If the sun became a black hole, how would the curvature of spacetime change in the region of Earth's orbit?

Question

And would this have na effect on the Earth's orbit?

I know the sun will not become a black hole. I am just asking about this theoretically.

Answer 1

It would not change at all, the same amount of mass would be in the same position, the Earth would continue in the same orbit.

Answer 2

The Sun cannot become a black hole. It is not massive enough and the other conditions do not exist.

However, let's make it a thought experiment:

The Sun is replace by a black hole with exactly the same mass as the Sun.

F = G M m / d^2

The gravitational force at Earth remains the same (Mass of central object unchanged, Earth still has same mass and is located at same distance).

The curvature of space-time is represented by the gradient: the change in the force of gravity over the change in location (especially, in the case of an orbit, the change in the force with the change in distance closer to or further from the central object).

The only change would be over time: The Sun puts out energy and this output costs a bit of mass (from E = mc^2). Approximately 4 million tonnes per second.

Over time, the force of gravity diminishes (because M, the mass of the Sun, diminishes) and the curvature becomes a tiny bit flatter. The orbit grows (extremely slowly)

With a black hole, there would be no reduction of the mass over time, maybe even a slight increase. Therefore, the curvature would become steeper (over extremely long periods of time) and the orbit could get smaller.

Also, the Earth generates gravitational waves. Not much. The "luminosity" of the radiated gravitational energy (due to the constant acceleration keeping us in an orbit) is equivalent to 300 Watts or so. By comparison, the Sun loses mass at a rate equivalent to 3.85x10^26 W, or 385,000,000,000,000,000,000,000,000 W.

Therefore, the gravitational energy lost by Earth is nothing compared to the energy/mass loss of the Sun. We still spiral outwards.

However, a black hole loses nothing (or so close to nothing that we might as well say nothing). Therefore, the 300 W lost, however small, is a net loss. Earth would eventually 'spiral' inwards (over gazillion years).

The inward rate would be calculated in atom-size per billion years.

Answer 3

An object of any mass has a characteristic Schwarzchild radius, where if that mass could be compressed to fit within that radius, no known force could keep it from collapsing into a gravitational singularity. A certain mass with a radius lower than it's Schwarzchild radius becomes a black hole. The Sun's Schwarzchild radius is about 3 km. This means that if you compressed the mass of the Sun into a sphere of radius below 3 km, it would collapse into a black hole. In general, for any non-rotating black hole, this Schwarzchild radius acts as the surface/limit of the event horizon.

So, to wrap this all up, if the Sun were to hypothetically become a black hole, its even horizon (within which no light or matter could escape) would be a sphere of radius 3 km. The Earth is some 150 million km away from the Sun, so everything in the Solar System would simply orbit this black hole as if it were still the Sun.

Answer 4

As the mass of Sun is less than Chandrasekhers limit it will not become a black hole
Suppose it becomes,mass of sun does not change.
Distance to earth does not change. So space time curvature near earth will not change.
Only near to sun space time curvature change
Chandramohan

Answer 5

It can't become a black hole. Period.

IF a black hole with the mass of the Sun were swapped for the sun, the Earth would continue to orbit as it does now.

Answer 6

If we've been to snap our hands and make it right away a black hollow, then theoretically, the orbit does not be affected; the mass could be an identical, with an extremely small experience horizon, so mathematically it may artwork out. besides the undeniable fact that, the traditional formation could be especially violent, and the marvel wave of fabric and skill despatched out could especially plenty make it moot how our orbit is affected; we does not be right here.

Answer 7

IF there was no minimum mass/density required for the formation of a black hole then the radius (event horizon) of the black hole is given by the formula (derived from Gen Rel.) :

R = 2Gm/c^2, where m is the solar mass.

R is the closest distance you can get without getting sucked in forever.

Good luck.

Answer 8

First...the sun will not become a black hole. It is far from big enough. and it will not have an effect on the earth cause when it dies it blasts and the earth would not exist.

Answer 9

If it does happen, perhaps by collision from a more massive star, our sun gets consumed, and that new massive star collapses, either we get broken down to atomic shreds, or hurled outward from orbit.

Answer 10

hypothetically lets say the sun does become a black hole, I dont understand the rest of the question but depending on the mass of the hole I would say it would probably suck earth into nothing ness, or it will be a worm hole and earth gets to go party with the midget planet of omercron 643