23 votes
Accepted

How could 99942 Apophis, in 2029, be captured and brought into a low Earth orbit?

The edge of Earth's Hill Sphere is about 929000 km, so in order to capture Apophis, it needs to decelerate from a hyperbolic orbit to an elliptical one with an apogee of at most 929000 km. In 2029, ...
user avatar
14 votes

Do two objects with intersecting orbits have to collide given enough time?

I can't offer analysis of your hypothetical ideal case, but in real cases of small or random objects in the solar system, it seems that the trajectory becomes sufficiently indeterminate with ...
user avatar
  • 748
12 votes

How far is the solar system's center of mass from the sun?

The solar system barycenter, as it's called, is a dynamic point that moves (or the Sun moves relative to, depending on how you think about it) depending on where the planets are in their orbits and ...
user avatar
12 votes

Do two objects with intersecting orbits have to collide given enough time?

One way to look at it, is in terms of the orbital periods. The gray dot will be at the intersection point on every multiple of its period, minus any initial offset: $k_gT_g - \theta_g$ If the purple ...
user avatar
  • 301
9 votes

How could 99942 Apophis, in 2029, be captured and brought into a low Earth orbit?

In 2029? We can't. I doubt that that the next two closest approaches after 2029 (2036 and 2051) are within reach. We might be able to do it by 2116, or maybe even 2066. An object as large as Apophis ...
user avatar
  • 62.8k
8 votes
Accepted

How to find the hyperbolic angle given the mean anomaly?

Like the corresponding eccentric anomaly for elliptical orbits, there is no closed-form formula for going from mean anomaly to hyperbolic anomaly. You're going to have to use some sort of numerical ...
user avatar
  • 4,251
7 votes

What is the maximum distance between two satellites orbiting at 400 km that would still allow them to communicate with each other using radio waves?

Imagine a circle (the circumference of the Earth) and a triangle with the angle points being the locations of the satellites and the centre of the Earth. (the centre of the circle) You can divide that ...
user avatar
  • 7,042
6 votes

What is the maximum distance between two satellites orbiting at 400 km that would still allow them to communicate with each other using radio waves?

Probably not quite what you're looking for, but two satellites on opposite sides of Earth, 13542 km apart, can still stay in almost-uninterrupted contact via EME communications (bouncing the signal ...
user avatar
6 votes

What is the maximum distance between two satellites orbiting at 400 km that would still allow them to communicate with each other using radio waves?

For line-of-sight communication it's not longer than $2\sqrt{ (6371+400)^2 - (6371)^2} = 4585$. Or $2\cos^{-1}\left(\frac{6371}{6371+400}\right)$ = 40 degrees, so 9 satellites at least.
user avatar
  • 1,249
5 votes
Accepted

What is the maximum distance between two satellites orbiting at 400 km that would still allow them to communicate with each other using radio waves?

If, for example, you have only 2 satellites separated by half the distance (i.e., 21, 271 km), will they be able to communicate with each other? I guess not because Earth would be in the way. ...
user avatar
4 votes

Do two objects with intersecting orbits have to collide given enough time?

Short answer: maybe. The answer depends on the depth of modelling and the nature of the bodies. In order to predict a collision at all, your modelling has to be accurate at least down to the objects' ...
user avatar
  • 1,682
3 votes

How could 99942 Apophis, in 2029, be captured and brought into a low Earth orbit?

The Hill sphere delta-V is the minimum possible for Earth to capture Apophis from the Sun. To go all the way to LEO, as in the question title, you have to decelerate a lot more than that. Note first ...
user avatar
  • 5,162
3 votes
Accepted

State vector conversion when changing central body

You can get velocities of planets (and other higher order derivatives also in fact) from the Chebyshev coefficients. As @DavidHammen points out in this answer, the Chebyshev polynomial coefficients ...
user avatar
  • 1,446
3 votes

State vector conversion when changing central body

SPICE only supports frame conversion when all of the state information is stored in one of the kernels. For your onboard GNC, you'll need to perform the vector summation independently. For example, if ...
user avatar
  • 5,775
3 votes

How does one calculate the look angle for non-geo satellites (i.e. LEO, HEO, etc.)

In your equation for $t_2$, the middle term ought to be $$-\sin(earth_{LAT})*\sin(earth_{LON})$$ not $$-\sin(earth_{LAT})*\sin(earth_{LAT})$$ Check to see if your code has the same error. You should ...
user avatar
  • 5,162
2 votes

How do I correctly convert State Vectors to Orbital Elements to State Vectors at t (sec since epoch) in 2D?

The full solution is to choose a different set of orbital elements, but in this case, you can get away with just tweaking how you calculate the standard ones. In Step 1a, the specific angular momentum,...
user avatar
  • 5,162
1 vote

How could 99942 Apophis, in 2029, be captured and brought into a low Earth orbit?

It depends on how much of Apophis you want to capture. As others have stated, Apophis is estimated to have a mass of 2.7e10 kg, which needs to experience a dv change of about 4187 m/s. However, a ...
user avatar
  • 111
1 vote
Accepted

Are there any studies on Mars-Earth ballistic cyclers taking Mars-gravity assist into account?

Earth-Mars-Earth trajectories are objectively possible, see the Rosetta mission and Europa Clipper. Mars' eccentricity and inclination causes problems finding periodic, repeating solutions (and is ...
user avatar
1 vote

What is the maximum distance between two satellites orbiting at 400 km that would still allow them to communicate with each other using radio waves?

This depends on the wavelength. While short waves spread more like a light, long waves bend over horizon and can cover distances in excess of 17,000 km even from the surface of the Earth. This is more ...
user avatar
  • 1,666
1 vote

State vector conversion when changing central body

You may look at the C library calceph for the evaluation of the state vectors of the solar system bodies : https://www.imcce.fr/inpop/calceph https://gitlab.obspm.fr/imcce_calceph Chebyshev ...
user avatar
1 vote

Do two objects with intersecting orbits have to collide given enough time?

In a pure three-body system, I think the Lagrange points L4 and L5 are examples. I think a small object close to L4 or L5 will stay close, but, viewed in the frame of the largest mass, the orbit of ...
user avatar
  • 6,903
1 vote

What is the relationship between the periapsis altitude and the change in velocity in a gravity assist?

The link in the question is 404 dead but I think this image from a different question could explain your observation: (Source) There is a maximum but this representation is not the scenario you ...
user avatar
1 vote

Determining the spacecraft position vector with respect to ICRF frame for Venus flyby

If you mean "obtaining the position vector of the spacecraft near Venus in the ICRF frame with respect to the solar system barycenter" or "obtaining the position vector of the ...
user avatar

Only top scored, non community-wiki answers of a minimum length are eligible