 47 * 7.35 × 10^22) / (3.84 × 10^8)^2
Now, let's calculate the gravitational force using these values:
F = (6.67430 × 10^-11 * 47 * 7.35 × 10^22) / (3.84 × 10^8)^2
= (3.17402 × 10^12) / (1.475136 × 10^17)
≈ 2.15 × 10^(-5) Newtons
Therefore, the gravitational force between Ellen and the moon is approximately 2.15 × 10^(-5) Newtons.
We are assuming that Ellen is on earth?
In that case
F = G Mellen Mmoon /d^2
= (6.67*10^-11)(47)(7.35*10^22)/(3.84*10^8)^2