4th ESO B
Unit 3: GRAVITY
IES Laguna de Joatzel
Force of gravity
Newton´s law of universal gravitation: 𝐹 = 𝐺 ∙
𝑚1 ∙𝑚2
𝑑2
𝐺 = 6.67 ∙ 10−11 𝑁 ∙ 𝑘𝑔−2 ∙ 𝑚2
1. Calculate the force of gravity between the Moon and the Earth if the distance between their
centres is 3.9·109 m. We know that the mass of the Earth is 5.98·1024 kg and the mass of the Moon
is 7.47·1022 kg.
2. Calculate how much an astronaut of 70 kg of mass weighs on the surface of the Moon. Compare
it with its weight on the Earth. We know that the mass of the Moon is 7.47·1022 kg and the radius of
the Moon is 1738 km.
3. Calculate the force of attraction between two bodies of 12 kg and 20 kg which are separated 50
cm.
4. Calculate the force of attraction between the Earth and the Sun. Data: MS=1.98·1030 kg;
ME=5.98·1024 kg; average distance between the Sun and the Earth=1.50·1011 m.
5. Two bodies of 200 kg are separated by a distance of 50 cm. How much is the force of gravity
between them? Draw the forces.
6. An astronaut of 60 kg of mass is attracted by a force of 270 N when her distance to the centre of a
planet is 5000 km. Calculate the mass of the planet.
Acceleration of gravity
𝑔=𝐺∙
𝑀
𝑀
=𝐺∙
2
𝑑
(𝑅 + ℎ)2
7. Calculate the acceleration of gravity at a height of 300 km on the Earth. Data: ME=5.98∙1024 kg.
RE=6378 km. G=6.67∙10-11 N∙m2∙kg-2.
8. a) Calculate the acceleration of gravity on the surface of the moon.
b) If we drop an object at a height of 10 m on the moon, calculate its velocity when it reaches the
ground.
c) Solve the same problem of letter b) if we now drop the object from the same height but in the
Earth.
MM=7.47∙1022 kg. RM=1738 km.
Orbital speed
𝐹𝑐 = 𝐹𝑔
𝑚∙
𝑣2
𝑀∙𝑚
=𝐺∙
𝑑
𝑑2
𝑣 = √𝐺 ∙
𝑀
𝑑
9. Calculate the orbital speed of a satellite that orbits around the Earth at a height of 650 km. Data:
ME=5.98·1024 kg; RE=6378 km.
10. Calculate the orbital speed of a satellite located at a height of 500 km on the Earth. Data:
ME=5.98∙1024 kg. RE=6378 km.
11. It is interesting for a satellite to have the same period (time it takes to turn one revolution) than
the planet it orbits around. For example, if we want a satellite to study a zone of the Earth, it would
be interesting that its period was 24 hours, so that it is always located in the position it studies.
Calculate the height of this satellite. Data: ME=5.98∙1024 kg. RE=6378 km.
12. Positive charges and negative charges are attracted by a force that is called electric force. You
can calculate this force using this formula:
Coulomb´s law: 𝐹 = 𝐾 ∙
|𝑞1 |∙|𝑞2 |
𝑑2
𝐾 = 9 ∙ 109 𝑁 ∙ 𝐶 −2 ∙ 𝑚2
Compare the force of gravity and the electric force between the proton and the electron on protium,
one of the isotopes of hydrogen (it has 1 proton and 1 electron).
What do you think is the force that makes electrons orbit around a nucleus?
Data:

Mass of a proton: 1.67∙10-27 kg.

Mass of an electron: 9.1∙10-31 kg.

Charge of a proton: +1.6∙10-19 C.

Charge of an electron: -1.6∙10-19 C.

Distance between the proton and the electron in protium: 5.3∙10-11 m.