In a one-g gravitational field, in one second, a light beam will curve beneath a perfectly straight line by.....Less than 4.9 m, 4.9m, or more than 4.9m?
4.9 m
To determine how much a light beam will curve beneath a perfectly straight line in a one-g gravitational field, we need to understand the concept of gravitational deflection.
The gravitational deflection of light, also known as gravitational lensing, occurs due to the curvature of spacetime caused by massive objects. According to general relativity, light follows a curved path when it passes close to a massive object.
In the case of a one-g gravitational field, which is the gravitational acceleration at the surface of the Earth, the light beam will exhibit a small amount of deflection. This deflection is responsible for phenomena such as the bending of starlight by the Sun's gravity during a solar eclipse.
Now, let's answer the question. In a one-g gravitational field, the amount of deflection for a light beam passing near a massive object (like the Sun) is approximately 1.7 arcseconds.
To calculate how much the light beam curves beneath a perfectly straight line, we need to consider the distance traveled by the light in one second. Since light travels at approximately 299,792 kilometers per second, we can convert that to meters by multiplying by 1,000, giving us 299,792,000 meters.
With a deflection of 1.7 arcseconds, we can calculate the corresponding distance that the light beam curves beneath a straight line using basic trigonometry. We use the small-angle approximation, which states that for small angles, the tangent of the angle is approximately equal to the angle measured in radians.
Using this approximation, we can calculate the distance as follows:
Distance curved = (1.7 arcseconds / 360 degrees) * (2π radians) * (299,792,000 meters)
Calculating this expression, we find that the light beam curves by approximately 4.8 meters (rounded to one decimal place).
Therefore, in one second, a light beam in a one-g gravitational field will curve beneath a perfectly straight line by less than 4.9 meters.