jete

2009-Jun-20, 03:10 PM

Picking back up from a thought that came to me while reading the “Brief History of Time” thread and from a reply that was given to me by Hornblower:

I am thinking that there may be a way to show students evidence of the “curvature of space”. I was thinking that using the moon as a mass to deflect the light from a star would be a good situation as it is easier to watch the moon eclipse a star than the sun (although yes the sun is a star). The problem it seems would come with the slight amount of deflection that the moon would create. I have come up with the following and was hoping that someone would critique what I have so far before I go any further.

The equation that I am seeing referring to the deflection angle would be equal to 4GMs/c^2b where G is the gravitational constant, Ms is mass of the sun, c is the velocity of light, and b is the minimum distance between the trajectory and the center of the Sun. First of all I assume that I can substitute the mass of any object (in this case the moon) for M, and the radius of any roughly spherical object for the sun. If I am understanding that correctly then with 4G and c^2 being constant values the issue comes down to a ratio of mass to radius (which I imagine has a name, but I am not aware of it), as the path of the photon could be tangent to the surface of the object. The mass of the sun being 1.9891 × 1030 kg, the radius being 6.955 × 108 m (equatorial), and a angle of deflection having been given at 1.75 (7/4) seconds of arc. Comparing that to the mass and radius of the moon being 7.347 7 × 1022 kg and 1,738.14 km (equatorial) respectively. You would have the sun’s “deflection factor” being about 2.860 x 10^21 kg/m and the moon’s being 4.227 x 10^19 kg/m. So the ratio of the moon’s “deflection factor” to the sun’s “deflection factor” seems to be about 1.478 x 10^-2 to 1. It is quite possible that my reasoning, or math, or both, are off, but if I am right then it would seem that the moon would deflect the angle of a photon moving along a path tangent to it’s surface by about a scale of 1/100 in comparison to the sun, or in terms of actual deflection; approximately 1/40 seconds of arc.

I am thinking that there may be a way to show students evidence of the “curvature of space”. I was thinking that using the moon as a mass to deflect the light from a star would be a good situation as it is easier to watch the moon eclipse a star than the sun (although yes the sun is a star). The problem it seems would come with the slight amount of deflection that the moon would create. I have come up with the following and was hoping that someone would critique what I have so far before I go any further.

The equation that I am seeing referring to the deflection angle would be equal to 4GMs/c^2b where G is the gravitational constant, Ms is mass of the sun, c is the velocity of light, and b is the minimum distance between the trajectory and the center of the Sun. First of all I assume that I can substitute the mass of any object (in this case the moon) for M, and the radius of any roughly spherical object for the sun. If I am understanding that correctly then with 4G and c^2 being constant values the issue comes down to a ratio of mass to radius (which I imagine has a name, but I am not aware of it), as the path of the photon could be tangent to the surface of the object. The mass of the sun being 1.9891 × 1030 kg, the radius being 6.955 × 108 m (equatorial), and a angle of deflection having been given at 1.75 (7/4) seconds of arc. Comparing that to the mass and radius of the moon being 7.347 7 × 1022 kg and 1,738.14 km (equatorial) respectively. You would have the sun’s “deflection factor” being about 2.860 x 10^21 kg/m and the moon’s being 4.227 x 10^19 kg/m. So the ratio of the moon’s “deflection factor” to the sun’s “deflection factor” seems to be about 1.478 x 10^-2 to 1. It is quite possible that my reasoning, or math, or both, are off, but if I am right then it would seem that the moon would deflect the angle of a photon moving along a path tangent to it’s surface by about a scale of 1/100 in comparison to the sun, or in terms of actual deflection; approximately 1/40 seconds of arc.