The diameter of the planet saturn is 10 times that of the earth but the mass of the planet is only 90 times greater than that of the earth.what isthe gravitational acceleration(or number of 'gs'you"ll feel)on saturn?
https://answers.yahoo.com/question/index?qid=20071224043314AAHPCut
To calculate the gravitational acceleration (or "g") on Saturn, we can use the formula:
g = G * (M / r^2)
Where:
- g represents the gravitational acceleration
- G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
- M is the mass of Saturn
- r is the radius of Saturn
Given that the diameter of Saturn is 10 times that of Earth, we can deduce that the radius of Saturn (rs) is 5 times that of Earth (re).
Since the mass of Saturn (Ms) is only 90 times greater than that of Earth (Me), we can express it as:
Ms = 90 * Me
Now, we need the mass of Earth (Me) and its mean radius (re), which are approximately:
- Me = 5.972 × 10^24 kg
- re = 6,371 km = 6.371 × 10^6 m
Since the radius of Saturn is 5 times that of Earth:
rs = 5 * re
Now we can calculate the gravitational acceleration on Saturn (gs):
gs = G * (Ms / rs^2)
Substituting the values and performing the calculations:
gs = 6.67430 x 10^-11 m^3 kg^-1 s^-2 * (90 * 5.972 × 10^24 kg) / ((5 * 6.371 × 10^6 m)^2)
gs ≈ 10.4383 m/s^2
Therefore, the gravitational acceleration (or number of "gs" you'll feel) on Saturn is approximately 10.44 m/s^2.
To calculate the gravitational acceleration on Saturn, we will use the formula for gravitational acceleration:
acceleration = G * (mass of Saturn) / (radius of Saturn)^2
Given that the diameter of Saturn is 10 times that of the Earth, we can find the radius of Saturn by dividing its diameter by 2. The radius of the Earth (rE) will be used for comparison.
Let's assume the radius of the Earth (rE) is 1 unit, so the diameter of the Earth (dE) will be 2 units.
radius of Saturn (rS) = (diameter of Saturn) / 2 = 10 * rE / 2 = 5 * rE
Next, we need to find the mass of Saturn (mS) in terms of Earth's mass (mE). Given that the mass of Saturn is only 90 times greater than that of the Earth:
mass of Saturn (mS) = 90 * mE
Now we have all the necessary information to calculate the gravitational acceleration on Saturn.
acceleration = G * (mass of Saturn) / (radius of Saturn)^2
Before we go further, however, let me explain a few details. The gravitational constant (G) is approximately 6.67 x 10^-11 N(m/kg)^2. For ease of calculation, we'll use the value 6.67 x 10^-11.
Substituting the values:
acceleration = (6.67 x 10^-11) * (90 * mE) / (5 * rE)^2
acceleration = (6.67 x 10^-11 * 90 * mE) / (25 * rE^2)
Now, let's compare this acceleration with the acceleration experienced on Earth, which is approximately 9.8 m/s^2.
To find the number of "gs" felt on Saturn, divide the calculated acceleration by the acceleration due to gravity on Earth:
gs = acceleration / (9.8 m/s^2)
Substituting the values found earlier:
gs = (6.67 x 10^-11 * 90 * mE) / (25 * rE^2 * 9.8)
Please note that the units of mass and radius are omitted in the final result because they cancel out during the calculation.
By plugging in the appropriate values for mE and rE, you can calculate the gravitational acceleration on Saturn and determine the number of "gs" you would feel on the planet.