how can I use string variable from text input to refer to an array of the same name

If planets_num is in global scope, you can also refer to it like this:

arraytouse = window['planets_num'];

Variables on objects are also indexable values on that object by the same name. For global scope variables, they're on the window object.

So you could do something like this:

arraytouse = window[document.getElementById('mynewtext').value];

If the arrays aren't in global scope then you can organize them as properties on some object and reference that object in the same way:

arraytouse = objectOfArrays[document.getElementById('mynewtext').value];

@David answer is cleaner is more efficient, but here is an alternative with an eval:

var my_array = [];

$("button")[0].onclick = function()
{
    var input_text = $("input")[0].value;
    var array_input = eval(input_text);
}

The fiddle is here:

http://jsfiddle.net/W3NW9/3/

Rather than creating global variables, you should consider using an object and properties:

var data = {
  planets_num: [],
  another_arr:[]
}

Now you can do:

var arraytouse = data[document.getElementById('mynewtext').value];

but of course you should be writing robust code like:

var input = document.getElementById('mynewtext');

// Make sure an element was found before trying to access its value
var arraytouse = input && data[input.value];

// Make sure the value resolved to something truthy before
// trying to use it
if (arraytouse) {
  ...
}