Gravity & Extrasolar Planets Pre-lab
Hand in this pre-lab at the beginning of the Gravity & Extrasolar Planets Lab.
Gravity is a familiar phenomenon - it keeps our feet on the floor, brings rain from clouds to the ground, and makes things fall when we drop them. Gravity is an essential part of our everyday lives, and plays such an important role in astronomy that it comes up often in the labs in Astronomy. This week, we take a first look at this prime mover.
Let's say you hop on a see-saw with your little cousin. Your mass is 75 kg, and your cousin's is 25 kg. What happens if you and your cousin each sit 3 meters from the fulcrum of the see-saw?
If your cousin is sitting 3 meters from the fulcrum, where do you have to sit to balance the see-saw: 1 meter or 9 meters?
Newton's Third Law says that if Object A exerts a force on Object B, then Object B exerts an equal and opposite force on Object A. Let's apply that to a familiar situation involving gravity. When you jump up from the ground, you push the Earth away. But it is you that soars into the air as a result - the Earth doesn't seem to fly away from you. Why does Newton's Third Law not seem to apply here?
Gravity is the force that keeps planets in orbit around stars, as we'll investigate in this lab. Gravity doesn't care if the two objects are a star and a planet or two stars or an apple and a pickup truck - orbits are orbits! We'll investigate orbits using the binary simulation:
https://www.astro.ucla.edu/undergrad/astro3/orbits.html
You can adjust various parameters for the two stars and see what happens to their spectra and their velocities relative to the Earth. The blue star has mass M1, and the red star has mass M2. Set 1=90° so that we have an edge-on view from Earth, a=1.0 for the separation and w=90° (this has to do with the viewing angle). Set the eccentricity to e=0.0, which is a circle.
Describe, and draw, the motion of the stars when their masses are equal. What are they orbiting?
Notice that the curves are labeled "Radial Velocity." How do we measure the radial velocity of the stars from Earth? (Hint: consider the spectrum!)
Now make one star much more massive than the other, say 40 - 100 times more (this is closer to the situation for a planet and a star). How do the motions of the two stars compare? Are both still orbiting? What are they orbiting?
Now, increase the eccentricity of the orbits (i.e., make them more elliptical), say e=0.2 to 14. How does the speed of the less-massive star change as it orbits the other star? When is it moving fastest? Where is the gravitational pull between the stars the strongest?