Final answer:
The linear momentum of Earth can be calculated by multiplying its mass by its orbital velocity.
Step-by-step explanation:
The linear momentum of an object can be calculated by multiplying its mass by its velocity. In this case, the mass of Earth is given as 5.972×10²4 kg and its orbital radius is 1.496×10¹1 m. To calculate the linear momentum, we need to determine the orbital velocity of Earth using the formula v = 2πr/T, where r is the orbital radius and T is the orbital period.
The average orbital period of Earth is about 365.25 days, or 3.154×10⁷ seconds. Plugging in the values, we get:
v = 2π(1.496×10¹1)/(3.154×10⁷) ≈ 2.977×10⁴ m/s
Now we can calculate the linear momentum using the formula p = mv, where m is the mass and v is the velocity:
p = (5.972×10²4 kg)(2.977×10⁴ m/s) ≈ 1.780×10²⁹ kg·m/s
Therefore, the linear momentum of Earth is approximately 1.780×10²⁹ kg·m/s.