Why do we think Space is Curved near the sun?

Einstein's 1911 & 1915 papers below:

Why do we think space is curved near the sun? Because we see Mercury's orbit precess. We thought it was due to gravitational effects of other planets. But, that accounts for about 92% of it. The remaining 8% comes from the spatial curvature of the sun as predicted by Einstein in his general theory of relativity. Also, to account for the deflection of light by our sun, we need to account for both space and time curvature.

The visuals are inspired from the book - 'Relativity Visualised by Lewis Caroll Epstein'.
Check it out, the book is awesome.

This video is sponsored by SquareSpace

[Mahesh_Shenoy]

FAQs
Q: Why would an apple take less time? Wouldn't it accelerate and then decelerate as it exits?
A: Say in the case without the planet, the apple's uniform velocity was 5 m/s. Then in the case with the planet, as the apple accelerates it's velocity becomes more than 5, reaches max, and then decreases to back to 5. So, look, for most of it's journey the velocity was MORE than 5. Hence, it reaches faster.

Q: Isn't gravity maximum on the surface and zero at the centre?
A: Yes, the strength of the Newtonian gravitational field - g - is maximum on the surface and zero at the centre (Assuming a perfect spherical planet with uniform density). But the radius of that rolled up space-propertime diagram doesn't represent the strength of gravity. It represents dilated proper time. As you go inside the planet, although the field deceases you are still LOWER in the gravitational field. That's why the clocks inside the planet will tick slower than on the surface. The clock will tick the slowest at the centre. Note that the slope of that rolled up diagram represents the strength of gravity, and as we go inside the planet, the slope decreases and becomes almost flat at the centre.

Q: Shouldn't all planet orbits precess?
A: Yes, they should but the spatial curvature weakens the farther you go from the sun. So the effect becomes negligible.

Q: Wait, shouldn't light be at 45 degrees on the space time diagram?
A: That's the Minkowski diagram in which we plot space vs co-ordinate time. (Basically, space and time as measured by your ruler and clock). The one shown here is the space-propertime diagram. So, it's space measured by your ruler but time measured by the object's clock. Not your clock. I have only seen this in Epstein's book. It's use case is pretty limited but it is incredibly intuitive. Both diagrams are equivalent though.

....will keep adding more...

[energeticoak]

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[kaustubhpandey]

Last night I sat down my mother and told her all about special relativity, time dilation, length contraction, Einstein's experiment in 1919, general relativity, gravitational lensing, and the Veritasium supernova video showing the same event 4 times on earth because of the presence of a black hole in the path

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[nickanderson]

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[nirbhay_raghav]

The sheer amount of thinking Einstein did and published a single author paper with less than 10 citations that revolutionized the way we thought about universe. Even after 100 years its still being fascinated upon and holds true.

[henrikantonsson]

I asked a physicist this question of the mercurian precession ten years ago when I studied physics.
I dropped out six months later but Now finally I got a fully understandable answer, Thank you!

[dvxc]

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These two observations - the precession of Mercury's orbit, and the deflection of starlight light by 1.7" in the sky by the sun - are prob my favorite two tests in all of science.

That they worked out this way in the very early 20th century is so beautiful and simple.

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