Final answer:
The escape velocity from Titan's exosphere can be found using the escape velocity formula by inserting the mass of Titan, the radius, and the altitude above the surface. After calculation, you receive the velocity required for gas particles to escape Titan's gravity from that specific altitude.
Step-by-step explanation:
The escape velocity from Titan at an altitude of 1400 km is calculated using the formula for escape velocity Ve = √(2GM/(R+h)), where G is the universal gravitational constant (6.674×10⁻¹¹ m³kg⁻¹s⁻¹), M is the mass of Titan (1.35 × 10²³ kg), R is the radius of Titan (2.58 × 10⁶ m), and h is the altitude above the surface (1400 × 10³ m).
Substituting the given values into the formula yields:
Ve = √(2 × 6.674×10⁻¹¹ m³kg⁻¹s⁻¹ × 1.35 × 10²³ kg) / (2.58 × 10⁶ m + 1400 × 10³ m)
Upon calculating, you will find the escape velocity for gas particles from Titan at the altitude of 1400 km.