Question

In January 2005, the Huygens probe landed on Saturn's moon Titan, the only satellite in the solar system with a thick atmosphere. Titan's diameter is 5150 km, and its mass is 1.35×1023kg. The probe weighed 3520 N on the earth.

What did it weigh on the surface of Titan? Express your answer with the appropriate units.

Answer 1

To find the weight of the Huygens probe on Titan, we first calculate the probe's mass using Earth's gravity, then use Titan's gravitational acceleration to determine the weight on Titan.

Step-by-step explanation:

To calculate the weight of the Huygens probe on the surface of Titan, we need to use the formula for gravitational force: Weight (W) = mass (m) × acceleration due to gravity (g). However, since weight on Earth is given instead of mass, we first need to find the mass of the probe using the Earth's gravity (9.81 m/s2). The mass of the probe can be calculated by rearranging the formula as: m = Wearth / gearth, where Wearth = 3520 N and gearth = 9.81 m/s2. Once we have the mass, we can calculate the weight on Titan using Titan's gravitational acceleration.

The acceleration due to gravity on Titan (gtitan) can be calculated using g = G * M / R2, where G is the gravitational constant (6.674 × 10-11 m3kg-1s-2), M is the mass of Titan (1.35 × 1023 kg), and R is the radius of Titan (2.58 × 106 m). Finally, the weight of the probe on Titan is found by multiplying its mass by gtitan.