A body in the solar system has a period of 10,759.22 days and a perihelion speed of 10.18 km/s. a. Calculate the aphelion radius in nautical miles (14 points). b. Calculate the eccentricity (2 points). c. Extra credit: Name the object. (6 points).

Explanation:

From the information given, by applying Kepler's 3rd law,

where;

T = period

a = semi major axis

T = 356 days (for earth)

a = 1 AU = 1.496

Therefore,

c = 3.9791

However, if the body in the solar system has a period of 10.759.22 days, then, a =?

∴

a = 1.4275

However, the velocity for a perihelion = 10.18 km/s

Using the formula

to calculate the radius, we have:

G =

M =

r = perihelion

Similarly, the perihelion is expressed by the equation,

r = a(1 - e)

where ;

e= eccentricity

∴

e ( eccentricity) = 0.0533

Aphelion radius in natural miles, r = a( 1+ e)

to nautical miles, we have:

radius of aphelion nautical miles

In respect to the value of a( i.e

the body of the solar system is Saturn

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