# Projectile angle (straight line) between 2 planets

• I
• thomasvt
In summary, the problem at hand is to calculate the angle or vector needed to shoot a projectile P from planet A to B in a planetary system with circular orbits. The orbit of planet A is irrelevant and the focus is on finding the point in time where the positions of P and B are equal. This can be approached by splitting the 2D problem into two 1D problems, one for the projectile's position and one for planet B's position. The equations to consider are xp = xp0 + v.t for the projectile's position and xb = cos(α0 + ω .t) for planet B's position. The goal is to solve for t where xp equals xb, but the speed of P (v) is
thomasvt
TL;DR Summary
Some tips in solving a linear math problem to predict the shooting angle of a projectile from one planet in orbit to another in orbit around the same center.
I have a planetary system with planets orbitting a central star (circular orbits). I want to shoot a projectile P in a straight line from planet A to B and need to calculate the angle or vector to shoot the projectile P. I know the straight line of the projectile is physically not correct, but it will probably get a lot more complex if add realistic orbits for P.

I know the orbit of the source planet A doesn't matter, since it has no influence on the problem once P has departed. So, I need to find the point in time t1 where the position of P equals the position of B.

I think that 2D problems can be split in 2 1D problems, so let's focus on the X-coordinate:

* the projectile's position in time:
xp = xp0 + v.t (xp0 = initial X position of P at t0)
* the planet B's angular position:
α = α0 + ω .t (α0 initial angle around the sun at t0, ω is angular velocity)
* the planet B's position:
xb = cos(α) = cos(α0 + ω .t)

I also think, I have to solve for t where xp == xb:

xp0 + v.t = cos(α0 + ω .t)

But i have no idea how to get the t out of that cosine :)

Thanks for any suggestion!

I just thought of the fact that I also don't know what the speed of P (v) is.. only that |v| is constant, but the angle and therefore its (x, y) are also unknown. damn :)

## 1. What is the definition of "Projectile angle (straight line) between 2 planets"?

Projectile angle (straight line) between 2 planets refers to the angle at which a projectile, such as a spacecraft or a meteor, is launched from one planet towards another planet in a straight line.

## 2. How is the projectile angle between 2 planets calculated?

The projectile angle between 2 planets is calculated using the laws of orbital mechanics, specifically the law of conservation of angular momentum. This involves taking into account the masses, distances, and velocities of the two planets to determine the optimal angle for the projectile to travel in a straight line between them.

## 3. What factors influence the projectile angle between 2 planets?

The main factors that influence the projectile angle between 2 planets are the masses and distances of the two planets, as well as their relative velocities. Other factors such as gravitational pull from other celestial bodies and atmospheric conditions may also play a role.

## 4. Can the projectile angle between 2 planets change over time?

Yes, the projectile angle between 2 planets can change over time due to the constantly changing positions and velocities of the two planets. This is why precise calculations and adjustments are necessary for successful interplanetary missions.

## 5. How is the projectile angle between 2 planets used in space exploration?

The projectile angle between 2 planets is crucial in space exploration as it determines the most efficient and accurate path for a spacecraft to travel between two planets. It is also used to plan and execute maneuvers, such as gravity assists, to conserve fuel and reduce travel time.

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