7.1.2 Gravity on Earth

Question 1

Gravity on Earth

Answer 1

• When calculating the force of gravity between two objects using Newton’s law of gravitation, r is the distance between the centers of mass of the objects.
• For practical purposes, the acceleration due to gravity is 9.8 m/s2anywhere near the surface of the Earth.
• Newton’ deduced that the law of gravitation was correct by comparing the acceleration of the Moon to the acceleration of objects near the Earth.
• Sir Henry Cavendish first measured Gin 1798 using a torsion balance.

Question 2

Consider two balls of masses 100 kg and 200 kg and radii of 0.1m and 0.2m respectively. The gravitational force between them is 5*10^-7N. What is the shortest distance between the surfaces of the two balls?

Answer 2

1.33 m

Question 3

Consider two balls of masses 100 kg and 200 kg and radii of 0.1m and 0.2m respectively. The centers of the two balls are separated by 2m. The gravitational force between them is 5*10^-7N. What is their mass?

Answer 3

173.16 kg

Question 4

Consider two balls of masses 100 kg and 200 kg and radii 0.1 m and 0.2 m respectively. Suppose that their centers are separated by 2 m. What is the gravitational force between them?

Answer 4

3.34*10^-7 N

Question 5

Consider a planet moving around a star in a near-circular orbit. The mass of the star is 6.0*10^35 kg. The period of the planet (the time it takes for the planet to go around the star once) is about 2.5 years. What is the distance between the star and the planet?

Answer 5

1.85*10^13 m

Question 6

Consider a planet moving around a star in a near-circular orbit. The period of the planet is 20 years. The distance between the star and the planet is 2.010^13m. The star’s radius (rs) is 3.010^9m. What is the gravitational acceleration on the surface of the start (as)?

Answer 6

8.82*10^4 m/s^2

Question 7

Consider a planet moving around a star in a near-circular orbit. The mass of the star is 6.010^35 kg. The period of the planet (the time it takes for the planet to go around the star once) is about 2.5 years. The distance between the star and the planet is about 2.010^13m. What is the mass of the star?

Answer 7

7.62*10^35 kg

Question 8

Consider two asteroids of masses 1.010^15 kg and 3.010^15 kg. Suppose that their centers are separated by 100 km. What is the acceleration of the asteroid with the smaller mass due to the mutual gravitational force?

Answer 8

2.00*10^-5 m/s^2

Question 9

Consider two asteroids of masses 1.010^15 kg and 3.010^15 kg. Suppose that the heavier asteroid experiences a gravitational acceleration of 3.0*10^-5 m/s^2.. What is the distance between the two asteroids?

Answer 9

47.2 km