¿Cuál es la diferencia entre He tried to launch the shuttle on his own y He tried to launch the shuttle himself ?Puedes dar oraciones como ejemplo.

HIMSELF means he does it without the help of anybody else and he does it when he is alone. He tried to launch the shuttle without any crew member assisting him.

ON HIS OWN is mostly used for a situation. When he tried to launch the shuttle, he felt lonely because the crew left him to do the work with no assistance. It could also mean he was doing it on his own initiative without anyone telling him to do it.

Another example is :
I live by myself.
I live on my own.

The first sentence connotates that I don't have any parents, siblings, housemates, or romantic partners that live with me. There is no other cohabitant in the house with me.

The second sentence connotates that no one visits me when I need them the most and I am lonely and isolated.

The first sentence can also be implied as a remark of loneliness while the second one is of independence and self sufficiency, as my explanation before.

Another example:
We're by ourselves now.
We are on our own now.

The first sentence implies that we are finally left without assistance, finally alone and have the freedom and time. The second one describes an opportunity to do more actions, though we are left to suffer to our own devices.