"If the Sun were magically replaced with a giant rock that had precisely the same mass, Earth’s orbit would not change. Explain why not."
I'm a little confused as to how to answer this. Is it because Earth doesn't orbit the exact center of the sun. Instead, both Earth and the Sun orbit their common center of mass. Therefore, if this new giant rock, has the same mass, it wouldn't make a difference to Earth's orbit.
Thanks
Earth's orbit would not change. The two masses remain the same, and that is what the causes the graivty which maintains orbit.
Well, isn't that a rock-solid question! Let me clarify this for you. You're absolutely right! The Earth and the Sun don't orbit around fixed points, like an overeager hula hoop dancer. Instead, they both dance around their common center of mass, kind of like two clumsy kangaroos hopping together.
Now, imaging if the Sun, the talented ball of gas that it is, suddenly transformed into a giant rock with the same mass. Well, even though it might be a bit of a change for the Sun's ego, the Earth wouldn't bat an eyelash. That's because its orbit is determined by the gravitational pull between the Earth and the Sun's mass, and that lovely attraction hasn't changed one bit.
So, just like a dedicated partner in a synchronized swimming routine, the Earth would keep on twirling around that center of mass, or the barycenter, if you want to be technical. It doesn't matter if the Sun is shining or if it's transformed into a huge, shiny rock – Earth's orbit would remain as steady as a rock concert without any fans. Rock on!
That is correct! Earth and the Sun actually orbit around their common center of mass, which is close to the center of the Sun but not exactly at the center. This is because the Sun also experiences a gravitational force due to Earth's mass.
If the Sun were magically replaced with a giant rock that had the same mass as the Sun, the center of mass for the Earth-rock system would remain the same. Therefore, Earth's orbit around this new giant rock would not change since the gravitational force between Earth and the rock would be the same as the gravitational force between Earth and the Sun.
That's correct! Earth and the Sun actually both orbit around their common center of mass, which is called the barycenter. The barycenter is the point at which the two objects in a system balance each other due to their mass and distance.
Since Earth's orbit is determined by the gravitational pull of the Sun, replacing the Sun with a giant rock of the same mass would not change the location of the barycenter. Therefore, Earth would still orbit around the same point in space, maintaining the same orbital path and distance from the barycenter.
This is because the gravitational force between two objects depends on their masses and the distance between them. So, even if the Sun is replaced with a giant rock, as long as the mass and distance remain the same, the gravitational force on Earth would be unchanged. Consequently, Earth's orbit would remain unaffected.