In 1970, Brian May, interrupted his PhD studies in astrophysics when his rock band Queen enjoyed success. Eventually he went back to school and completed his degree in 2007. He investigated the radial velocity of stars and later improved public awareness of asteroids by creating Asteroid Day.
There are 1.2 million of them, mostly between Jupiter and Mars. Most of the time they orbit the sun in very slightly elliptical orbits. But occasionally Jupiter’s powerful gravity and other effects disturb some of their orbits, allowing them to approach Earth too closely for comfort. There are currently several large known craters on Earth that have been created by asteroid impacts. The oldest, about 2 billion years old, is Vredefort Crater in South Africa; a much younger one, 35 million years old, is Chesapeake Bay Crater in the USA.
Of course, the most notorious one is Chicxulub Crater in Mexico. That asteroid was about 200 to 300 km in diameter, and it contributed to the demise of large dinosaurs and large marsupials. The survivors of this mass extinction were little placental mammals and the small-sized, close-relatives of the dinosaurs that evolved into today’s mammals and birds, respectively.
A moon or a spacecraft, such as Mission Galileo(1989-2003), allows astronomers to find an asteroid’s mass because of the asteroid’s gravitational effects on the orbit of its small neighbour. Radar gives an idea of size. Divide the two measurements and you get a good estimate of its density. This has led to the recent realization that not all asteroids are of the same composition. We not only have S-type asteroids, which are a mixture of rock and metals such as nickel, iron and magnesium. M-types seem to be entirely made of metal, while C-type asteroids are far less dense because they are probably rich in carbon and water-ice.
A few even have their own moons, like Florence, which has a pair. The Florence-trio came within 4 million miles of the Earth on September 1, 2017. Radar allowed astronomers to detect the two moons. The inner one takes about 8 hours to orbit Florence, while the outer moon’s period is estimated to be in the neighborhood of 22 to 27 hours. Is this consistent with Kepler’s 3rd Law?
Kepler based all of his laws on observations. Newton was the first to make sense of them. Using vector calculus, he showed that the first of Kepler’s laws—that bodies follow an elliptical path—is consistent with his inverse square law. The second law, which reveals that planets and moons sweep equal areas in equal times, is consistent with the conservation of angular momentum. If you have a central gravitational force, there is no torque, and since torque is the rate of change of angular momentum with respect to time, given that the derivative is zero, momentum must be a constant number. If you combine these concepts mathematically, it can be shown that the the square of a moon’s period is proportional to the cube of its semi-major axis. That’s Kepler’s 3rd law.
Using the radar image of Florence and its moons, I did a very rough calculation to see if the measurements are in agreement with Kepler’s 3rd law. I used the period of the inner moon which is known more accurately and set out to calculate the period of the outer moon. Based on the radar image of Florence on my desktop computer, I simply used a ruler to measure each moon’s respective distance from the center of Florence( its parent asteroid, not the city of Galileo’s museum. :)Then, since they orbit the same asteroid, you can use Kepler’s 3rd law to set up a ratio. The gravitational constant, Florence’s mass and the kilometer-to-centimetre-from-the-image ratio, all cancel out, leaving us with:
(x/8.0 hours)2= (20.9cm/9.2cm)3.
x = 27 hours, which is near the upper range of possibilities.