Would an object shot from earth fall into the sun?

  • Would an object shot from earth fall into the sun?

    If an object is shot at 107,000 km/h via rocket or otherwise, in the opposite direction to our orbit about the sun, it will be traveling at 0 km/h relative to the sun. The moon is not close enough to the object to have a significant force for the purposes of this question.

    Will this object start accelerating towards the sun or will it somehow fall into another stable orbit?

    Could it instead get trapped in the L4 Earth-Sun Lagrange point?


    If you're interested in calculating the details of that trajectory, see https://en.wikipedia.org/wiki/Radial_trajectory

    There is a bit of significant ambiguity left in your question, and that's how far it is from Earth when it reaches 0 velocity relative to the Sun. If it's still anywhere near the Earth (e.g. within the L4 point), it's likely the Earth will have enough effect on it to put it into a very eccentric orbit around the Sun rather than it hitting the Sun. Same with other planets.

    @GregMiller I don't agree: when the rocket is at 0 km/h relative to the sun, the Earth is still moving "very fast" away, so the gravitational field will have died out pretty quickly. But I suppose we should quantify our claims :-)

  • Assume that a spacecraft is instantaneously accelerated at the Earth's surface (disregarding the atmosphere for simplicity). We'll consider this from the Sun's reference frame; in other words, the Sun is stationary and the Earth is moving around it.

    The spacecraft is accelerated to a velocity which is precisely equal and opposite to the orbital velocity of the Earth around the Sun, making it completely stationary in the instant after the acceleration.

    What happens next? Well, we can consider the forces acting on the spacecraft:

    • The Earth's gravity causes a force in the direction of Earth.

    • The Sun's gravity causes a force in the direction of the Sun.

    The stationary spacecraft is therefore going to accelerate towards the Earth and towards the Sun. Since the Earth is moving away quickly on its orbital path, the gravitational force is not enough to pull the spacecraft back into an Earth orbit; however, it will nudge the spacecraft into an elliptical orbit.

    To demonstrate the situation, I have created a small simulation which can be viewed in a desktop browser. Click here to try the simulation. (You can click "View this program" to check the code, and refresh the page to restart the simulation.)

    The simulation is physically accurate (ignoring the effects of other planets), but the spheres have been enlarged for easy interpretation. The Earth is represented as green, while the Sun is orange and the spacecraft is white. Note that, while the spheres representing the spacecraft and Sun intersect, the distance between the two physical objects is always larger than 3.35 solar radii.

    This screenshot shows how the spacecraft has been pulled into an elliptical orbit by the Earth:

    Screenshot of simulation demonstrating the spacecraft entering an elliptical orbit.

    Finally, we could consider a more realistic scenario where the spacecraft is accelerated until it reaches zero velocity (again, in the Sun's reference frame) at a certain distance from the Earth. At the instant it reaches zero velocity, the engine is stopped.

    In this case, the result is essentially the same: there are still forces exerted by the Earth and the Sun, so an elliptical orbit will result. The further the rocket is from the Earth when it reaches zero velocity, the more elliptical the orbit. If the Earth is so far away that its gravity is negligible, the spacecraft will fall directly towards the Sun.

    I suppose this is due to enlarging the spheres, but on your simulation it seems that the object crashes into the Sun. I imagine that it actually passes very close from the Sun, but can you preicse how far ?

    @Evargalo Thanks, I've updated the simulation so that it prints the closest approach to the Sun. The simulation will also stop if the spacecraft hits the Sun. In the first orbit the spacecraft travels within 3.4 solar radii of the Sun's centre, but the perihelion seems to get further away in subsequent orbits.

    But an accurate simulation depends on the positions of Venus and Mercury, among other things. As an example, the Galileo Jupiter probe was actually launched towards the Sun, so that it could get gravity boosts from Venus & Earth: https://www.noao.edu/jagi/sepo/atjup/io/launch_to_g29_full.jpg

    @TheGreatCabbage, your simulation uses simple Euler integration, which accumulates errors rather quickly (particularly when the body is moving rapidly, such as during perhelion). I'd trust your simulation when it says the object won't collide with the Sun on the first pass, but after that first pass, the simulation's predictions are questionable at best.

    @TheGreatCabbage thank you for creating that example script! This is exactly what I wanted to know. So depending on how far the object is ejected, Earth may still have enough force to pull the object into a non-colliding path with the Sun. I found that anything above 1.43*Earths Radius from the Earth at 0m/s results in a collision with the Sun and anything below results in an orbit.

    TLDR: hitting the sun is hard.

    Surely there is an acceleration that counteracts it - so if we are moving at V then instantly accelerating it to V+K will counter the Earth's pull and fall into the Sun.

    @jamesqf That's true, but I think it's beyond the scope of the question and I didn't want to overcomplicate my answer.

    @TheGreatCabbage You could just add a simple note to that effect: "The simulation is physically accurate (assuming the effect from Venus, Mercury and all the planets other than Earth is negligible) ...".

    @corsiKa Yes, it's possible to accelerate it to a speed which will cause it to hit the Sun. However, it will never follow a straight line into the Sun; the trajectory will always be slightly curved due to Earth's gravity.

    @Draco18s : that's why, if you want to land on the Sun, you should go there by night.

    Of note is that if your space probe has a perihelion of 3.4 solar radii, it doesn't matter that it _technically_ didn't collide (for comparison, Mercury is about 30x farther), it's still going to melt into a nice diffuse gas of various metals. I do suspect that the effect of the solar wind might have a say in where the metals ultimately end up though.

    @TheGreatCabbage: Unless you give it enough of an additional push to cancel out the pull of Earth's gravity.

    That's not gravity. That is an intelligent being pushing down on the rocket so it misses the sun, a.k.a. intelligent falling. How did you get the being in your model?

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Content dated before 7/24/2021 11:53 AM