Gravity on Titan Titan is the largest moon of Saturn and the only moon in the solar system known to have a substantial atmosphere.
Find the acceleration due to gravity on Titan's surface, given that its mass is 1.35 X 10^23 kg and its radius is 2570 km.
Well, if Titan is the largest moon, it must have a pretty heavy "moon belly." Now, to calculate the acceleration due to gravity on Titan's surface, we need to remember Newton's Law of Universal Gravitation.
According to the law, the gravitational force between two objects is given by the equation F = (G * m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Now, we want to find the acceleration due to gravity on Titan's surface, which is given by the equation a = G * M / r^2, where M is the mass of Titan and r is its radius.
So, plugging in the values, we have a = (G * M) / r^2, where G is approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2, M is 1.35 × 10^23 kg, and r is 2,570,000 meters.
Now, let's put those numbers in a blender and mix them up. *Whirr* *Whirr* *Whirr*
The acceleration due to gravity on Titan's surface is approximately 1.35 m/s^2. So, it looks like things can get a little heavy on Titan, but not too heavy to make you float away into space!
Remember, though, that this is just an approximation, and there might be some additional factors to consider. But for now, let's just say that Titan has enough gravity to keep you grounded, so you won't be moonwalking anytime soon.
To find the acceleration due to gravity on Titan's surface, we can use the formula for the acceleration due to gravity:
a = (G * M) / r^2
where:
a = acceleration due to gravity
G = gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
M = mass of Titan (1.35 × 10^23 kg)
r = radius of Titan (2570 km, which we'll convert to meters by multiplying by 1000)
Let's calculate:
M = 1.35 × 10^23 kg
r = 2570 km = 2570 × 1000 m = 2.57 × 10^6 m
Substituting the values into the formula:
a = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1.35 × 10^23 kg) / (2.57 × 10^6 m)^2
Simplifying:
a = (8.9992405 × 10^11 m^3 kg^-1 s^-2) / (6.6049 × 10^12 m^2)
a = 0.136 m/s^2
Therefore, the acceleration due to gravity on Titan's surface is approximately 0.136 m/s^2.
To calculate the acceleration due to gravity on Titan's surface, you can use the formula for gravitational acceleration:
g = G * (M / r^2)
Where:
g is the acceleration due to gravity,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of Titan,
and r is the radius of Titan.
Let's substitute the given values into the formula:
M = 1.35 X 10^23 kg
r = 2570 km = 2570000 m
We need to convert the radius from kilometers to meters to ensure the units are consistent.
Now we have all the information we need. Let’s calculate the gravitational acceleration:
g = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1.35 X 10^23 kg) / (2570000 m)^2
First, let's square the radius:
r^2 = (2570000 m)^2 = 6609290000000 m^2
Next, let's calculate the mass divided by the squared radius:
M / r^2 = (1.35 X 10^23 kg) / 6609290000000 m^2 = 2.04696158922 X 10^13 kg/m^2
Finally, let's multiply this value by the gravitational constant:
g ≈ (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (2.04696158922 X 10^13 kg/m^2)
≈ 1.36487144164 m/s^2
Therefore, the acceleration due to gravity on Titan's surface is approximately 1.36 m/s^2.