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1

There is quite a nice explanation on this web page. A key passage is this: in curved spacetime there aren't these "best" co-ordinate systems, the inertial ones. So even very reasonable different choices of co-ordinates can give disagreements about particles vs antiparticles, or what's the vacuum. These disagreements don't mean that "everything is ...

11

The rough answer is: just like the sun makes it hard or impossible to see planets and stars during the day, it dominates the gravity sky. But there are interesting patterns there if we view the sky using a logarithmic scale. The above plots are a combination of the gravitational force of the sun, moon and planets, the stars in the Hipparchos catalog, the ...

0

There are hard limits on what types of gas that Mars can retain based on its temperature and mass (Graph of what gasses an astronomical body can retain). Volume wise, it's not clear. Currently Mars is still losing its atmosphere, so it can't even retain that amount of atmosphere. But if you continually added gas to Mars, there isn't an end point where the ...

0

I find this comparison of tangential velocities on Wikipedia very confusing. … According to it, the tangential speed of Earth's surface (465.1 m/s) is different from the tangential speed required to "orbit" at Earth's surface (7.9 km/s). That might be, but they have explicitly elaborated "… Earth's own rotation at surface (for comparison— not an orbit) …...

3

An interesting corollary to this question: if the ground is not in orbit, how does it move (roughly) in a circle? If we model a section of ground as an isolated particle, it's clear that in order to move in a circle despite having a relatively low tangential velocity, it would need to have an ongoing force being applied to counteract the direction the ...

51

1. Is material on Earth's surface not in free fall around Earth's center? No. Material on the Earth's surface -- or inside it -- is not in orbit, and so is not in free fall. You can temporarily put yourself into an orbit (and thus into free fall) by jumping up into the air, or jumping off a higher surface. When you do this, you are briefly in a very ...

5

Imagine you are in orbit around the earth, several 100 km upwards. What happens when you slow down? That's right, you fall down until some force stops your fall. That force is the pushback from the ground. So next imagine: What happens when you throw a ball in the air? It falls back down to the ground. So it follows, that the ball is too slow to be in orbit....

2

Judging by the fact that after cubing the distance you have ended up with an exponent of 1021 (21 = 6×3+3) at the first point you have substituted the numbers into the equation, you appear to be assuming that 1 km3 is 1000 m3. However, if you write the same linear quantity in metres and kilometres and cube them, you can see this is not ...

5

Here's how I would do it. I'd convert everything to a single, standard set of units as recommended in the comments, and also stick to one digit before the decimal in scientific notation: $$T^2=\frac{4\pi^2r^3}{G\cdot M_{Sun}}$$ Using all numbers in the same units: $r \ 4.5 \times 10^{11} \ (m)$ $G = 6.674 \times 10^{-11} \ (m^3 \ kg^{-1} s^{-2})$ \$M ...

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