Question

Gravitational constant = 6.674 × 10^-11 m^2 /^2Mass of Pluto = 1.3 × 10^22 Radius of Pluto = 1200 m = 1.2 × 10^6 mBoltzmann constant = 1.4 × 10^(-23) J/K= 1.4 × 10^(-23) m^2 ^-2 ^ -1Mass of nitrogen molecule ( 2 ): m = 4.7 × 10^(-26) 1. What is Pluto’s escape velocity?2. If Pluto’s surface temperature is 50 K, what is the thermal velocity of a nitrogen molecule? Based on your answers to problems 2 and 3, do you think it is likely Pluto has a nitrogen-rich atmosphere like Earth’s?

Answer 1

1. Pluto's escape velocity can be calculated using the formula Ve = √(2GM/r), where G is the gravitational constant, M is the mass of Pluto, and r is the radius of Pluto. Plugging in the given values, we get Ve = √(2 x 6.674 x 10^-11 x 1.3 x 10^22 / 1.2 x 10^6) = 1.23 km/s.

2. The thermal velocity of a nitrogen molecule can be calculated using the formula Vth = √(3kT/m), where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the molecule. Plugging in the given values, we get Vth = √(3 x 1.4 x 10^-23 x 50 / 4.7 x 10^-26) = 533.6 m/s.

3. Based on the calculated thermal velocity, it is unlikely that Pluto has a nitrogen-rich atmosphere like Earth's, as the escape velocity is much higher than the thermal velocity. This means that the nitrogen molecules are not likely to be trapped by Pluto's gravity and form an atmosphere. However, other factors such as the composition and history of Pluto's atmosphere could also play a role in determining its composition.