# 6.6 Satellites and kepler’s laws: an argument for simplicity  (Page 5/5)

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## Conceptual questions

In what frame(s) of reference are Kepler’s laws valid? Are Kepler’s laws purely descriptive, or do they contain causal information?

## Problem exercises

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day. Such orbits are useful for communication and weather observation because the satellite remains above the same point on Earth (provided it orbits in the equatorial plane in the same direction as Earth’s rotation). Calculate the radius of such an orbit based on the data for the moon in [link] .

Calculate the mass of the Sun based on data for Earth’s orbit and compare the value obtained with the Sun’s actual mass.

$1.98×{\text{10}}^{\text{30}}\phantom{\rule{0.25em}{0ex}}\text{kg}$

Find the mass of Jupiter based on data for the orbit of one of its moons, and compare your result with its actual mass.

Find the ratio of the mass of Jupiter to that of Earth based on data in [link] .

$\frac{{M}_{J}}{{M}_{E}}=\text{316}$

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about $8\text{.}0×{\text{10}}^{\text{11}}$ solar masses. A star orbiting on the galaxy’s periphery is about $6\text{.}0×{\text{10}}^{4}$ light years from its center. (a) What should the orbital period of that star be? (b) If its period is $6\text{.}0×{\text{10}}^{7}$ instead, what is the mass of the galaxy? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.

Integrated Concepts

Space debris left from old satellites and their launchers is becoming a hazard to other satellites. (a) Calculate the speed of a satellite in an orbit 900 km above Earth’s surface. (b) Suppose a loose rivet is in an orbit of the same radius that intersects the satellite’s orbit at an angle of $\text{90º}$ relative to Earth. What is the velocity of the rivet relative to the satellite just before striking it? (c) Given the rivet is 3.00 mm in size, how long will its collision with the satellite last? (d) If its mass is 0.500 g, what is the average force it exerts on the satellite? (e) How much energy in joules is generated by the collision? (The satellite’s velocity does not change appreciably, because its mass is much greater than the rivet’s.)

a) $7\text{.}\text{4}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

b) $1\text{.}\text{05}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

c) $2\text{.}\text{86}×{\text{10}}^{-7}\phantom{\rule{0.25em}{0ex}}\text{s}$

d) $1\text{.}\text{84}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{N}$

e) $2\text{.}\text{76}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{J}$

Unreasonable Results

(a) Based on Kepler’s laws and information on the orbital characteristics of the Moon, calculate the orbital radius for an Earth satellite having a period of 1.00 h. (b) What is unreasonable about this result? (c) What is unreasonable or inconsistent about the premise of a 1.00 h orbit?

a) $5\text{.}\text{08}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{km}$

b) This radius is unreasonable because it is less than the radius of earth.

c) The premise of a one-hour orbit is inconsistent with the known radius of the earth.

Construct Your Own Problem

On February 14, 2000, the NEAR spacecraft was successfully inserted into orbit around Eros, becoming the first artificial satellite of an asteroid. Construct a problem in which you determine the orbital speed for a satellite near Eros. You will need to find the mass of the asteroid and consider such things as a safe distance for the orbit. Although Eros is not spherical, calculate the acceleration due to gravity on its surface at a point an average distance from its center of mass. Your instructor may also wish to have you calculate the escape velocity from this point on Eros.

#### Questions & Answers

a15kg powerexerted by the foresafter 3second
what is displacement
movement in a direction
Jason
hello
Hosea
Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
Hi
saeid
hi
Yimam
What is thê principle behind movement of thê taps control
while
Hosea
what is atomic mass
this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Explain why it is difficult to have an ideal machine in real life situations.
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
if the classica theory of specific heat is valid,what would be the thermal energy of one kmol of copper at the debye temperature (for copper is 340k)
can i get all formulas of physics
yes
haider
what affects fluid
pressure
Oluwakayode
Dimension for force MLT-2
what is the dimensions of Force?
how do you calculate the 5% uncertainty of 4cm?
4cm/100×5= 0.2cm
haider
how do you calculate the 5% absolute uncertainty of a 200g mass?
= 200g±(5%)10g
haider
use the 10g as the uncertainty?
melia
which topic u discussing about?
haider
topic of question?
haider
the relationship between the applied force and the deflection
melia
sorry wrong question i meant the 5% uncertainty of 4cm?
melia
its 0.2 cm or 2mm
haider
thank you
melia
Hello group...
Chioma
hi
haider
well hello there
sean
hi
Noks
hii
Chibueze
10g
Olokuntoye
0.2m
Olokuntoye
hi guys
thomas
the meaning of phrase in physics
is the meaning of phrase in physics
Chovwe