2. calculate the average magnitude of the force of gravity on the planet neptune (mass of 1.02*10^ 26 kg) due to the sun (mass of 1.99*10^ 30 kg) , assuming an average orbital distance of 4.50*10^ 12 m.

The answer to your question is: F = 6.69 x 10²⁰ N

Explanation:

To solve this problem we need to use the Newton's law of universal gravitation.

F = G(m1m2)/r²

where

F = ?

G = 6.674×10−11 N · (m/kg)2  is the gravitational constant

m1 = Neptune mass = 1.02 x 10²⁶ kg

m2 = Sun mass = 1.99 x 10³⁰ kg

r orbital distance among the planets = 4.50 x 10¹² m

Substitution

F = 6.674×10−11 N · (m/kg) x 1.02 x 10²⁶ kg x 1.99 x 10³⁰ kg / (4.50 x 10¹² m)²

F = 1.355 x 10⁴⁶ / 2.025 x 10²⁵

F = 6.69 x 10²⁰ N

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

scientific laws are the result of testing theories and proving them to be facts.