The Gravity To Mass Calculator belongs to the physics and astronomy category. It helps in determining the mass of an object or a celestial body based on the gravitational force it exerts. This tool is very useful in scientific studies, astrophysics, and even in engineering projects where gravity-based calculations are important. By using this calculator, you can estimate the mass of unknown objects such as planets, stars, or large structures when their gravitational influence is known. It ensures accurate results and makes complex calculations easier for both students and professionals.
formula
Primary Formula
Mass (m1) = (Gravitational Force * Distance²) / (Gravitational Constant * Mass (m2))
Variables for Primary Formula
Gravitational Force (F): The measured force of gravity between the two objects.
Distance (r): The distance between the centers of the two masses.
Gravitational Constant (G): A universal constant, approximately 6.674×10⁻¹¹ N(m/kg)².
Mass (m2): The known mass of the second object.
Formula to Calculate Mass using a Planet's Gravitational Field
Mass of Planet = (Gravitational Acceleration at Surface * Planet's Radius²) / Gravitational Constant
Variables for This Formula
Gravitational Acceleration at Surface (g): The acceleration due to gravity on the surface of the planet (for Earth, this is approximately 9.81 m/s²).
Planet's Radius (r): The radius of the planet.
Gravitational Constant (G): Approximately 6.674×10⁻¹¹ N(m/kg)².
This second formula is especially helpful in astrophysics because it allows scientists to calculate the mass of entire planets or moons by simply knowing their radius and surface gravity.
Reference Table for Quick Use
Here is a table showing approximate planetary masses based on their gravitational acceleration and radius values. These values are useful for quick reference.
| Celestial Body | Gravitational Acceleration (m/s²) | Radius (m) | Approx Mass (kg) |
|---|---|---|---|
| Earth | 9.81 | 6.371×10⁶ | 5.97×10²⁴ |
| Moon | 1.62 | 1.737×10⁶ | 7.35×10²² |
| Mars | 3.71 | 3.389×10⁶ | 6.42×10²³ |
| Jupiter | 24.79 | 6.9911×10⁷ | 1.90×10²⁷ |
| Saturn | 10.44 | 5.8232×10⁷ | 5.68×10²⁶ |
This table helps users quickly compare planetary data without performing detailed calculations every time.
Example
Let’s calculate the mass of Earth using the second formula.
Given values:
Gravitational Acceleration (g) = 9.81 m/s²
Radius of Earth (r) = 6.371×10⁶ m
Gravitational Constant (G) = 6.674×10⁻¹¹ N(m/kg)²
Step 1: Apply the formula
Mass = (g × r²) / G
Step 2: Insert values
Mass = (9.81 × (6.371×10⁶)²) / (6.674×10⁻¹¹)
Step 3: Simplify
Mass ≈ (9.81 × 4.06×10¹³) / 6.674×10⁻¹¹
Mass ≈ 3.98×10¹⁴ / 6.674×10⁻¹¹
Final Result: Mass ≈ 5.97×10²⁴ kg
This matches the known scientific value of Earth’s mass, showing the formula’s accuracy.
Most Common FAQs
It is used to determine the mass of an object or planet when the gravitational force, radius, or surface gravity is known. It is very useful in physics and astronomy.
Yes, you can use the same formula for Mars, Jupiter, or any other celestial body by entering their surface gravity and radius values.
The gravitational constant provides a universal value to connect mass, force, and distance. Without it, calculating planetary or object masses would not be accurate.