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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.

Hornblower
2009-Jun-21, 12:49 AM
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.You muffed your number crunching by a factor of 1,000. My best guess is that you used the numbers as is, neglecting to correct for the fact that your number for the Sun's radius is in meters while that for the Moon is in kilometers.

The Moon's gravitational deflection should be about 1/40,000 aresecond.

jete
2009-Jun-21, 05:01 AM
Thanks for the correction Hornblower. :embarrassed: I am thankful that you caught this before I went any further. I was beginning to think that this might be a task for the “Time Warp” team on the Discover Channel.

During my research I did find an interesting picture that was taken by Hubble of a galaxy acting as a gravitational lens for another galaxy, not as much of a discovery activity as measuring the deflection of light by the moon would have been, but evidence nonetheless.