by Nitpicker » Fri Apr 28, 2017 3:55 am
Having never given much thought to meteor showers, I've never previously considered or attempted the following calculation, so I might rely on someone like Chris (or someone exactly like Chris) to check my method ...
Around April 22, Earth was hurtling through the solar system at ~30 km/s, in the direction of Capricornus, about 90 degrees west of the Sun (in Aries) along the ecliptic. As shown in the APOD (and Stellarium), the apparent radiant of the Lyrids was in Hercules (close to its border with Lyra), forming an angle of about 62-63 degrees in the sky, from the position of Earth's velocity vector in Capricornus.
From the semi-major axis of C/1861 G1 (Thatcher), determined in 1861 to be ~55.7 AU, I calculated the true orbital speed of the comet's meteoroid trail, to be ~42 km/s, when crossing Earth's orbit.
From this and a bit of vector arithmetic, I calculated the
true radiant of the Lyrids (that is, the apparent radiant if the Earth was motionless in the solar system at this point in its orbit) to be about 101-102 degrees from the position of Earth's velocity vector, measured through the point of the apparent radiant. This places the true radiant in Draco, roughly 20 degrees from the ecliptic north pole.
I've attempted to display this graphically (using Stellarium) against an ecliptic grid. The blue arc shows the true sky angle measurement shown in a stereographic projection, from the position of Earth's velocity vector (bottom), to the true radiant of the Lyrids (top), passing through the apparent radiant (nicely annotated by the [brilliant] software):
I calculate the relative, or geocentric velocity of the Lyrids, prior to striking Earth's atmosphere (and ignoring the localised gravitational effects on their speed), to be ~46 km/s. This seems to match pretty closely to the number I just found on the web.
Is my method sound and are my numbers close? Is it possible to determine these numbers without knowing the semi-major axis of the meteoroid trail? Interesting stuff ... I may just have found yet another new way to enjoy my astronomy hobby.
Having never given much thought to meteor showers, I've never previously considered or attempted the following calculation, so I might rely on someone like Chris (or someone exactly like Chris) to check my method ...
Around April 22, Earth was hurtling through the solar system at ~30 km/s, in the direction of Capricornus, about 90 degrees west of the Sun (in Aries) along the ecliptic. As shown in the APOD (and Stellarium), the apparent radiant of the Lyrids was in Hercules (close to its border with Lyra), forming an angle of about 62-63 degrees in the sky, from the position of Earth's velocity vector in Capricornus.
From the semi-major axis of C/1861 G1 (Thatcher), determined in 1861 to be ~55.7 AU, I calculated the true orbital speed of the comet's meteoroid trail, to be ~42 km/s, when crossing Earth's orbit.
From this and a bit of vector arithmetic, I calculated the [i]true[/i] radiant of the Lyrids (that is, the apparent radiant if the Earth was motionless in the solar system at this point in its orbit) to be about 101-102 degrees from the position of Earth's velocity vector, measured through the point of the apparent radiant. This places the true radiant in Draco, roughly 20 degrees from the ecliptic north pole.
I've attempted to display this graphically (using Stellarium) against an ecliptic grid. The blue arc shows the true sky angle measurement shown in a stereographic projection, from the position of Earth's velocity vector (bottom), to the true radiant of the Lyrids (top), passing through the apparent radiant (nicely annotated by the [brilliant] software):
[attachment=0]lyrids.jpg[/attachment]
I calculate the relative, or geocentric velocity of the Lyrids, prior to striking Earth's atmosphere (and ignoring the localised gravitational effects on their speed), to be ~46 km/s. This seems to match pretty closely to the number I just found on the web.
Is my method sound and are my numbers close? Is it possible to determine these numbers without knowing the semi-major axis of the meteoroid trail? Interesting stuff ... I may just have found yet another new way to enjoy my astronomy hobby.