I thought that centripetal force is an external force that is needed in order for the planet to follow a curved path/orbit?
I also think that the explaination is...
They look like Sphere because of the nature or gravity, think of gravity as a force that pulls inwards, towards the centre, hence why we when we jump, when are pulled/attracted back to eath again (the earth also is attracted to us when we jump) towards the centre. So every part of the planet is being pulled towards the centre, forming a sphere shape, apart from mountians etc. The larger a planet gets, gravity gets stronger, so any large mountians etc are crushed, making it a more perfect sphere. Hence why we don't have mountians that are 50 miles high or sky scrappers with loads of stories.
But they are not always a perfect sphere, take Earth for example. If a car was to travel non stop around the equator at 100km/h (about 62mph), it would take 16 days 16 hours and 45 minutes. A car driving around the Earth from North Pole to South Pole and back round would finish 80 minutes earlier. (I read it somewhere). This is because the earth's diameter at the equator is 7, 926 miles as opposed to between the poles at only 7, 900 miles (roughly). The Earth bulges at teh equator because of the Earthis 24 hour rotation.
If you want to know more about Orbits, its Keplers laws I think you need
Em