Samuel Chiltern answered
The Earth, Sun and the Moon are all roughly-spherical, but if you want a more accurate description, then I'm afraid it won't be easy. I'll try to explain our best understanding of these three astronomical bodies in the rest of my answer.
The Shape of the Sun
The Sun has been the most challenging object (of those you mentioned) of which to accurately measure the shape. Over the years, scientists have taken a lot of measurements, but most of them don't agree.
Until recently, we believed that the shape of the Sun varied with the flow of material within its interior and atmosphere, in particular as the heavy metals inside the star move around. However, a recent study has suggested that this is not the case.
It would seem that the Sun is spherical, with a slightly-flattened shape. This gives it a more width at the equator, and less distance between its poles, and we now believe that it stays this way all the time.
The Shape of the Earth
Generally, the Earth is considered to be perfectly spherical (I'm sure most people have looked at a globe before), and this model is fine for everyday understanding.
However, if accurate measurements are needed, then the approximate shape of the Earth should be considered to be an oblate spheroid, which again is the same kind of shape as the Sun.
The Shape of the Moon
Again, the Moon has a broadly similar shape, and it too bulges at the equator. But the most interesting thing is that the near side of the Moon is several kilometres higher.
The near side is the only side we can see from Earth, due to the way the Earth and Moon rotate in relation to each other, so scientists think this is due to the effects of the gravitational pull of the Earth upon the Moon.
The Shape of the Sun
The Sun has been the most challenging object (of those you mentioned) of which to accurately measure the shape. Over the years, scientists have taken a lot of measurements, but most of them don't agree.
Until recently, we believed that the shape of the Sun varied with the flow of material within its interior and atmosphere, in particular as the heavy metals inside the star move around. However, a recent study has suggested that this is not the case.
It would seem that the Sun is spherical, with a slightly-flattened shape. This gives it a more width at the equator, and less distance between its poles, and we now believe that it stays this way all the time.
The Shape of the Earth
Generally, the Earth is considered to be perfectly spherical (I'm sure most people have looked at a globe before), and this model is fine for everyday understanding.
However, if accurate measurements are needed, then the approximate shape of the Earth should be considered to be an oblate spheroid, which again is the same kind of shape as the Sun.
The Shape of the Moon
Again, the Moon has a broadly similar shape, and it too bulges at the equator. But the most interesting thing is that the near side of the Moon is several kilometres higher.
The near side is the only side we can see from Earth, due to the way the Earth and Moon rotate in relation to each other, so scientists think this is due to the effects of the gravitational pull of the Earth upon the Moon.
