Question

if the sun were to disappear right now, eight minutes and 30 seconds later, the earth would travel along a straight-line path. calculate the magnitude of the linear momentum of the earth assuming its orbital radius takes the average value of and the known duration of a year. include units as appropriate.

Answer 1

To calculate the Earth's linear momentum, we use the formula p=mv with Earth's mass and its velocity in orbit. Earth's orbital speed of approximately 110,000 kilometers per hour is converted to meters per second, and Earth’s mass is factored in to find the linear momentum.

Step-by-step explanation:

If the Sun were to disappear right now, Earth would continue in a straight line path eight minutes and 30 seconds later due to inertia. To calculate the magnitude of the Earth's linear momentum, we can use the formula p = mv, where p is linear momentum, m is mass, and v is velocity.

The Earth's velocity can be derived from its orbital speed, which is approximately 110,000 kilometers per hour (or 66,000 miles per hour when converted). The Earth's mass is approximately 5.972 × 10^24 kilograms. Converting Earth's orbital speed to meters per second, we get:
110,000 km/h × (1000 m/km) × (1 h/3600 s) = 30,555.56 m/s.

Therefore, the magnitude of Earth's linear momentum is
p = (5.972 × 10^24 kg) × (30,555.56 m/s)
p ≈ 1.826 × 10^29 kg·m/s.