Methods of calculating gravitational influence.

[arianabedi]

Dear Physicsforumians!

I've posted a detailed version of this as a "home work", so I hope its ok to ask this here, (its just a personal project) the link is : https://www.physicsforums.com/showthread.php?t=527047"

My question is how would you know if a projectile (passing Earth) won't impact the planet because of its gravitational influence?

I know the distance that the comet is passing Earth from (234,803.4KM), and its trajectory is strait from Mars's North pole, heading towards Sun's North pole, so we assume that Earth is in alignment with Mars (and stays constant).

The only clue I have is : http://en.wikipedia.org/wiki/Gravitational_acceleration"
$$\hat{g}=-\frac{GM}{r^2}\hat{r}$$
However I am not sure how to measure the unit vector between the object and the planet (r-hat).

I assume astronomers or mission planners use simulators but I haven't found any semi-accurate ones that are free to use (at least for a Mac).

Thank you for putting time to read this.
-Arian

 

[AndyW]

Dear Arian,

Thank you for your interesting question. I can suggest a few ways to determine if a projectile will impact Earth based on its gravitational influence:

1. Calculate the trajectory: Using the equation you mentioned, along with other equations related to projectile motion, you can calculate the trajectory of the projectile and determine if it will pass close enough to Earth to be affected by its gravitational pull. This will require knowledge of the projectile's mass, velocity, and distance from Earth.

2. Use simulations: As you mentioned, astronomers and mission planners often use simulations to predict the trajectory of objects in space. These simulations take into account various factors such as gravity, velocity, and mass to accurately predict the path of a projectile. You can try finding a free simulation tool online or consult with an astronomer for assistance.

3. Observe the object: If the projectile is visible from Earth, astronomers can track its movement and use telescopes to measure its distance from Earth. By observing its trajectory over time, they can determine if it will pass close enough to be influenced by Earth's gravity.

4. Collaborate with other scientists: In the field of astronomy, collaboration is key. Scientists often work together to analyze data and make predictions about celestial objects. You can reach out to other scientists or join online forums to discuss your project and receive feedback from experts in the field.

I hope these suggestions will help you in your project. Good luck!