The gravitational force is directly proportional to Mass of the objects. Since the Earth has much larger mass than the Moon, it's gravitational pull is stronger.

Dr Robert Holmes and Dr Hamish Dsouza thank you for your contribution to the discussion

Gravity is the main force to be dealt with in space, and thrust is the force that allows a spacecraft to get into space and maneuver. A spacecraft in orbit is not beyond the reach of Earth's gravity. In fact, gravity is what holds it in orbit without gravity; the spacecraft would fly off in a straight path. To move in a curved path, a planet must have acceleration toward the center of the circle. This is called centripetal acceleration and is supplied by the mutual gravitational attraction between the Sun and the planet. The planets all formed from this spinning disk-shaped cloud, and continued this rotating course around the Sun after they were formed. The gravity of the Sun keeps the planets in their orbits. They stay in their orbits because there is no other force in the Solar System which can stop them. The gravity of the sun keeps all the planets in orbit in our solar system. However, each planet, moon and asteroid have their own gravitational pull defined by their density, size, mass, and proximity to other celestial bodies. The gravity on Jupiter is greater than the gravity on Earth because Jupiter is more massive. Although Jupiter is a great deal larger in size, its surface gravity is just 2.4 times that of the surface gravity of Earth. Not only is the Moon smaller than the Earth, but it is only about 60 percent as dense as Earth. Thus, the gravitational attraction on the Moon is much less than it is here on Earth, and a person weighs less on the Moon. Gravitational force on the surface of the moon is only 16 as strong as gravitational force on the earth. Earth's gravity comes from all its mass. All its mass makes a combined gravitational pull on all the mass in your body. That's what gives you weight and if you were on a planet with less mass than Earth, you would weigh less than you do here.Earth has 6 times the gravitational acceleration at its surface than the moon has at its surface.

Dr Robert Holmes thank you for your contribution to the discussion

Not only is the Moon smaller than the Earth, but it is only about 60 percent as dense as Earth. Thus, the gravitational attraction on the Moon is much less than it is here on Earth, and a person weighs less on the Moon. The Earth has a mass of about 5.972 × 10^24 kilograms, while the Moon has a mass of about 7.347 × 10^22 kilograms. This means that the Earth's gravity is about 6 times stronger than the Moon's gravity. Even though the sun is much more massive and therefore has stronger overall gravity than the moon, the moon is closer to the earth so that its gravitational gradient is stronger than that of the sun. Since the Moon has a force of gravity which is 6 times lesser than Earth's, why doesn't it collapse into the Earth? Earth's mass is about 81 times the mass of the Moon; therefore Earth's gravity is about 81 times greater than the gravity of the Moon. However, given that the Moon is smaller than Earth, the pull of gravity on Earth's surface is only about 6 times greater than the pull of gravity on the Moon's surface. Gravitational force on the surface of the moon is only 16 as strong as gravitational force on the earth. Earth's gravity comes from all its mass. All its mass makes a combined gravitational pull on all the mass in your body. That's what gives you weight. And if you were on a planet with less mass than Earth, you would weigh less than you do here.The gravitational attraction between the Earth and the moon is strongest on the side of the Earth that happens to be facing the moon, simply because it is closer. This attraction causes the water on this “near side” of Earth to be pulled toward the moon. The planets all formed from this spinning disk-shaped cloud, and continued this rotating course around the Sun after they were formed. The gravity of the Sun keeps the planets in their orbits. They stay in their orbits because there is no other force in the Solar System which can stop them. To move in a curved path, a planet must have acceleration toward the center of the circle. This is called centripetal acceleration and is supplied by the mutual gravitational attraction between the Sun and the planet. That's because the planets weigh different amounts, and therefore the force of gravity is different from planet to planet. For example, if you weigh 100 pounds on Earth, you would weigh only 38 pounds on Mercury. That's because Mercury weighs less than Earth, and therefore its gravity would pull less on your body. The gravity of the sun keeps all the planets in orbit in our solar system. However, each planet, moon and asteroid have their own gravitational pull defined by their density, size, mass, and proximity to other celestial bodies.