Try these "busters" to exercise your brain ... they should help you grasp the concepts underlying gravity. To gain the maximum effect you should attempt to answer them before looking at the answers!
[1] Somewhere between the Earth and Moon the gravitational attraction of these two objects would cancel out. Where is the location?
[2] The weight of an apple near the Earth's surface is about 1N. What is the weight of the Earth in the gravitational field of the apple?
[3] If you want to make a profit by buying precious metals at one altitude and selling at a different altitude for the same price per body weight, should you buy or sell at the higher altitude?
[4] The planet Jupiter is more than 300 times the mass of the Earth, so it may seem that an object on the surface of Jupiter should weight more than 300 as much as it does on Earth. However, it so happens that an object would weigh only about 3 times as much ... why is that?
[5] Can you estimate the radius of Jupiter relative to the Earth from the data in question [4]?
[6] Imagine a skydiver falling at terminal speed ... is she weightless? What about a scuba diver hovering in water? How about a "space-walking" astronaut?
[7] If the mass of the Earth increased, you weight would increase also. What would happen to your weight if the mass of the Sun increased?
[8] If the Earth were of uniform density, i.e., the same mass/volume throughout, what would be the value of g be inside the Earth at one-half its radius?
[9] It so happens that your weight increases when you go down a mineshaft. What conclusions can you draw from that observation?
[10] If you could somehow tunnel inside a star, would you weight increase or decrease? If, instead you stood on a shrinking star, what would happen to your weight?
[11] To get an idea of the strength of the gravitational force between the Earth and the Sun, pretend that gravity is switched off and that, instead, there is a steel cable attaching the Earth to the Sun. Estimate the diameter of such a cable if you know that the tensile strength of the cable is 5 × 108N/m2, i.e., each square meter of cross section can support a force of 5 × 108N. Do you find the result surprising?
[12] Can you think of the reason why satellites are normally sent into orbit by firing them in an easterly direction?
[13] Neglecting air resistance, could a satellite be put into orbit in a tunnel below the Earth's surface?
[14] I like this one! Using only the fact that the radius of the Earth is 6400km and g ~9.8m/s2 can you show that the tangential speed of a satellite in a near-Earth orbit is ~8000m/s? (You do not need to know ... the Gravitational constant, the mass of the Earth, etc!)
[15] If a mechanic drops a wrench from a jumbo jet flying at 550mph at 30,000ft, you know that the wrench will fall towards the Earth and crash into the surface. If an astronaut on an orbiting space lab drops a wrench, would it crash into the Earth also?
[16] Imagine a space station traveling at 8km/s with respect to the Earth's surface. Suppose a capsule is ejected rearward at 8km/s, with respect to the space station. What will happen to the capsule?
[17] Here's a nice one! What is the maximum possible speed of impact on the surface of the Earth for a very distant object, initially at rest, that falls towards the Earth under the influence of the Earth's gravity alone? Neglect air resistance.
[18] Assuming that the rocket engines only operate for a short time, which requires more fuel, to send a spacecraft from the Earth to the Moon or the same spacecraft from the Moon to the Earth? Why? What about a journey from the Moon to Mars and the return journey from Mars to the Moon?
[19] (You don't need formulas here!) A rocket is fired from the surface of the Earth at a speed that is twice the escape speed. What would its speed be a great distance from the Earth?
[20] (I wonder if Newton thought about this one!) Newton's Law of gravitation tells us that, if we have concentrated masses, like point masses or spherical balls, the attractive force increases as the masses are brought closer together. Can you think of any situation where that is not the case, i.e., where the attractive decreases as the masses are brought closer together?