Page 107 - text book form physics kssm 2020

Chapter 3
Gravitation
(a) Th e radius of the orbit of planet Mars can be determined by comparing the orbit of Mars
with the orbit of the Earth. What information is needed to determine the radius of the
orbit of Mars?
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(b) Th e radius of the orbit of the Earth is 1.50 × 10 m, orbital period of the Earth and Mars
is 1.00 year and 1.88 years respectively. Calculate the radius of the orbit of Mars.
Solution:

(a) Radius of the orbit of the Earth, orbital period of the Earth and orbital period of Mars.
(b) Radius of orbit of the Earth, r = 1.50 × 10 m
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Step 1
Radius of orbit of Mars = r
List the given information 14243 Orbital period of Mars, T = 1.88 years
2
in symbols. Orbital period of the Earth, T = 1.00 years
1
2
Step T 2 r 3 SMART
SMART
Identify and write down the 14243 T 1 2 = r 1 3 INFO
formula used. 2 2 T 2 r 3
The equation 1 2 = 1 3 involves
1.00 2 (1.50 × 10 ) T 2 r 2
11 3
= the orbital period of a planet
1.88 2 r 3
2 divided by the orbital period
Step (1.50 × 10 ) × 1.88 2 of another planet. The same
11 3
3
Substitute numerical values r = 1.00 2 unit needs to be used for
2
into the formula and 14444244443 both periods.
11 3
perform the calculations. 2 2
3 (1.50 × 10 ) × 1.88
r =
1.00 2
= 2.28 × 10 m
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Example 2
Figure 3.31 shows that a research satellite needs to orbit at a height of 380 km to capture clear
images of the surface of the Earth. What is the orbital period of the satellite?
Moon

r
2
Earth

r
h 1
2
Satellite 1
h
1

Earth at the centre

Figure 3.31
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[Radius of the orbit of the Moon = 3.83 × 10 m, orbital period of the Moon = 655.2 hours]
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3.2.3 101
3.2.3