Answer:
3.523 * 10²² N
Explanation:
Newton's Law of Universal Gravitation:
- [tex]\displaystyle \bf{F=G\frac{m_1 m_2}{r^2}[/tex]
- F = force of gravity between two objects
- G = gravitational constant (6.67 * 10⁻¹¹ Nm²kg⁻²)
- m₁ = mass of object #1
- m₂ = mass of object #2
- r = distance between the center of mass of two objects
We are given the mass of the sun (m₁) and its distance from Earth (r). We want to find the value of F.
The mass of Earth (m₂) is 5.972 * 10²⁴ kg and we know the gravitational constant (G).
Let's plug these known values into the equation to solve for F.
- [tex]\displaystyle \bf{F=6.67\cdot10^-^1^1 \Big [ \frac{(1.99\cdot 10^3^0)(5.972\cdot 10^2^4)}{(150\cdot 10^9)^2} \Big ][/tex]
Plugging this into your calculator will output a value of
- [tex]\displaystyle \bf{ F = 3.523028782\cdot 10^2^2[/tex]
The gravitational force between the sun and the Earth is approximately:
- [tex]\displaystyle \bf{F=3.523\cdot 10^2^2 \ N[/tex]
