Question

How big is the moon Titan compared to the earth? How is the gravity different between these two planetary bodies?

Answer 1

Hint: Saturn has 82 moons in total from which 53 are confirmed with the names and remaining are yet to confirm, Titan is the largest moon among them and second largest moon in the solar system after Jupiter’s moon Ganymede ,It is a moon but acts like a planet because of its huge size with a radius of 2574.4 KM.

Complete solution:
Earth is flattened at the poles and bulges at the equator. The earth is 12,756km at the equator and 12,714km from pole to pole. We round this up to 13,000km and for an overall average radius with 6371 km, so the radius of earth is around 2.61 times that of Titan moon, but it is larger than earth’s moon.
Now,
Mass of Earth = $5.972\times {{10}^{24}}kg$
Mass of Titan = $1.345\times {{10}^{23}}kg$

And we know that acceleration due to gravity $g$ is defined as in terms of $G$(gravitational constant), $M$ mass of an object (planet) and $R$(radius).
So, $g=\dfrac{GM}{{{R}^{2}}}$

Here G is constant, by putting values of radius and mass of titan and earth we can calculate acceleration due to gravity $g$ and by experimental data we know that,
$g$ on Titan is $1.352{m}/{{{s}^{2}}}\;$ and on earth is $9.8{m}/{{{s}^{2}}}\;$ so it clearly states that gravity is higher on earth with respect to on Titan.

Note:
Titan was discovered on March 25, 1655, by the Dutch astronomer Christiaan Huygens, Titan orbits Saturn once every 15 days 22 hours like Earth's moon. Titan is primarily composed of ice and rocky material, that is probably going differentiated into a rocky core encircled by varied layers of ice, together with a crust of ice and an undersea layer of ammonia-rich liquid water.