- #1
RandallB
- 1,550
- 0
Unless you have orbital geometry down cold this might take a little thinking.
SET UP
A large independent planet with a thick atmosphere included is 100 Mega-meters in diameter. Beyond that diameter we can consider that we have a real vacuum outside that diameter. “Independent” only means we will be ignoring any affect from a sun. It has a non-wobbling spin so we can always locate “the spot” 100 Mega-meters above the North Pole. An object is propelled straight up from the North Pole so that it will just reach “the spot” before gravity will return to the North Pole starting point on the surface.
When the object momentarily stops at “the spot” we can give it a velocity of X or less on any heading we choose.
We will consider headings as viewed from the side measured as 00 continuing straight away from the planet (north); around to 1800 for straight back down to the north pole surface; and around to 3600 for the same direction as 00 straight away.
The max speed of X is exactly the escape velocity for a heading of 900.
1. At what other headings can escape be achieved?
2. At what headings does X need to be reduced so the object just reaches the infinity escape without any extra speed?
3. By how much do we need to reduce X, in order to establish the maximum possible orbits that allow a free return to “the spot”.
4. And what headings can we use to achieve those free returns to “the spot”?
(note: ignore "progresion")
For the orbital pros that know they know, use white for the first few days.
If you're guessing, no need for white.
RB
SET UP
A large independent planet with a thick atmosphere included is 100 Mega-meters in diameter. Beyond that diameter we can consider that we have a real vacuum outside that diameter. “Independent” only means we will be ignoring any affect from a sun. It has a non-wobbling spin so we can always locate “the spot” 100 Mega-meters above the North Pole. An object is propelled straight up from the North Pole so that it will just reach “the spot” before gravity will return to the North Pole starting point on the surface.
When the object momentarily stops at “the spot” we can give it a velocity of X or less on any heading we choose.
We will consider headings as viewed from the side measured as 00 continuing straight away from the planet (north); around to 1800 for straight back down to the north pole surface; and around to 3600 for the same direction as 00 straight away.
The max speed of X is exactly the escape velocity for a heading of 900.
1. At what other headings can escape be achieved?
2. At what headings does X need to be reduced so the object just reaches the infinity escape without any extra speed?
3. By how much do we need to reduce X, in order to establish the maximum possible orbits that allow a free return to “the spot”.
4. And what headings can we use to achieve those free returns to “the spot”?
(note: ignore "progresion")
For the orbital pros that know they know, use white for the first few days.
If you're guessing, no need for white.
RB