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
g=(9.8 * 95/(9)^2
To estimate the gravitational field on the surface of Saturn compared to that on Earth, we can use Newton's law of gravitation.
The gravitational field is a measure of the gravitational force experienced by an object per unit mass. It is given by the equation:
g = G * (M / r^2)
Where:
- g is the gravitational field strength
- G is the universal gravitational constant (approximately 6.674 × 10^-11 Nm^2/kg^2)
- M is the mass of the celestial body
- r is the radius of the celestial body
Let's calculate the gravitational field on the surface of Saturn relative to that on Earth step by step:
1. Determine the radius of Saturn in meters:
The radius of Saturn is given as 9.0 Earth radii.
Earth's radius = 6,371 km = 6,371,000 meters (approximately)
Saturn's radius = 9.0 * Earth's radius = 9.0 * 6,371,000 meters
2. Calculate the mass of Saturn relative to Earth's mass:
Saturn's mass = 95 * Earth's mass
3. Plug the values into the gravitational field equation and compare the results:
g_saturn / g_earth = (G * M_saturn / r_saturn^2) / (G * M_earth / r_earth^2)
The gravitational constant G appears on both sides of the equation, so we can cancel it out:
g_saturn / g_earth = (M_saturn / r_saturn^2) / (M_earth / r_earth^2)
Substitute the values we calculated earlier:
g_saturn / g_earth = ((95 * Earth's mass) / (9.0 * Earth's radius)^2) / Earth's mass / Earth's radius^2
Simplify the expression:
g_saturn / g_earth = (95 * Earth's radius^2) / (9.0 * Earth's radius)^2
Calculate the values:
g_saturn / g_earth = (95 * 6,371,000^2) / (9.0 * 6,371,000)^2
After performing the calculations, you will get the ratio of the gravitational field on the surface of Saturn compared to that on Earth.