2. Saturn has a radius of about 9.0 earth radii, and a mass 95 times the Earth’s mass. Estimate the gravitational field on the surface of Saturn compared to that on the Earth. Show your work.
Answer:
g= GM/r²
G= 6.67 * 10^-11 Nm²/kg² ME= 5.98 * 10^24 kg RE=6.37* 10^7m Ms=95Me Rs=9.0re
g=(6.67x 10^-11 Nm²/kg² ) (95x5.98x10^24 kg)/ (9.0)(6.37x 10^7m)²
I think this equation is right at end don't know how to solve it though please help
Its right
To solve the equation, you need to plug in the values and calculate the result step by step. Here are the calculations:
1. First, calculate the mass of Saturn (Ms):
Ms = 95 * Me
Ms = 95 * 5.98 * 10^24 kg
Ms = 5.68 * 10^26 kg (rounded to two significant figures)
2. Next, calculate the radius of Saturn (Rs):
Rs = 9.0 * Re
Rs = 9.0 * 6.37 * 10^7 m
Rs = 5.73 * 10^8 m (rounded to two significant figures)
3. Now, substitute the values of G, Ms, and Rs into the equation for gravitational field:
g = (6.67 * 10^-11 Nm²/kg²) * (5.68 * 10^26 kg) / (5.73 * 10^8 m)²
4. Calculate the numerator:
(6.67 * 10^-11 Nm²/kg²) * (5.68 * 10^26 kg) = 3.79 * 10^16 Nm²/kg
5. Calculate the denominator:
(5.73 * 10^8 m)² = 3.28 * 10^17 m²
6. Finally, divide the numerator by the denominator:
g = (3.79 * 10^16 Nm²/kg) / (3.28 * 10^17 m²)
g = 0.115 N/kg (rounded to three significant figures)
The gravitational field on the surface of Saturn is approximately 0.115 times that on Earth.
To estimate the gravitational field on the surface of Saturn compared to that on Earth, you can use the equation you provided:
g = (GM / r^2)
Where:
- G is the gravitational constant (6.67 x 10^-11 Nm²/kg²)
- M is the mass of the celestial body
- r is the radius of the celestial body
You already have the values for G, the Earth's mass (ME), Earth's radius (RE), Saturn's mass (Ms), and Saturn's radius (Rs).
First, let's calculate the gravitational field on Earth's surface:
gE = (6.67 x 10^-11 Nm²/kg²) * (5.98 x 10^24 kg) / (6.37 x 10^7 m)²
Now, let's calculate the gravitational field on Saturn's surface:
gS = (6.67 x 10^-11 Nm²/kg²) * (95 x 5.98 x 10^24 kg) / (9.0 x 6.37 x 10^7 m)²
To solve these equations, follow these steps:
1. Calculate the mass of Saturn:
Ms = 95 * ME
2. Calculate the gravitational field on Earth:
gE = (6.67 x 10^-11 Nm²/kg²) * (ME) / (RE)²
3. Calculate the gravitational field on Saturn:
gS = (6.67 x 10^-11 Nm²/kg²) * (Ms) / (Rs)²
Simply substitute the values you have into the equations, and then calculate the results.