titan is the largest moon of Saturn. if a 60 kg person stood on titan, they would have a weight of 81 N.
a. what is titan's mass if it has a radius of 2576 km?
b. what is the gravitational field strength of titan near its surface?
Look up the value of G
F = GMm/r^2
So to find M, use GM*60/(2576*10^3)^2 = 81
g for Titan is GM/r^2
g Titan = m g / m = 81 N / 60 kg = (81/60) m/s^2
To find the answers to these questions, we can use the formulas related to gravitational force and gravitational field strength.
a. To calculate the mass of Titan, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2,
where F is the gravitational force between two objects, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
In this case, the force (F) is given to be 81 N, the mass of the person (m1) is 60 kg, and the radius of Titan (r) is 2576 km = 2,576,000 meters. We need to solve for the mass of Titan (m2).
Let's rearrange the equation to solve for m2:
m2 = (F * r^2) / (G * m1).
The gravitational constant, G, is approximately 6.67430 × 10^(-11) N(m/kg)^2.
Substituting the given values, we get:
m2 = (81 * (2,576,000)^2) / (6.67430 × 10^(-11) * 60).
Calculating this, we can find the mass of Titan.
b. The gravitational field strength near the surface of Titan can be determined using the formula:
g = (G * M) / r^2,
where g is the gravitational field strength, M is the mass of Titan, G is the gravitational constant, and r is the radius of Titan.
Using the mass of Titan (obtained in part a) and the radius of Titan (given as 2576 km = 2,576,000 meters), we can calculate the gravitational field strength near its surface (g).