What is the largest mass the sun can have without destroying the Earth?

• haiku11
In summary: It will not reach the sun's surface. The pieces may then spiral in, but that is irrelevant to the question.In summary, the question is whether any significant change in the mass of the Sun would cause the Earth to spiral either towards or away from the Sun, and if this change could potentially destroy life on Earth. There are various factors to consider, such as the Earth's orbital velocity and the Roche limit, but ultimately it is unlikely that a change in the Sun's mass would have a catastrophic effect on the Earth's orbit.

haiku11

This is one of the questions on a small exercise but I don't understand it.

I thought that the Earth is in orbit because the mass of the Earth and the Sun combine perfectly such that the orbital velocity is exactly the same as the pull of the sun so the Earth is forever falling towards it. If this is the case, then any significant change to the mass would (I'm actually not sure) alter the magnitude of the pull, causing the Earth to either slowly spiral into the Sun or away from it, kind of like a satellite orbiting the Earth. So wouldn't any change to the Sun's mass kill us?

That was my first thought, then it occurred to me that the Sun has solar flares which expel tons and tons of mass. So technically the Sun should be getting less massive and it's been doing this for at least 4.5 billion years cause that's how old the Earth is. So with this is mind, I have no idea how the Earth isn't spiralling away from the Sun as we speak.

These are the 2 thoughts I had on this question and I really don't know how to answer it.

IIRC, the Earth's orbital radius is increasing, but very slowly, as the Sun's mass-loss is a very, very tiny fraction of the remaining mass.

Bad news is that such increase is unlikely to save us when the Sun goes red-giant...
;-(

haiku11 said:
I thought that the Earth is in orbit because the mass of the Earth and the Sun combine perfectly such that the orbital velocity is exactly the same as the pull of the sun so the Earth is forever falling towards it. If this is the case, then any significant change to the mass would (I'm actually not sure) alter the magnitude of the pull, causing the Earth to either slowly spiral into the Sun or away from it, kind of like a satellite orbiting the Earth. So wouldn't any change to the Sun's mass kill us?
Yes and no.

1] If the sun's mass increased, the Earth would not spiral inward to its death. It would change to a highly elliptical path whose apogee is right where the Earth is now, but whose perigee would be proportionally closer to the sun. The new orbit would be stable.

2] This is true if you don't allow for a change in the orbital velocity to compensate. I suspect that the question assumes you would.

What you might want to read up on is Roche Limits. It may not be the answer, but it is an answer.

I'm not even sure what the question means. Does it mean to destroy all life on Earth or does it mean to literally destroy the Earth? Does it mean the volume increases along with this increased mass or does the volume stay constant and only the mass increases?

If it means to literally destroy the Earth, the Earth's orbit has to change essentially until perigee reaches the Sun's surface (or at least until the Sun's atmosphere, solar flares, etc, start slowing the Earth down). The only way this question would make sense is if the Earth kept it's current velocity while increasing the Sun's mass.

If it means to destroy life on Earth, then you first have to figure out how high the temperature has to get in order for the Earth to be uninhabitable - and is that uninhabitable by life or uninhabitable by human life?

Saying an average temperature of 373 degrees Kelvin (100 deg C) would at least be reasonable, except I'm not positive that would really be accurate (you'd have to research life existing near fissures on the ocean floor, etc since I'm not sure what their environment is - just that it's pretty extreme). Since intensity of light (and the energy from the Sun) is inversely proportional to the square of the distance, you could calculate how close the Earth's perigee would have to get to the Sun to boil all life periodically (average temperature on Earth is about 288 deg K, or about 15 deg C).

If you're talking about human life, then it would take a much smaller temperature difference to upset the ecosystem and pretty much change life on Earth as we know it even if it doesn't destroy all life.

Or, is the question assuming the density of the Sun stays as it is and the increase in mass also results in an increase in volume, thereby reducing the distance between the Earth and Sun by that means? And, once again, does it mean to literally destroy the Earth or to destroy the Earth as a life sustaining planet?

Or, the question is asking about the Roche limit, as Dave suggested.

BobG said:
If it means to literally destroy the Earth, the Earth's orbit has to change essentially until perigee reaches the Sun's surface (or at least until the Sun's atmosphere, solar flares, etc, start slowing the Earth down).

No. As I said, the Earth will break up once inside the Sun's Roche limit, which is several solar radii above the sun.

1. What is the maximum mass of the sun that will not cause Earth's destruction?

The maximum mass that the sun can have without causing Earth's destruction is about 1.1 times its current mass. This is known as the Chandrasekhar limit, named after the Indian astrophysicist Subrahmanyan Chandrasekhar who first calculated it in the 1930s.

2. Will the sun eventually reach its maximum mass and destroy Earth?

No, the sun will not reach its maximum mass and destroy Earth. As the sun ages, it will gradually lose mass through solar wind and nuclear fusion. It is estimated that the sun will lose about 30% of its mass over its lifetime, making it impossible for it to reach the Chandrasekhar limit.

3. How does the sun's mass affect Earth?

The sun's mass plays a crucial role in maintaining Earth's orbit and providing the necessary energy for life to exist on our planet. A higher mass would result in a stronger gravitational pull, causing Earth's orbit to become unstable and potentially leading to its destruction.

4. Is there a correlation between the mass of the sun and the number of planets in its solar system?

There is no direct correlation between the mass of the sun and the number of planets in its solar system. However, the sun's mass does play a role in determining the formation and stability of planetary systems. A higher mass can result in a larger number of planets, but other factors such as distance from the sun and planetary composition also play important roles.

5. Can other stars have a larger mass than the sun without destroying their planets?

Yes, it is possible for other stars to have a larger mass than the sun without destroying their planets. This is because other stars may have different compositions and structures that can accommodate a higher mass without causing destructive effects on their planets. However, the exact limit for each star would depend on its individual characteristics and cannot be generalized.