Newton's Law of Gravitation
Key Questions

Answer:
The Sun's gravitational force pulls on the planets which move perpendicular to this force at all times creating a elliptical (ideally circular) path around the Sun.
Explanation:
Let's use the Earth as an example:
As the Sun pulls the Earth towards it, the Earth moves very quickly (velocity around 30km/s) perpendicular to the force of gravity. These two forces create a resultant force pointed between the Sun and the Earth's path (let's just say this 30 degrees). Therefore, at all points around the Sun, the Earth will move at a 30 degree angle, creating a circle with radius r (r=93 million miles). 
In a stronger gravitational field a given mass will have a larger weight.
An object's weight is given by this equation:
#w=mg# Gravitational field strength at a distance, r, from a centre of mass is given by this equation:
#g=(GM)/r^2# If an object is nearer a centre of mass then r will be smaller so g will be larger. In that case the weight of the object will be larger. If an object is moved from a distance R away from one centre of mass and placed a distance R away from the centre of a smaller mass then g will be smaller. In that case the weight of the object will be smaller.
A practical example: if an astronaut on earth has a weight of 833 N, on the moon he/she will have a weight of 136 N.
Using
#m=w/g# the mass of the astronaut is#833/9.8=85 kg# .So the weight on the moon (
#g_M=1.6 Nkg^1# ) is:#w_M=mg_M=85×1.6=136 N#