1. Sun (3×3)

4	9	2
3	5	7
8	1	6

Method: Use the Siamese method for odd orders:

Start in the middle of the top row (2,1).
Move diagonally up and right; if you go off the grid, you wrap around. If a cell is already filled, move down instead.
Fill in numbers from 1 to 9.

2. Moon (9×9)

4	14	15	1	2	12	23	24	34
32	3	13	8	9	19	22	31	35
17	27	2	7	11	21	26	30	40
37	36	33	16	10	20	25	29	41
18	28	42	5	6	38	43	39	44
45	55	54	51	46	53	48	47	50
56	61	59	57	52	60	49	58	64
62	63	71	66	65	70	68	69	67
81	76	74	72	73	75	77	78	79

Method: Use a modified version of the Siamese method with additional rules for wrapping and filling in specific patterns.

3. Mercury (8×8)

8	58	59	5	4	62	63	1
49	15	14	52	53	11	10	56
41	23	22	44	45	19	18	48
32	34	35	29	28	38	39	25
40	26	27	37	36	30	31	33
17	47	46	20	21	43	42	24
9	55	54	12	13	51	50	16
64	2	3	61	60	6	7	57

Method: Use the LUX method for even number squares:

Fill the square with numbers 1 to 64 sequentially.
Swap numbers based on a particular pattern to achieve the magic property.

4. Venus (7×7)

22	47	16	41	10	35	4
5	23	48	17	42	11	29
30	6	24	49	18	36	12
13	31	7	25	43	19	37
38	14	32	1	26	44	20
21	39	8	33	2	27	45
46	15	40	9	34	3	28

Method: Use the Siamese method, similar to the Sun square but for 7×7.

5. Mars (5×5)

11	18	25	2	9
10	12	19	21	3
4	6	13	20	22
23	5	7	14	16
17	24	1	8	15

Method: Use the Siamese method for odd orders.

6. Jupiter (4×4)

4	14	15	1
9	7	6	12
5	11	10	8
16	2	3	13

Method: A simple pattern for 4×4:

Place 1 in the top right corner, then move diagonally down-left, wrapping around edges. Place numbers in sequence, but there are specific rules for 4×4 like swapping numbers to achieve magic properties.

7. Saturn (3×3)

Same as Sun’s square but traditionally has different connotations:

4	9	2
3	5	7
8	1	6

Method: Same Siamese method as described for the Sun.

Note:

Each square’s magic constant (sum of numbers in any row, column, or diagonal) is unique to its size and the numbers used.
These methods are traditional; there are modern algorithms, but these instructions give you a straightforward way to construct each planetary kamea manually.
For complex squares like the Moon’s, you might need to refer to detailed instructions or diagrams for exact placement due to the complexity of wrapping and pattern filling.

Explanation of the Siamese Method for Magic Squares

The Siamese method, also known as the “De la Loubère method,” is a technique for constructing odd-order magic squares. Here’s how it works:

Steps for Creating an Odd-Order Magic Square Using the Siamese Method:

Start Positioning:
- Begin by placing the number 1 in the middle cell of the top row. For example, in a 3×3 square, you would place 1 in the cell at position (1,2) where rows are numbered from top to bottom and columns from left to right.
Movement Rule:
- After placing each number, the next number moves diagonally up and to the right. If this move takes you:
  - Off the top of the grid: Wrap around to the bottom row (last row).
  - Off the right side of the grid: Wrap around to the left column (first column).
Handling Obstacles:
- If the next diagonal up and right position is already occupied (i.e., if you encounter a number you’ve already placed), then instead of moving diagonally, move straight down one cell from your current position.
Continue Until Complete:
- Keep placing numbers in sequence, following these rules until the square is filled with numbers from 1 to n², where n is the order of the square.

Example for a 3×3 Square:

Step 1: Place 1 in the middle of the top row (position 1,2):

–	–	1
–	–	–
–	–	–

Step 2: Move diagonally up-right (which wraps to bottom-left), place 2:

–	–	1
–	–	–
2	–	–

Step 3: Move up-right, place 3:

–	–	1
–	3	–
2	–	–

Step 4: Move up-right, but since 1 is there, move down instead, place 4:

–	4	1
–	3	–
2	–	–

Step 5: Move up-right, place 5:

–	4	1
–	3	5
2	–	–

Step 6: Move up-right, but since 3 is there, move down instead, place 6:

–	4	1
6	3	5
2	–	–

Step 7: Move up-right, place 7:

–	4	1
6	3	5
2	–	7

Step 8: Move up-right, place 8:

8	4	1
6	3	5
2	–	7

Step 9: Move up-right, but since 4 is there, move down instead, place 9:

8	4	1
6	3	5
2	9	7

This results in the completed 3×3 magic square where the sum of each row, column, and diagonal is 15.

Characteristics:

This method works for all odd-order squares (3×3, 5×5, 7×7, etc.).
It ensures that every number from 1 to n² is used exactly once, maintaining the magic property of the square.

This method is quite intuitive once you get the hang of the movement rules, making it an effective way to manually construct magic squares.