Final answer:
Using Newton's third law and the formula for acceleration, the acceleration of the Earth caused by a 65.0 kg skydiver is an extremely small number, effectively considered to be zero due to the large mass difference between the Earth and the skydiver.
Step-by-step explanation:
The student asked about the magnitude of the acceleration of the Earth due to a 65.0 kg skydiver accelerating towards it at 9.80 m/s². This question can be answered by applying Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force exerted on the earth by the skydiver is the same as the force exerted on the skydiver by the Earth.
To find this, we use the formula for force: F = m × a, where m is mass and a is acceleration. For the skydiver, the force can be calculated as follows: F = 65.0 kg × 9.80 m/s², resulting in a force of 637 N (newtons).
Now, to find the Earth's acceleration (ae), we rearrange the formula to ae = F / me, where me is the Earth's mass. Substituting in the values, we get ae = 637 N / (5.97 × 10²⁴ kg).
When you calculate this, the resulting acceleration is an extremely small number, so small that for all practical purposes it can be considered zero. This is because the Earth's mass is so large compared to the mass of the skydiver.